Structure of Atom: Class 11 Chemistry Chapter 2 Hinglish mein

Chemistry Part 1 · Hinglish notes, simulations aur practice · Official NCERT chapter PDF ↗

Published 18 Oct 2026 · Updated 18 Oct 2026

120 min
1 simulation
71 practice questions
39 MCQs

Is chapter mein aap kya seekhenge

Un experiments ko describe karo jinse electrons, protons aur neutrons ka pata chala, aur unke charges aur masses batao
Thomson aur Rutherford ke models, alpha-scattering ka saboot aur har model ki kamiyan samjhao
Atoms aur ions ke liye atomic number, mass number aur A-Z-X symbols use karo, aur isotopes ko isobars se alag pehchano
Wavelength, frequency, wavenumber aur photon energy ko aapas mein jodo, aur photon aur photoelectric problems mein Planck aur Einstein ki equations use karo
Bohr's model se line spectra samjhao aur hydrogen aur hydrogen-like ions ke liye energies, radii aur spectral lines calculate karo
de Broglie relation aur uncertainty principle apply karo, aur samjhao ki yeh Bohr orbits ko kyun rule out karte hain
Chaar quantum numbers se orbitals describe karo, s, p aur d orbitals ka sketch banao aur unke nodes gino
Aufbau principle, Pauli's principle aur Hund's rule se electronic configurations aur orbital diagrams likho, Cr aur Cu exceptions ke saath

NCERT Chemistry Class 11, Chapter 2, pp. 29–73 par based original companion text. Yeh NCERT se juda nahi hai aur NCERT ne ise endorse nahi kiya hai.

Sodium paani mein aag kyun pakad leta hai jabki neon kisi se bhi react nahi karta? Copper chamakdaar metal kyun hai aur sulphur bhurbhura peela solid kyun? Chemistry ka koi bhi sawaal kaafi aage tak le jao, to jawaab atom ke andar hi milta hai.

Sabse chhote, na kat sakne wale particle ka idea purana hai. India mein Vaisheshika school, jo sage Kanad se juda hai, ne paramanu (परमाणु) ki baat ki; Greece mein Leucippus aur Democritus ne ise atomos, yaani 'na katne wala', kaha. Yeh soojh-boojh bhare andaaze the jinhe koi test nahi kar sakta tha.

John Dalton ne 1808 mein atoms ko testable banaya: har element ka apna alag type ka atom hota hai jiska apna mass hota hai, aur compounds tab bante hain jab atoms chhote whole-number ratios mein judte hain. Isse laws of chemical combination (Chapter 1) samajh aa gaye, lekin yeh nahi ki sookhe baalon mein phiraya gaya plastic comb kaagaz ke tukde kyun utha leta hai. Agar atoms bina kisi feature wali balls hote, to electric charge kahan se aata? 1800s ke end mein hue experiments ne jawaab diya: atoms ke parts hote hain.

2.1 Sub-atomic Particles ki Discovery

Atom ke parts gases mein se electricity pass karke mile. Aage ki har cheez mein ek rule chalta hai: like charges repel karte hain, aur opposite charges attract karte hain.

2.1.1 Electron ki Discovery

Pehla ishaara solutions se mila. 1830s mein Michael Faraday ne dikhaya ki ghule hue ya pighle hue salt mein se charge ki ek fixed quantity pass karne par electrode par hamesha substance ki utni hi amount jamti hai (unke laws tum Class 12 mein padhoge). Lagne laga ki shaayad electricity bhi particles mein aati hai.

1850s se Faraday aur doosre scientists ne band glass tubes mein se electricity pass ki, jinki zyaadatar gas pump karke nikaal di gayi thi aur dono ends par ek metal electrode tha. Bahut kam pressure aur high voltage par current behta hai, jise koi cheez le jaati hai jo negative electrode (cathode) se nikalkar positive electrode (anode) ki taraf jaati hai. In streams ko cathode rays naam diya gaya. Agar anode mein ek chhed ho aur tube ka door wala end zinc sulphide se coated ho, to chhed se guzarne wali rays wahan ek chamakdaar spot banati hain (Fig. 2.1).

Yeh rays kya hain? Aisi kai tubes ke saath kiye gaye experiments ne baat saaf kar di:

Yeh negative particles hain. Electric field beam ko positive plate ki taraf kheenchta hai, aur magnet ise waise hi ghumaata hai jaise cathode se door ja rahe negative charges ko ghumaata. In particles ko electrons naam diya gaya.
Har atom mein yeh hote hain. Electrode ka metal ya tube ki gas badlo, phir bhi rays waise hi behave karti hain, isliye electrons har element ke atoms ka part hain.
Yeh seedhi lines mein chalte hain. Fields se door, inke raaste mein rakha metal object ek sharp shadow banata hai.
Hum sirf inke effects dekhte hain. Rays dikhti nahi, lekin jahan woh girti hain wahan fluorescent coatings chamakti hain; purane (CRT) television ki picture tube isi tarah kaam karti thi.

2/4Charged plates beam ko positive plate ki taraf modti hain: particles negative hain.

Fig. 2.1Cathode rays cathode se screen tak seedhi chalti hain; electric aur magnetic fields unhe opposite directions mein modte hain.NCERT Fig. 2.1 · p. 30

Ek glass tube mein left par cathode hai, beech mein chhed wala anode hai, horizontal plates ka ek pair hai, magnetic coils hain, aur right par ek chamakti screen hai. Step 1 mein fields off hain aur seedha beam screen ke centre mein ek spot chamkaata hai. Step 2 mein sirf plates charged hain, upar wali positive, aur beam upar mudta hai. Step 3 mein sirf coils on hain aur beam neeche mudta hai. Step 4 mein dono fields kaam karte hain, aise adjust kiye gaye ki beam seedha chale aur spot wapas centre mein aa jaaye.

2.1.2 Electron ka Charge to Mass Ratio

1897 mein J. J. Thomson ne naapa ki cathode rays kitni zor se mudti hain; iske liye unhone ek electric field aur ek magnetic field use kiya jo ek doosre se aur beam se right angles par the. Chalte hue charged particle ka deflection teen cheezon par depend karta hai: bada charge bada force mehsoos karta hai, halka particle aasaani se mudta hai, aur strong field (plates par zyada voltage ya coils mein zyada current) zyada zor se dhakelta hai.

Har field akela spot ko hilata hai, opposite directions mein. Thomson ne dono ko tab tak adjust kiya jab tak spot apni bina mude wali position par wapas nahi aa gaya, aur zaroori field strengths aur sirf ek field se hue deflection se unhone electron ke charge aur mass ka ratio nikaala. Aaj ki value hai

\begin{aligned} \frac{e}{m_{e}} & = 1.758820 \times 10^{11} \\ C k g^{- 1} \end{aligned}

(2.1)

jahan

$e$: electron ke charge ka magnitude (C)
$m_{e}$: electron ka mass (kg)

Electron negative hai, isliye uska charge $- e$ likha jaata hai; $e$ khud hamesha positive hota hai.Per kilogram, electrons hydrogen ions se lagbhag 1800 guna zyada charge le jaate hain: shuruaati ishaara ki electron kisi bhi atom se bahut halka hai.

2.1.3 Electron par Charge

Robert Millikan ne 1909 se 1913 ke beech apne oil-drop experiment (Fig. 2.2) se charge ko khud naapa. Do horizontal plates ke beech girti chhoti oil drops ek steady speed par pahunchti hain jisse unka size aur mass pata chalta hai. X-rays hawa ko ionise karti hain, aur kuch drops ions se charge utha leti hain. Phir plates par voltage lagakar charged drop ko slow kiya, roka ya upar bhi uthaya ja sakta hai. Ek ke baad ek drop ke liye zaroori field naapkar Millikan ne paaya ki har charge $q$ ek sabse chhoti amount $e$ ka whole-number multiple tha:

\begin{array}{c} q = n e \\ n = 1, 2, 3, \dots \end{array}

3/3Field tune karne par electric force $q E$ weight $m g$ ko balance karta hai aur drop ruki rehti hai.

Fig. 2.2Drag se drop ka weight naapo, phir electric field se use rok kar rakho: isse uska charge pata chalta hai.NCERT Fig. 2.3 · p. 32

Do horizontal metal plates aamne-saamne hain aur unke beech ek oil drop hai. Step 1 mein plates uncharged hain aur weight aur drag label wale barabar arrows dikhate hain ki drop steady speed se gir rahi hai. Step 2 mein ek X-ray beam andar aata hai aur drop par minus signs dikhte hain. Step 3 mein upar wali plate positive hai aur electric force label wala upar ka arrow weight ko balance karta hai, isliye drop ruki rehti hai.

Woh sabse chhota charge ek single electron ka hai. Millikan ki value $1.6 \times 10^{- 19} C$ ke kareeb thi; 2019 se elementary charge definition se bilkul $e = 1.602176634 \times 10^{- 19} C$ fix kar diya gaya hai. $e$ ko Thomson ke ratio ke saath milane se electron ka mass milta hai:

\begin{array}{c} m_{e} = \frac{e}{(e / m_{e})} \\ = 9.1094 \times 10^{- 31} k g \end{array}

(2.2)

2.1.4 Protons aur Neutrons ki Discovery

Atoms neutral hote hain, isliye koi positive cheez electrons ko balance karti hogi. 1886 mein Eugen Goldstein ne aisi tube use ki jiske cathode mein chhed the, aur dekha ki rays chhedon se ulti taraf, cathode rays ke opposite, beh rahi hain. Yeh canal rays bilkul alag tarah behave karti thi:

fields unhe waise modte hain jaise positive charges ko modte hain;
unka mass aur charge-to-mass ratio tube ki gas ke saath badalta hai: yeh us gas ke positive ions hain, jo tab bante hain jab uske atoms se electrons nikal jaate hain;
kuch ions par do ya zyada units charge hota hai, hamesha $e$ ka whole multiple.

Sabse halka positive ion hydrogen se aata hai. Lagbhag 1919 mein Rutherford ne dikhaya ki yeh particle doosre nuclei se bhi nikaala ja sakta hai, aur ise proton (प्रोटॉन) naam diya gaya. Iska charge electron ke charge ke barabar aur opposite hai, lekin yeh lagbhag 1836 guna bhaari hai.

Masses phir bhi match nahi ho rahe the: helium hydrogen se lagbhag chaar guna bhaari hai, phir bhi usmein sirf do protons hain. 1932 mein James Chadwick ne beryllium par alpha particles barsaaye aur aise uncharged particles detect kiye jo protons se thode bhaari the: neutrons (न्यूट्रॉन). Table 2.1 teeno particles ko compare karta hai.

Table 2.1Atom ke teen fundamental particles

Particle	Charge (C)	Relative charge	Mass (kg)	Mass (u)	Mass ÷ $m_{e}$
electron, e	$- 1.602 \times 10^{- 19}$	−1	$9.109 \times 10^{- 31}$	0.000549	1
proton, p	$+ 1.602 \times 10^{- 19}$	+1	$1.6726 \times 10^{- 27}$	1.00728	1836
neutron, n	0	0	$1.6749 \times 10^{- 27}$	1.00866	1839

Quick check

3 mein se 1

Hydrogen, neon ya air wali tubes se, iron ya aluminium electrodes ke saath, nikalne wali cathode rays ka charge-to-mass ratio same hota hai. Isse kya pata chalta hai?

Cathode rays light ka ek form hainRays glass ki deewaron se aati hainSaari gases ka atomic mass same haiElectrons har atom mein hote hain

Answer dekho

Answer (D) Electrons har atom mein hote hain

Gas ya electrode kuch bhi ho, same particle dikhta hai, isliye woh har atom ka part hai. Iske ulat canal rays gas ke saath badalti hain, kyunki woh us gas ke ions hain.

2.2 Atomic Models

1900s ki shuruaat tak scientists jaante the ki atoms mein electrons aur kuch positive hota hai. Inki arrangement ka achha model yeh samjhaane wala hona chahiye tha ki atoms stable kyun hain, elements apne physical aur chemical behaviour mein alag kyun hain, atoms molecules mein kaise judte hain, aur har type ka atom apni khaas radiation kyun absorb aur emit karta hai. Hum do shuruaati koshishon ko dekhte hain.

2.2.1 Atom ka Thomson Model

Thomson ne atom ko lagbhag $10^{- 10} m$ radius wala sphere socha, jo positive charge se barabar bhara ho, aur electrons usmein wahan dhanse hon jahan arrangement electrically sabse stable ho: jaise laddoo mein kishmish. English mein ise plum-pudding model kehte hain. Isse ek neutral atom milta hai jiska mass poore sphere mein barabar faila hai, aur yahi doosra feature agle experiment ne test kiya. (Thomson ko gases mein electricity ke conduction par kaam ke liye 1906 ka Nobel Prize in Physics mila.)

2.2.2 Atom ka Rutherford Nuclear Model

Agar Thomson sahi the, to ek tez, bhaari alpha particle gold atom ke paar waise hi nikal jaana chahiye jaise baadal mein se goli, zyada se zyada ek degree ke chhote hisse jitna mudkar. 1909 mein Ernest Rutherford ki laboratory mein Hans Geiger aur Ernest Marsden ne ek radioactive source se alpha particles ek micrometre se bhi patli gold foil par daage aur zinc sulphide screen par alag-alag angles par bani chamak gini (Fig. 2.3). Unhe yeh mila:

lagbhag saare alpha particles seedhe paar nikal gaye, jaise wahan kuch tha hi nahi;
ek chhota hissa side mein mud gaya, zyaadatar chhote angles se;
bahut kam, lagbhag kai hazaar mein ek, lagbhag seedhe wapas aa gaye.

2/3Zyaadatar seedhe nikle, kuch mude, aur bahut kam wapas uchhle.

Fig. 2.3Zyaadatar alpha particles seedhe paar nikal jaate hain; jo kabhi-kabhaar wapas uchhalte hain woh ek chhote, dense, positive nucleus ka pata dete hain.NCERT Fig. 2.5 · p. 34

Left par source se aata alpha particles ka beam ek curved detecting screen ke andar patli gold foil se milta hai. Step 1 mein ek inset Thomson ka atom dikhata hai aur har path lagbhag seedha nikal jaata hai. Step 2 mein zyaadatar paths seedhe hain, kuch thoda mudte hain aur ek source ki taraf wapas mudta hai. Step 3 mein ek close-up plus mark wale chhote nuclei ke saath atoms dikhata hai: door ke paths seedhe hain, paas se guzarne wala tezi se mudta hai aur seedha takrane wala wapas mud jaata hai.

Rutherford ne socha ki agar zyaadatar particles kuch mehsoos nahi karte, to atom ka zyaadatar hissa khaali jagah hai; aur ek bhaari, tez alpha particle ko wapas modne ke liye bahut bada repulsion chahiye, jo tabhi possible hai jab atom ka positive charge, lagbhag saare mass ke saath, ek chhote se region mein bhara ho: yahi nucleus hai. Iska radius lagbhag $10^{- 15} m$ hai, jabki atom ka $10^{- 10} m$ : 100 000 ka factor. Agar nucleus ko cricket ground ke centre spot par rakhe sarson ke daane jitna chhota kar do, to atom ka kinaara boundary rope ke paas hoga.

SimulationNucleus ke paas repulsion

Centre ke left mein plus 5 ka ek fixed positive charge hai jisse field lines bahar ki taraf failti hain, aur plus 2 ka ek movable test charge alpha particle ki jagah hai. Test charge par ek arrow repulsive force dikhata hai, aur ek readout uska size batata hai. Test charge ko paas drag karne par arrow aur readout tezi se badhte hain: distance aadhi hone par chaar guna.

Fig. 2.4Ek fixed +5 charge nucleus ki jagah hai aur ek +2 test charge alpha particle ki. Alpha particle ko drag karo aur force padho.

Try karo

Alpha particle door ho tab force padho, phir use aadhi distance tak drag karo. Force kitne guna badhta hai?
Ise nucleus ke bilkul paas le aao. Sirf lagbhag seedhi takkar hi alpha particle ko wapas kyun mod sakti hai?

Try karke dekho

Marbles se Rutherford ka method

Tumhe chahiye

ek bada board ya tray
chaar kitaabein
marbles
cardboard ke shapes aur tape

Pehle guess karo

Agar chhupa hua target bahut chhota hai, to zyaadatar marbles…

bina chhue seedhe nikal jaayengitumhari taraf wapas uchhlengiboard ke neeche ruk jaayengi

Ek dost chaar kitaabon par rakhe bade board ke beech mein neeche ek cardboard shape tape kar deta hai, tumhe dikhaye bina.
Board ke neeche har taraf se marbles ludhkao. Note karo ki har marble kahan se nikli, aur woh seedhi gayi, mudi ya wapas aayi.
Lagbhag 30 baar ludhkaane ke baad chhupe shape ka sketch banao. Bahut chhote target ke saath dobara karo.

Abhi nahi kar sakte? Simulation try karo · Fig. 2.4

Rutherford ka nuclear model (1911): positive charge aur lagbhag saara mass ek chhote central nucleus mein concentrated hai; electrons uske chaaron taraf circular orbits mein high speed se ghoomte hain, jaise planets Sun ke chakkar lagaate hain; aur electrostatic attraction electrons aur nucleus ko saath baandhe rakhta hai.

2.2.3 Atomic Number aur Mass Number

Nucleus ka charge uske protons se aata hai. Unki sankhya atomic number, $Z$ (परमाणु क्रमांक) hai: har carbon nucleus mein 6 hote hain, har iron nucleus mein 26. Neutral atom mein jitne protons hote hain utne hi electrons, isliye

neutral atom mein

\begin{aligned} Z & = no. of protons \\ = no. of electrons \end{aligned}

(2.3)

Protons aur neutrons ko milakar nucleons kehte hain, aur lagbhag saara mass inhi mein hota hai. Inka total mass number, $A$ (द्रव्यमान संख्या) hai:

A = Z + N

(2.4)

jahan

$A$: mass number (kul nucleons)
$N$: neutrons ki sankhya

2.2.4 Isobars aur Isotopes

Ek nucleus, ya uska atom, $_{}^{}_{Z}^{A} X$ likha jaata hai: element ka symbol, left superscript mein mass number aur left subscript mein atomic number. Uranium-235 $_{}^{}_{92}^{235} U$ hai, jismein 92 protons aur $235 - 92 = 143$ neutrons hain. Symbol pehle se hi $Z$ fix kar deta hai, isliye subscript aksar hata diya jaata hai: $_{}^{}_{}^{235} U$ ya 'U-235'.

Definition

Isotopes

Ek hi element (same $Z$ ) ke aise atoms jinmein neutrons ki sankhya alag hai, aur isliye mass numbers alag hain.

Example $_{}^{}_{8}^{16} O$ , $_{}^{}_{8}^{17} O$ aur $_{}^{}_{8}^{18} O$

Definition

Isobars

Alag-alag elements ke aise atoms jinka mass number same hai.

Example $_{}^{}_{18}^{40} A r$ , $_{}^{}_{19}^{40} K$ aur $_{}^{}_{20}^{40} C a$

Hydrogen mein isotopes (समस्थानिक) sabse saaf dikhte hain. Iske lagbhag 99.985% atoms protium, $_{}^{}_{1}^{1} H$ , hain jinmein koi neutron nahi; lagbhag 0.015% deuterium, $_{}^{}_{1}^{2} H$ ya D, hain jinmein ek neutron hai; aur thoda sa radioactive tritium, $_{}^{}_{1}^{3} H$ ya T, hai jismein do. Natural chlorine mein lagbhag teen hisse $_{}^{}_{}^{35} C l$ aur ek hissa $_{}^{}_{}^{37} C l$ hota hai, aur carbon mein $_{}^{}_{}^{12} C$ , $_{}^{}_{}^{13} C$ aur dating mein use hone wala radioactive $_{}^{}_{}^{14} C$ shaamil hain. Isobars (समभारिक) alag-alag elements ke hote hain, isliye woh kaafi alag behave karte hain.

Isotopes ek jaisa react kyun karte hain? Chemistry electrons ki baat hai, aur unki sankhya protons ki sankhya se fix hoti hai. Neutrons mass to badhaate hain lekin electrons ki ginti nahi badalte, isliye isotopes ki chemical properties lagbhag ek jaisi hoti hain. Chhote farq rates aur physical properties mein dikhte hain, sabse zyada hydrogen mein, kyunki D, H se do guna bhaari hai: heavy water, $D_{2} O$ , 3.8 °C par jamta hai.

Example 2.1NCERT Problem 2.1

Ek nuclide mein particles ginna

$_{}^{}_{53}^{127} I$ ke neutral atom mein protons, electrons aur neutrons ki sankhya nikaalo.

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Example 2.2NCERT Problem 2.2

Particles se species ka naam batana

Ek species mein 12 protons, 12 neutrons aur 10 electrons hain. Iska poora symbol likho.

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Quick check

3 mein se 1

Kaun sa pair isobars hai?

_{}^{}_{26}^{56} F e

aur

_{}^{}_{26}^{58} F e

_{}^{}_{8}^{16} O

aur

_{}^{}_{8}^{16} O^{2 -}

_{}^{}_{26}^{58} F e

aur

_{}^{}_{28}^{58} N i

_{}^{}_{1}^{1} H

aur

_{}^{}_{1}^{2} H

Answer dekho

Answer (C) $_{}^{}_{26}^{58} F e$ aur $_{}^{}_{28}^{58} N i$

Isobars ka

A

same hota hai lekin

Z

alag: iron-58 aur nickel-58. Iron aur hydrogen wale pairs isotopes hain; oxygen wala pair ek hi nuclide hai, bas electrons ki ginti alag hai.

2.2.5 Rutherford Model ki Kamiyan

Rutherford ki picture solar system se li gayi hai. Gravity se bandha planet, $F = G m_{1} m_{2} / r^{2}$ , ek steady orbit mein chalta hai jise Newton ki mechanics bilkul sahi predict karti hai, aur electron aur nucleus ke beech electrical attraction, $F = k q_{1} q_{2} / r^{2}$ , ka form bhi wahi hai. To electrons ko bhi utni hi smoothly orbit karna chahiye.

Dikkat yeh hai: circle mein chalne wali koi bhi cheez accelerate kar rahi hoti hai, kyunki uski direction lagaataar badalti hai. Maxwell ki theory kehti hai ki accelerate karta charge electromagnetic waves radiate karta hai (planets par net charge nahi hota, isliye woh bach jaate hain). Orbit karne wale electron ko energy khoni chahiye, spiral karte hue andar jaana chahiye aur ek microsecond se kaafi kam samay mein nucleus mein gir jaana chahiye (Fig. 2.5); aam andaaza lagbhag $10^{- 8} s$ hai. Asli atoms hamesha tikte hain. Electrons ruke hue bhi nahi reh sakte, kyunki tab nucleus unhe seedha andar kheench lega aur atom ek chhote Thomson-jaise atom mein collapse ho jaayega.

2/2Accelerate karta charge radiate karta hai, isliye electron ko spiral karke andar aana chahiye.

Fig. 2.5Classical physics predict karti hai ki orbit karta electron apni energy radiate kar deta hai aur spiral karte hue nucleus mein gir jaata hai.

Centre mein plus mark wala nucleus hai. Step 1 mein minus mark wala electron circular orbit par chalta hai, jaise Rutherford ke model mein. Step 2 mein ek spiral andar nucleus tak ghoomta hai, uske saath wavy arrows dikhate hain ki electron energy khote hue radiation chhodta hai.

Yeh model yeh bhi nahi batata ki electrons kaise arranged hain ya unki energies kya hain, aur chemistry ko theek yahi chahiye.

2.3 Bohr's Model of Atom tak le jaane wale Developments

1913 mein Niels Bohr ne do tarah ke saboot jodkar Rutherford ke atom ko bachaya: electromagnetic radiation wave ki tarah bhi behave karti hai aur particles ki stream ki tarah bhi, aur atoms light ko sirf bilkul fixed wavelengths par emit aur absorb karte hain. Hum inhe ek-ek karke dekhte hain.

2.3.1 Electromagnetic Radiation ka Wave Nature

Newton ka maanna tha ki light chhote particles (corpuscles) ki stream hai, lekin 1800s ki shuruaat mein interference par hue experiments ne zyaadatar physicists ko yakeen dila diya ki yeh ek wave hai. 1860s aur 1870s mein James Clerk Maxwell ne dikhaya ki kis type ki: accelerate karta charge badalte electric aur magnetic fields banata hai, jo ek doosre ko phir se banaate rehte hain, isliye disturbance ek electromagnetic wave ki tarah bahar failta hai. Heinrich Hertz ne 1887–88 mein aisi waves banaayi aur detect ki, aur unki speed light ki speed se match hui. Garam objects se nikalne wali thermal radiation bhi electromagnetic waves hi nikli.

Yahan teen properties maayne rakhti hain (Fig. 2.6):

electric aur magnetic fields ek doosre se aur travel ki direction se right angles par oscillate karte hain;
kisi medium ki zaroorat nahi: sound ko hawa chahiye, lekin sunlight khaali space paar kar leti hai;
wavelengths ek bahut bade range mein failti hain, yahi electromagnetic spectrum hai (Fig. 2.7), aur hamari aankhein sirf lagbhag 400 nm (violet) se 750 nm (red) tak ki patli band ko pakadti hain.

3/3Ek wavelength $λ$ crest se crest tak hoti hai; har second $ν$ crests guzarte hain, isliye $c = ν λ$ .

Fig. 2.6Electric aur magnetic fields saath-saath oscillate karte hain, ek doosre se aur travel ki direction se right angles par.NCERT Fig. 2.6 · p. 37

Ek horizontal axis travel ki direction dikhata hai. Step 1 mein vertical plane ki ek wave electric field dikhati hai. Step 2 mein horizontal plane mein flat bani ek wave magnetic field dikhati hai, electric field ke saath-saath lekin usse right angle par. Step 3 mein ek bracket crest se crest tak ek wavelength mark karta hai, saath mein note hai ki speed frequency guna wavelength ke barabar hai.

Wave ki ek wavelength $λ$ hoti hai, yaani ek crest se agle crest tak ki distance (m, nm, pm ya purane ångström mein, 1 Å = $10^{- 10}$ m), aur ek frequency $ν$ , yaani har second ek point se guzarne wale crests ki sankhya (hertz mein, 1 Hz = 1 s⁻¹). Vacuum mein har electromagnetic wave $c = 2.998 \times 10^{8} m s^{- 1}$ par chalti hai, jise aam taur par $3.0 \times 10^{8} m s^{- 1}$ round kiya jaata hai. Har second $ν$ crests guzarte hain, har ek $λ$ lamba, isliye

c = ν λ

(2.5)

Spectroscopists wavenumber $\overset{ˉ}{ν}$ bhi use karte hain: ek metre mein kitni wavelengths aati hain (SI unit m⁻¹) ya, practice mein zyaadatar, ek centimetre mein (cm⁻¹).

\overset{ˉ}{ν} = \frac{1}{λ} = \frac{ν}{c}

Fig. 2.7Left se right frequency badhti hai aur wavelength ghatti hai; visible light

10^{15}

Hz ke paas ek patla sa hissa hai.NCERT Fig. 2.7 · p. 38

Ek lambi band radio, microwave, infrared, visible, ultraviolet, X-ray aur gamma regions mein bati hai. Upar ek frequency arrow ten to the six hertz se ten to the twenty hertz tak jaata hai, aur neeche ek wavelength arrow ulti taraf, 100 metres se 1 picometre tak. Patla visible hissa neeche bada karke dikhaya gaya hai, 750 nanometres par red se 400 par violet tak.

Example 2.3NCERT Problem 2.3

Ek FM broadcast ki wavelength

Ek FM radio channel 102.6 MHz par transmit karta hai. Wavelength aur spectrum ka region nikaalo.

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Example 2.4NCERT Problem 2.4

Do LEDs ki frequencies

Ek blue LED 450 nm par emit karti hai aur ek red LED 650 nm par. Dono ki frequency nikaalo.

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Example 2.5NCERT Problem 2.5

Hydrogen ki red line

Hydrogen ki sabse chamakdaar visible line ki wavelength 6563 Å hai. Nikaalo (a) cm⁻¹ aur m⁻¹ mein iska wavenumber aur (b) iski frequency.

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Quick check

3 mein se 1

Ek Wi-Fi router 2.4 GHz par transmit karta hai. Centimetres mein wavelength kya hai?

Answer dekho

Answer 12.5 cm

λ = c / ν = 3.0 \times 10^{8} / 2.4 \times 10^{9} = 0.125 m = 12.5 c m

: microwaves.

2.3.2 Electromagnetic Radiation ka Particle Nature: Planck's Quantum Theory

Wave picture interference aur diffraction (obstacles ke chaaron taraf waves ka mudna) ko samjhaati hai. Phir bhi 1900 tak kai observations isme fit nahi ho rahe the: garam objects se nikalne wali light (black-body radiation), light se metals se electrons ka nikalna (photoelectric effect), kam temperature par solids ki heat capacity ka girna, aur atoms ke line spectra. Sab ek ajeeb nateeje ki taraf ishaara karte the: energy sirf fixed amounts mein hi lene-dene hoti hai.

Electric heater ki coil garam hote hue pehle halki laal chamakti hai, phir orange, phir peeli-safed, aur Sun se zyada garam taare blue-white dikhte hain: temperature badhne par garam body ki light chhoti wavelengths ki taraf khisakti hai. Ise saaf tarah padhne ke liye physicists ne ek black body socha, ek ideal object jo har wavelength absorb karta hai aur kuch reflect nahi karta; equilibrium mein yeh utna hi emit karta hai jitna absorb karta hai, aur iski radiation sirf iske temperature par depend karti hai. Kaalikh iske kareeb hai, aur ek chhote chhed wala khokhla box lagbhag perfect hai, kyunki chhed mein ghusi light bahar nikalne se pehle hi absorb ho jaati hai. Fixed temperature par intensity wavelength ke saath ek peak tak badhti hai aur phir girti hai; zyada garam body har wavelength par zyada emit karti hai aur uska peak chhoti wavelength par hota hai (Fig. 2.8).

3/36000 K par, jo Sun ki surface ke kareeb hai, peak lagbhag 480 nm par hai.

Fig. 2.8Zyada garam black body har wavelength par zyada emit karti hai, aur uska peak chhoti wavelengths ki taraf khisakta hai.NCERT Fig. 2.8 · p. 40

Axes wavelength ke against intensity dikhate hain, aur visible band shaded hai. Step 1 mein 4000 kelvin ka neecha, chauda curve hai jiska peak visible band ke red kinaare par hai. Step 2 mein 5000 kelvin ka ooncha curve judta hai jiska peak visible band ke beech mein hai. Step 3 mein 6000 kelvin ka kaafi ooncha curve judta hai jiska peak blue-green mein hai. Har peak par ek dot hai, aur temperature badhne par peaks chhoti wavelengths ki taraf khisakte hain.

Wave theory in curves ko nahi bana paayi. 1900 mein Max Planck ne ek formula dhoondha jo inse bilkul fit hua, yeh maankar ki deewaron ke vibrate karte atoms energy sirf poore packets mein absorb ya emit kar sakte hain, jinhe unhone quanta (singular quantum) kaha. Ek quantum ki energy frequency ke proportional hoti hai:

E = h ν

(2.6)

jahan

$h$: Planck's constant, $6.626 \times 10^{- 34} J s$

Frequency $ν$ wala oscillator energy $0, h ν, 2 h ν, \dots$ rakh sakta hai lekin inke beech ka kuch nahi, kuch waise hi jaise sirf ₹1 ke sikkon se payment karna: ₹7 ya ₹8, kabhi ₹7.50 nahi. $h$ itna chhota hai ki rozmarra ki zindagi mein yeh steps dikhte nahi; atoms ke liye yahi sab kuch tay karte hain.

Photoelectric effect

1887 mein Heinrich Hertz ne dekha ki ultraviolet light se electrodes ke beech sparks aasaani se koodte hain. Baad mein pata chala ki saaf metal par padne wali light usmein se electrons nikaal sakti hai: yahi photoelectric effect hai. Caesium aur potassium visible light par bhi respond karte hain; zinc aur copper ko ultraviolet chahiye. Evacuated tubes mein hue experiments (Fig. 2.9) ne chaar baatein dikhaayi:

Koi deri nahi. Light pahunchte hi electrons nikal jaate hain, chahe woh kitni bhi dheemi ho.
Ek threshold. Har metal ki ek minimum frequency $ν_{0}$ hoti hai, uski threshold frequency (देहली आवृत्ति); isse neeche koi electron nahi nikalta, chahe light kitni bhi tez ho ya kitni der tak pade.
Brightness number tay karti hai. $ν_{0}$ se upar, zyada bright light har second zyada electrons nikaalti hai.
Frequency energy tay karti hai. Electrons ki maximum kinetic energy frequency ke saath badhti hai aur brightness par depend nahi karti.

Wave theory lagbhag har point par ulta predict karti hai: bright red light ko aakhir mein electrons nikaal dene chahiye, dheemi light ko samay lagna chahiye, aur zyada bright light se tez electrons milne chahiye. Iske bajaye, potassium kisi bhi brightness ki red light mein koi electron nahi chhodta, jabki halki violet light bhi turant electrons nikaal deti hai.

2/3Har violet photon mein kaafi energy hai: electrons turant nikalte hain.

Fig. 2.9Frequency tay karti hai ki electrons niklenge ya nahi aur kitni tezi se; brightness sirf yeh tay karti hai ki kitne.NCERT Fig. 2.9 · p. 41

Ek potassium plate par upar-left se light padti hai. Step 1 mein bahut saare red photons takraate hain aur koi electron nahi nikalta. Step 2 mein kuch violet photons takraate hain aur kuch electrons udte hain, har ek ke saath uski kinetic energy ka arrow. Step 3 mein bahut saare violet photons bahut saare electrons nikaalte hain, arrows pehle jitne hi lambe.

1905 mein Albert Einstein ne Planck ke idea ko seedha-seedha maana: light $h ν$ energy ke packets ke roop mein chalti hai, jinhe ab photons (फोटॉन) kehte hain. Ek photon apni saari energy ek hi baar mein ek electron ko de deta hai. Electron ko bahar kheenchne ke liye kam se kam $h ν_{0}$ chahiye; yeh minimum metal ka work function, $W_{0}$ (कार्यफलन) hai. Baaki energy kinetic energy ban jaati hai:

h ν = h ν_{0} + \frac{1}{2} m_{e} v^{2}

(2.7)

jahan

$h ν_{0} = W_{0}$: metal ka work function
$v$: sabse tez nikle electrons ki speed

Har observation isi se nikalta hai. Threshold se neeche koi single photon electron ko nahi nikaal sakta, aur electron kai photons se energy jama nahi kar sakta. Usse upar, bachi hui $h (ν - ν_{0})$ kinetic energy ban jaati hai, jo isliye frequency ke saath badhti hai. Zyada bright light ka matlab zyada photons, isliye zyada electrons, har ek ki maximum energy same. Ek photon turant kaam karta hai, isliye koi deri nahi hoti.Metal ke andar gehraai se aane wale electrons bahar aate hue kuch energy kho dete hain, isliye Eq. (2.7) maximum kinetic energy deti hai.

Work functions aam taur par electron volts mein diye jaate hain: 1 eV, yaani 1 V paar karne par electron ko milne wali energy, $1.602 \times 10^{- 19} J$ hai. Ek kaam ka shortcut: eV mein photon energy ≈ 1240 ÷ nm mein wavelength (Table 2.2).

Table 2.2Lagbhag work functions (values surface ki haalat ke saath badalti hain)

Metal	$W_{0}$ (eV)	Threshold wavelength (nm)
caesium	2.1	590
potassium	2.3	539
calcium	2.9	428
zinc	4.3	288
iron	4.5	276
gold	5.1	243

InteractivePhotoelectric lab

Ek lamp vacuum tube mein ek metal plate par chamakta hai. Tum chhe metals mein se ek chunte ho aur sliders se wavelength (200 se 700 nanometres) aur brightness set karte ho. Readouts photon energy, threshold wavelength, electrons ki maximum kinetic energy aur speed, aur har second relative number batate hain. Shine photons ka aana aur electrons ka nikalna animate karta hai, ya threshold se neeche kuch nahi. Frequency ke against maximum kinetic energy ka graph metal ki slope h wali seedhi line dikhata hai, aur abhi ki setting ke liye ek dot.

Fig. 2.10Ek metal chuno, wavelength aur brightness set karo, aur Shine dabao, yeh dekhne ke liye ki electrons nikalte hain ya nahi aur kitni tezi se.

To light wave hai ya particles ki stream? Yeh dual behaviour dikhati hai: chalte waqt yeh wave ki tarah interfere aur diffract karti hai, lekin particles ki tarah poore photons mein absorb ya emit hoti hai. Hum kaun sa roop dekhte hain yeh experiment par depend karta hai, aur Section 2.5.1 mein tum dekhoge ki electrons bhi waves ki tarah behave karte hain.

Example 2.6NCERT Problem 2.6

Ek mole photons mein energy

$6.0 \times 10^{14}$ Hz frequency (green light, 500 nm) ke ek photon ki, aur ek mole photons ki energy nikaalo.

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Example 2.7NCERT Problem 2.7

Laser pointer se photons

Ek green laser pointer 532 nm wavelength ki 5.0 mW light emit karta hai. Yeh har second kitne photons emit karta hai?

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Example 2.8NCERT Problem 2.8

Experiment se work function

250 nm wavelength ki light ek metal se 0.66 eV maximum kinetic energy wale electrons nikaalti hai. Work function aur threshold wavelength nikaalo.

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Example 2.9NCERT Problem 2.9

Photoelectrons ki kinetic energy aur speed

Ek metal ki threshold frequency $5.5 \times 10^{14}$ Hz hai. Uspar $8.0 \times 10^{14}$ Hz ki light padti hai. Electrons ki maximum kinetic energy aur speed nikaalo.

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Quick check

3 mein se 1

Threshold frequency se upar ki light ek metal par padti hai. Agar uski intensity double kar di jaaye, to kya hoga?

Electrons ki maximum kinetic energy double ho jaati haiHar second do guna electrons nikalte hainThreshold frequency aadhi ho jaati haiKuch nahi badalta

Answer dekho

Answer (B) Har second do guna electrons nikalte hain

Do guna intensity ka matlab do guna photons, isliye do guna electrons, har ek ki maximum energy same, jo sirf frequency par depend karti hai.

2.3.3 Quantized Electronic Energy Levels ka Saboot: Atomic Spectra

Glass prism white light ko rangon ki ek band mein faila deta hai. Glass mein light dheemi ho jaati hai, chhoti wavelengths zyada, isliye violet sabse zyada mudti hai aur red sabse kam. Red se violet tak har rang maujood hota hai, agle rang mein ghulta hua: yeh continuous spectrum hai, rainbow jaisa.

Atoms bhi light emit kar sakte hain. Unhe flame mein garam karo ya gas mein se discharge guzaaro to woh higher-energy states mein excite ho jaate hain; wapas girte hue woh energy ko radiation ke roop mein chhodte hain, jisse emission spectrum banta hai. Iske bajaye ek thande sample mein se continuous light guzaaro, to atoms kuch khaas wavelengths absorb kar lete hain aur kaale gaps chhod dete hain: yeh absorption spectrum hai, emission spectrum ke photographic negative jaisa. Spectra ki padhai spectroscopy hai (Fig. 2.11).

Sabse zaroori clue: free atoms sirf kuch sharp wavelengths emit karte hain, jo beech mein andhere ke saath chamakti lines ki tarah dikhti hain; yeh line spectrum ya atomic spectrum (रेखा स्पेक्ट्रम) hai. Kisi element ki absorption lines theek wahin padti hain jahan uski emission lines hoti hain. Har element ka pattern fingerprint jitna apna hota hai: sodium street lamps ka peela rang aur neon signs ka laal rang do jaani-pehchaani misaalein hain. Lagbhag 1860 mein Robert Bunsen aur Gustav Kirchhoff ne spectra ki nayi lines se caesium aur rubidium khoje, aur thallium, indium, gallium aur scandium bhi pehli baar isi tarah pakde gaye.

3/3Thanda hydrogen white light se wahi chaar wavelengths hata deta hai.

Fig. 2.11Hydrogen ki chamakti emission lines aur kaali absorption lines same wavelengths par padti hain.NCERT Fig. 2.10 · p. 45

Teen strips left mein violet se right mein red tak chalti hain. Step 1 white light se rangon ki ek smooth band dikhata hai. Step 2 ek kaali strip jodta hai jismein hydrogen ki chaar chamakti lines hain, 410, 434, 486 aur 656 nanometres label ke saath. Step 3 continuous band jodta hai jise same positions par chaar kaali lines kaat-ti hain, thande hydrogen se guzri white light se.

Hydrogen ka line spectrum

Hydrogen mein ek electron hai, isliye uska spectrum sabse simple hai. Discharge $H_{2}$ ko excited atoms mein tod deta hai, jo alag-alag frequencies ke ek set par light emit karte hain. 1885 mein Swiss schoolteacher Johann Balmer ne paaya ki hydrogen ki visible lines, wavenumbers mein likhne par, is formula mein fit hoti hain

n = 3, 4, 5, …

\begin{array}{c} \overset{ˉ}{ν} = 109 677 \\ \times (\frac{1}{2^{2}} - \frac{1}{n^{2}}) c m^{- 1} \end{array}

(2.8)

Inse Balmer series banti hai. Phir Johannes Rydberg ne dikhaya ki hydrogen lines ki har series ek hi expression mein fit hoti hai:

n₂ > n₁

\begin{array}{c} \overset{ˉ}{ν} = 109 677 \\ \times (\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}) c m^{- 1} \end{array}

(2.9)

jahan $n_{1} = 1, 2, 3, \dots$ aur $n_{2} = n_{1} + 1, n_{1} + 2, \dots$ ; $109 677 c m^{- 1}$ hydrogen ka Rydberg constant hai. Har $n_{1}$ se ek series milti hai (Table 2.3). Har element ka line spectrum unique aur regular hota hai, lekin whole numbers aate hi kyun hain? Bohr ne iska jawaab diya.

Table 2.3Hydrogen spectrum mein lines ki series

Series	$n_{1}$	$n_{2}$	Region	Sabse lambi wavelength
Lyman	1	2, 3, …	ultraviolet	122 nm
Balmer	2	3, 4, …	visible, near UV	656 nm
Paschen	3	4, 5, …	infrared	1876 nm
Brackett	4	5, 6, …	infrared	4052 nm
Pfund	5	6, 7, …	infrared	7460 nm

Quick check

3 mein se 1

Sodium vapour ka absorption spectrum uske emission spectrum se kaise compare hota hai?

Uski kaali lines wahin hain jahan chamakti emission lines hainYeh bina gaps ki ek continuous band haiUski lines bilkul alag wavelengths par hainUsmein lines sirf infrared mein hain

Answer dekho

Answer (A) Uski kaali lines wahin hain jahan chamakti emission lines hain

Atom theek wahi photons absorb karta hai jo woh emit kar sakta hai, kyunki dono same energy gaps se match karte hain.

2.4 Hydrogen Atom ke liye Bohr's Model

1913 mein Niels Bohr ne maana ki atoms ke andar classical physics fail ho jaati hai, aur naye rules banaaye, jo Rutherford ka nucleus rakhte hue hydrogen ke spectrum se fit hon. Yeh modern quantum mechanics nahi hai, lekin hydrogen ke liye iske numbers aaj bhi sahi hain. Unke postulates:

Electron sirf kuch khaas circular orbits mein chalta hai jinka radius aur energy fixed hai; yeh stationary states ya allowed energy levels (स्थिर अवस्था) hain, jo nucleus ke chaaron taraf concentric arranged hain.
Stationary state mein electron na energy leta hai na khota hai, isliye atom radiate ya collapse nahi karta.
Electron states ke beech jump kar sakta hai: upar jaane ke liye theek energy difference $Δ E$ absorb karta hai aur neeche girte hue use ek photon ke roop mein emit karta hai, jiski frequency Bohr ke frequency rule, Eq. (2.10), se milti hai.
Sirf woh orbits allowed hain jinmein angular momentum $h / 2 π$ ka whole-number multiple ho, Eq. (2.11).

ν = \frac{Δ E}{h} = \frac{E_{2} - E_{1}}{h}

(2.10)

jahan

$E_{2}, E_{1}$: upar wali aur neeche wali states ki energies

n = 1, 2, 3, …

m_{e} v r = n \frac{h}{2 π}

(2.11)

Chautha postulate hi nayi physics hai: beech ke orbits forbidden hain, aur Maxwell ka rule ki orbit karte charges radiate karte hain, side mein rakh diya jaata hai. Iske teen nateeje hain (neeche derive kiye gaye). Orbits ko number diye jaate hain, principal quantum number $n = 1, 2, 3, \dots$ se (Section 2.6.1). Radii $n^{2}$ ke hisaab se badhte hain:

r_{n} = n^{2} a_{0}

(2.12)

jahan

$a_{0}$: Bohr radius, $52.9 p m$

isliye electron aam taur par nucleus se $52.9 p m$ door rehta hai, aur doosra aur teesra orbit 4 aur 9 guna door hain. Energies negative hain aur $n$ badhne ke saath paas-paas aati jaati hain:

E_{n} = - R_{H} (\frac{1}{n^{2}})

(2.13)

jahan

$R_{H}$: $2.18 \times 10^{- 18} J$ , energy units mein Rydberg constant

Ground state mein $E_{1} = - 2.18 \times 10^{- 18} J$ hai, aur $E_{2} = - 5.45 \times 10^{- 19} J$ . Lines ki tarah banaane par yeh ek energy-level diagram banaate hain (Fig. 2.12). $n \to \infty$ hone par energy zero tak badhti hai: electron free hai aur atom ionised.

Yeh theory kisi bhi hydrogen-like species ke liye kaam karti hai, yaani ek electron wala ion jaise $H e^{+}$ , $L i^{2 +}$ ya $B e^{3 +}$ . Nuclear charge $Z e$ ke liye:

\begin{aligned} E_{n} & = - 2.18 \times 10^{- 18} \\ \times \frac{Z^{2}}{n^{2}} J \end{aligned}

(2.14)

r_{n} = \frac{52.9 n^{2}}{Z} p m

(2.15)

Bada $Z$ electron ko zyada kas ke aur zyada paas baandhta hai. Electron ki speed $Z$ ke saath badhti hai aur $n$ ke saath ghatti hai; hydrogen ke pehle orbit mein yeh lagbhag $2.2 \times 10^{6} m s^{- 1}$ hai.

DerivationBohr ke numbers kahan se aate hain

Coulomb attraction centripetal force deta hai ( $k = 1 / 4 π ε_{0}$ ):

\frac{m_{e} v^{2}}{r} = \frac{k Z e^{2}}{r^{2}}

Bohr ki condition, $v = n h / 2 π m_{e} r$ , se $v$ hatane par:

\begin{aligned} r_{n} & = \frac{n^{2} h^{2}}{4 π^{2} m_{e} k Z e^{2}} \\ = \frac{52.9 n^{2}}{Z} p m \end{aligned}

Kinetic energy $k Z e^{2} / 2 r$ hai aur potential energy $- k Z e^{2} / r$ , isliye

\begin{array}{c} E_{n} = - \frac{k Z e^{2}}{2 r_{n}} \\ = - 2.18 \times 10^{- 18} \\ \times \frac{Z^{2}}{n^{2}} J \end{array}

Total energy kinetic energy ka minus hai, aur speed $v_{n} = 2.18 \times 10^{6} Z / n m s^{- 1}$ hai. Class 12 Physics (Atoms) mein yeh phir aayega.

2.4.1 Hydrogen ke Line Spectrum ki Explanation

Jab electron level $n_{i}$ se level $n_{f}$ par jump karta hai, to atom ki energy itni badalti hai

Δ E = E_{f} - E_{i}

(2.16)

\begin{aligned} Δ E & = R_{H} (\frac{1}{n_{i}^{2}} - \frac{1}{n_{f}^{2}}) \\ = 2.18 \times 10^{- 18} \\ \times (\frac{1}{n_{i}^{2}} - \frac{1}{n_{f}^{2}}) J \end{aligned}

(2.17)

Upar jaane par ( $n_{f} > n_{i}$ ), $Δ E$ positive hai: energy absorb hoti hai (absorption line). Girne par ( $n_{i} > n_{f}$ ), $Δ E$ negative hai: ek photon emit hota hai (emission line). Photon ki frequency gap se tay hoti hai; neeche wale level ke liye $n_{1}$ aur upar wale ke liye $n_{2}$ likhne par:

ν = \frac{∣ Δ E ∣}{h}

(2.18)

\begin{array}{c} ν = 3.29 \times 10^{15} \\ \times (\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}) H z \end{array}

(2.19)

\overset{ˉ}{ν} = \frac{ν}{c}

(2.20)

\begin{array}{c} \overset{ˉ}{ν} = 1.097 \times 10^{7} \\ \times (\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}) m^{- 1} \end{array}

(2.21)

Equation (2.21) Rydberg ka formula hai, kyunki $109 677 c m^{- 1} = 1.097 \times 10^{7} m^{- 1}$ , lekin ab fit nahi balki derive kiya gaya: yahi Bohr ki jeet thi. Har line ek jump hai: $n = 1$ tak neeche ke jumps Lyman series dete hain, $n = 2$ tak Balmer series, aur aage isi tarah (Fig. 2.12). Ek atom ek samay mein ek hi jump karta hai, lekin tube mein anginat atoms har possible jump karte hain, isliye saari lines ek saath dikhti hain; line tab chamakdaar hoti hai jab bahut saare atoms woh jump karte hain.

3/4 $n = 2$ tak neeche ke jumps: visible lines.

Fig. 2.12Har series un jumps ka set hai jo same neeche wale level par khatam hote hain.NCERT Fig. 2.11 · p. 46

Horizontal lines n barabar 1 se 6 aur infinity tak ke levels mark karti hain, energies n barabar 1 ke liye minus 2.18 times ten to the minus eighteen joules se zero tak, upar ki taraf paas-paas (spacing compressed hai, scale par nahi). Step 1 sirf levels dikhata hai. Step 2 n barabar 1 par khatam hone wale neeche ke arrows jodta hai, label Lyman, ultraviolet. Step 3 n barabar 2 par khatam hone wale arrows jodta hai, label Balmer, visible. Step 4 n barabar 3 par khatam hone wale arrows jodta hai, label Paschen, infrared.

InteractiveHydrogen spectrum lab

Ek electron wali species ka energy-level diagram levels 1 se 7 aur infinity dikhata hai. Tum hydrogen, helium ion ya doubly charged lithium ion chunte ho, ek upar wala aur ek neeche wala level, aur emission ya absorption. Ek arrow levels ko jodta hai aur readouts joules aur electron volts mein energy change, frequency, wavelength aur wavenumber, series aur region batate hain. Ek spectrum strip mark karti hai ki line kahan padti hai, aur ek counter batata hai ki dono levels ke beech kitni alag lines emit ho sakti hain.

Fig. 2.13Photon ki energy, frequency, wavelength aur series dekhne ke liye do levels chuno;

Z^{2}

ka effect dekhne ke liye

H e^{+}

L i^{2 +}

par switch karo.

Example 2.10NCERT Problem 2.10

Hydrogen ki ek violet line

Hydrogen mein transition $n = 6 \to n = 2$ ke liye $Δ E$ , frequency aur wavelength nikaalo, aur series ka naam batao.

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Example 2.11NCERT Problem 2.11

Ek hydrogen-like lithium ion

$L i^{2 +}$ ke $n = 2$ orbit ki energy aur radius nikaalo.

Pehle khud try karo. Phir solution ek-ek step karke kholo.

2.4.2 Bohr's Model ki Limitations

Bohr's model hydrogen ki stability samjhaata hai aur hydrogen aur $H e^{+}$ aur $L i^{2 +}$ jaise one-electron ions ke spectra kamaal ki tarah predict karta hai. Uske aage yeh fail ho jaata hai:

yeh do ya zyada electrons wale kisi bhi atom ka spectrum predict nahi kar sakta, helium ka bhi nahi;
high resolution par dekhne se hydrogen ki kai lines paas-paas ke pairs (doublets) hain, ek fine structure jo model se chhoot jaata hai;
yeh Zeeman aur Stark effects ko nahi samjha sakta, jinmein atom ke magnetic ya electric field mein hone par lines split ho jaati hain;
yeh kuch nahi batata ki atoms molecules mein kaise bond karte hain.

Quick check

4 mein se 1

Hydrogen ke teesre Bohr orbit ka radius pm mein kya hai?

Answer dekho

Answer 476 pm

r_{3} = 3^{2} \times 52.9 = 476 p m

: radius

n^{2}

ke hisaab se badhta hai,

n

ke hisaab se nahi.

2.5 Atom ke Quantum Mechanical Model ki Taraf

1920s ki do discoveries ne dikhaya ki Bohr's model ko fail kyun hona hi tha, aur uski jagah kya aayega iska ishaara diya. Matter bhi light ki tarah dual nature rakhta hai; aur is baat ki ek basic limit hai ki hum ek saath kitni sahi tarah jaan sakte hain ki particle kahan hai aur kaise chal raha hai.

2.5.1 Matter ka Dual Behaviour

1924 mein Louis de Broglie ne photon wale idea ko ulta kar diya: agar light waves momentum wale particles ki tarah behave kar sakti hain, to shaayad electrons jaise particles waves ki tarah behave kar sakte hain. Photon ka momentum $p = h / λ$ hai; de Broglie ne mass $m$ aur speed $v$ wale kisi bhi particle ke liye yahi rishta propose kiya:

λ = \frac{h}{m v} = \frac{h}{p}

(2.22)

jahan

$p$: particle ka momentum
$λ$: uski de Broglie wavelength

1927 mein USA mein Clinton Davisson aur Lester Germer ne, aur Scotland mein George Paget Thomson ne paaya ki electron beams crystals se waise hi diffract hote hain jaise X-rays. (G. P. Thomson, J. J. Thomson ke bete the: pita ne dikhaya ki electron particle hai, bete ne ki woh wave bhi hai.) Electron microscope isi wave behaviour ka use karta hai; electron wavelengths light ki wavelengths se bahut chhoti hain, isliye yeh hazaaron guna baareek detail dikhata hai, single atoms tak.

Har chalti cheez ki ek de Broglie wavelength hoti hai, lekin rozmarra ki cheezon ke liye yeh behad chhoti hoti hai: cricket ball ki lagbhag $10^{- 34}$ m (Example 2.12), detect karne ke liye bahut hi chhoti. Sirf electrons jaise bahut halke particles ke liye hi yeh atoms ke size jitni hoti hai.

Yeh Bohr ki condition ko bhi samjhaata hai. Orbit ke chaaron taraf chalti wave tabhi bachti hai jab woh khud se jud jaaye, isliye circumference mein wavelengths ki whole number fit honi chahiye, $2 π r = n λ$ (Fig. 2.14). $λ = h / m_{e} v$ ke saath isse $m_{e} v r = n h / 2 π$ milta hai, bilkul Eq. (2.11).

1/3Orbit ke chaaron taraf theek teen wavelengths fit hoti hain: $2 π r = 3 λ$ .

Fig. 2.14Sirf woh orbits allowed hain jinmein electron wavelengths ki whole number aati hai, aur yahi Bohr ki condition hai.

Ek nucleus dashed circular orbit ke andar hai aur uske chaaron taraf ek wave chal rahi hai. Step 1 mein wave ki teen wavelengths hain aur woh khud se smoothly judti hai (n barabar 3). Step 2 mein bada orbit chaar wavelengths rakhta hai jo bhi judti hain (n barabar 4). Step 3 mein saadhe teen wavelengths nahi milti: end start ke saath step mein nahi hai, cross se mark kiya gaya.

Example 2.12NCERT Problem 2.12

Cricket ball ki wavelength

40 m s⁻¹ par phenki gayi 160 g ki cricket ball ki de Broglie wavelength nikaalo.

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Example 2.13NCERT Problem 2.13

Dheeme electron ki wavelength

Ek electron ki kinetic energy $4.0 \times 10^{- 19}$ J (lagbhag 2.5 eV) hai. Uski de Broglie wavelength nikaalo.

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Example 2.14NCERT Problem 2.14

Photon ka mass equivalent

Photon ka rest mass nahi hota, lekin uske momentum $p = h / λ$ ko $m c$ likhne se ek mass equivalent $m = h / λ c$ define hota hai. 1.0 nm wavelength wale X-ray photon ke liye $m$ nikaalo.

Pehle khud try karo. Phir solution ek-ek step karke kholo.

2.5.2 Heisenberg's Uncertainty Principle

Agar electron wave hai, to woh theek kahan hai? 1927 mein Werner Heisenberg ne dikhaya ki iska koi sharp jawaab nahi hai. Unka uncertainty principle (अनिश्चितता सिद्धांत) kehta hai ki electron jaise particle ki exact position aur exact momentum (ya velocity) dono ek saath determine nahi kiye ja sakte:

Δ x Δ p_{x} \geq \frac{h}{4 π}

(2.23)

jahan

$Δ x$: position mein uncertainty
$Δ p_{x}$: usi direction mein momentum mein uncertainty

Kyunki $p_{x} = m v_{x}$ , isliye $Δ x Δ v_{x} \geq h / 4 π m$ bhi: position jitni sharp pata ho, velocity utni dhundhli, aur ulta bhi.

Socho ki ek andhere kamre mein tum ping-pong ball ko tennis balls phenk kar dhoondh rahe ho: har takkar batati hai ki woh kahan thi, lekin use kahin aur dhakel deti hai. Electron ko sharp tarah locate karne ke liye bahut chhoti wavelength ki light chahiye, aur aise photons ka momentum, $p = h / λ$ , bada hota hai, isliye har ek electron ko zor ki kick deta hai. Humein pata chalta hai ki woh kahan tha, lekin yeh kho dete hain ki woh kaise chal raha hai (Fig. 2.15).

Fig. 2.15Position ko sahi naapna momentum ko disturb karta hai; halke se naapna position ko dhundhla chhod deta hai.

Do panels. Left mein ek short-wavelength photon sharp dot ki tarah bane electron se takraata hai, aur ek lamba arrow dikhata hai ki woh door dhakel diya gaya: position sharp, velocity disturbed. Right mein ek long-wavelength photon dhundhle blob ki tarah bane electron se milta hai jiske saath sirf chhota arrow hai: velocity mushkil se badli, position dhundhli.

Isliye electrons ke koi definite paths, ya trajectories, nahi hote: path ke liye position aur velocity dono ek saath pata honi chahiye. Rozmarra ki cheezon ke liye yeh limit koi maayne nahi rakhti: 0.02 g ke chawal ke daane ko ek micrometre tak locate karo, to uski speed mein sirf lagbhag $3 \times 10^{- 24} m s^{- 1}$ ki uncertainty hogi. Electron ko 0.1 nm tak, yaani atom ke size tak, locate karo, to uski speed mein lagbhag $6 \times 10^{5} m s^{- 1}$ ki uncertainty hogi, jo uski orbital speed ka bada hissa hai. Atoms mein electrons ke liye exact positions ki jagah probabilities leni padti hain.

Example 2.15NCERT Problem 2.15

Quantum dot mein ek electron

Ek electron lagbhag 2.0 nm chaude ek chhote semiconductor crystal (quantum dot) mein phansa hai, isliye $Δ x \approx 2.0$ nm. Uski velocity mein minimum uncertainty nikaalo.

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Example 2.16NCERT Problem 2.16

Ek table-tennis ball

2.7 g ki table-tennis ball 20 m s⁻¹ par chal rahi hai, aur uski speed 1% tak naapi gayi hai. Uski position mein minimum uncertainty nikaalo.

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Bohr model ke fail hone ke kaaran

Ab hum samajhte hain ki Bohr's model fail kyun hota hai. Yeh electron ko ek sharp defined orbit par particle maanta hai aur uske wave nature ko ignore karta hai, aur aise orbit ke liye har pal exact position aur velocity chahiye, jise uncertainty principle mana karta hai. Duality ko ignore karke aur uncertainty principle ke khilaaf jaakar, yeh model doosre atoms tak nahi badhaya ja saka; duality par bani ek theory ki zaroorat thi.

Quick check

3 mein se 1

Ek proton aur ek electron same speed se chal rahe hain. Kiski de Broglie wavelength lambi hai?

Proton ki, kyunki woh bhaari haiElectron ki, kyunki uska momentum kam haiDono barabar, kyunki unki speeds barabar hainKisi ki nahi: sirf photons ki wavelengths hoti hain

Answer dekho

Answer (B) Electron ki, kyunki uska momentum kam hai

λ = h / m v

: barabar speed par halke electron ka momentum kam hota hai, isliye wavelength lambi (proton ki 1836 guna).

2.6 Atom ka Quantum Mechanical Model

Newton ki classical mechanics pattharon, cricket balls aur planets ke liye kaam karti hai, jinka wave nature negligible hai, lekin electrons, atoms aur molecules ke liye fail ho jaati hai kyunki yeh duality aur uncertainty ko ignore karti hai. Quantum mechanics inhe shaamil karti hai; badi cheezon ke liye yeh classical mechanics jaise hi jawaab deti hai.

Ise 1925–26 mein do equivalent forms mein develop kiya gaya, Heisenberg aur Erwin Schrödinger ne. Schrödinger ke wave form mein, constant energy wale system (jaise akela chhoda gaya atom) ke liye central equation aise likhi jaati hai

Schrödinger equation

\hat{H} ψ = E ψ

jahan $ψ$ wave function hai aur $\hat{H}$ Hamiltonian operator, jo total energy se bana hai: electrons aur nuclei ki kinetic energies, electron–nucleus attractions, aur electron–electron aur nucleus–nucleus repulsions. Ise solve karne se allowed energies $E$ aur wave functions $ψ$ milte hain; iski maths aage ki classes mein aati hai.

Hydrogen ke liye ise exactly solve kiya ja sakta hai, jisse energy levels milte hain aur har ek ke liye ek wave function, jise teen quantum numbers, $n$ , $l$ aur $m_{l}$ , se label kiya jaata hai; yeh solution se khud nikalte hain, Bohr ke $n$ ki tarah maan nahi liye jaate. Aisa one-electron wave function ek atomic orbital (कक्षक) hai. $ψ$ ka khud koi physical matlab nahi hai, lekin kisi point par $∣ ψ ∣^{2}$ wahan electron milne ki probability ke proportional hota hai. Results hydrogen ke spectrum ka har feature dobara bana dete hain, un details samet jo Bohr se chhoot gayi thi.

Ek se zyada electrons hon to equation exactly solve nahi ho sakti, kyunki electrons ek doosre ko repel karte hain. Approximate computer methods hydrogen jaise orbitals dikhate hain, jo bade nuclear charge se thode sikud jaate hain, aur jinki energies $n$ aur $l$ dono par depend karti hain (Section 2.6.3).

In results ko saath rakhne par atom ka quantum mechanical model banta hai:

har electron ko ek orbital se describe kiya jaata hai, ek wave function $ψ$ jismein uske baare mein jaanne laayak sab kuch hai; ek orbital ki ek definite energy hoti hai aur usmein zyada se zyada do electrons ki jagah hoti hai, aur electrons pehle sabse kam energy wale orbitals lete hain;
hum electron ka path follow nahi kar sakte, kyunki uski position aur velocity kabhi dono sharp nahi hoti; iske bajaye $ψ$ humein $∣ ψ ∣^{2}$ deta hai, ek kabhi negative na hone wali probability density jo map karti hai ki electron kahan hone ki sambhaavna hai;
bandhe hue electron ki sirf kuch energies ho sakti hain, aur yeh quantisation bahar se thopa nahi jaata: yeh electron ke wave ki tarah behave karne se, Schrödinger equation ke allowed solutions ke roop mein, khud nikalta hai.

2.6.1 Orbitals aur Quantum Numbers

Definition

Atomic orbital

Atom mein electron ka wave function $ψ$ , jise quantum numbers $n$ , $l$ aur $m_{l}$ se label kiya jaata hai; $∣ ψ ∣^{2}$ har point par electron milne ki probability density deta hai.

Example $m_{l} = 0$ wala 2p orbital.

Orbitals size (electron nucleus ke kitne paas rehta hai), shape aur orientation (kin directions mein uske milne ki sambhaavna zyada hai) mein alag hote hain. Har ek ko teen quantum numbers (क्वांटम संख्याएँ) se label kiya jaata hai; chautha number khud electron ko describe karta hai.

Principal quantum number, $n$ (1, 2, 3, …) orbital ka size aur kaafi had tak uski energy fix karta hai; one-electron species mein energy aur size sirf $n$ par depend karte hain. Same $n$ wale orbitals ek shell banaate hain: $n$ = 1, 2, 3, 4 K, L, M, N shells hain. Bada $n$ electron ko average mein zyada door rakhta hai, aur use nucleus se door kheenchne mein energy lagti hai, isliye energy $n$ ke saath badhti hai. $n$ th shell mein $n^{2}$ orbitals hote hain.

Azimuthal quantum number, $l$ (orbital angular momentum ya subsidiary quantum number) shape fix karta hai. Diye gaye $n$ ke liye yeh $n$ values $0, 1, \dots, (n - 1)$ leta hai, aur har value ek subshell define karti hai. Values $l$ = 0, 1, 2, 3, 4, 5 ko s, p, d, f, g, h kehte hain, aur subshell ka naam $n$ aur letter se hota hai: $n = 3$ , $l = 1$ 3p hai.

Magnetic quantum number, $m_{l}$ chune hue axes ke relative orientation fix karta hai. Diye gaye $l$ ke liye yeh $- l$ se $+ l$ tak $2 l + 1$ values leta hai, isliye s, p, d aur f subshells mein 1, 3, 5 aur 7 orbitals hote hain. $n$ $l$ ko limit karta hai, aur $l$ $m_{l}$ ko (Table 2.4).

Table 2.4Shells subshells aur orbitals mein kaise bat-te hain

Shell ( $n$ )	Allowed $l$	Subshells	Orbitals ( $n^{2}$ )	Max. electrons ( $2 n^{2}$ )
K (1)	0	1s	1	2
L (2)	0, 1	2s, 2p	1 + 3 = 4	8
M (3)	0, 1, 2	3s, 3p, 3d	1 + 3 + 5 = 9	18
N (4)	0, 1, 2, 3	4s, 4p, 4d, 4f	1 + 3 + 5 + 7 = 16	32

Spin quantum number, $m_{s}$ . Many-electron spectra mein lines ke paas-paas ke pairs aur triplets ke liye teen numbers se zyada levels chahiye. George Uhlenbeck aur Samuel Goudsmit ne 1925 mein suggest kiya ki electron ka apna angular momentum hota hai, spin, jise mote taur par Earth ki tarah apne axis par ghoomte hue socha jaata hai. Yeh sirf do taraf point kar sakta hai: $m_{s} = + \frac{1}{2}$ (↑) ya $- \frac{1}{2}$ (↓). Ek orbital mein zyada se zyada do electrons hote hain, opposite spins ke saath, aur isi se Table 2.4 mein electrons ki ginti milti hai.

Short mein: $n$ shell, size aur zyaadatar energy deta hai; $l$ subshell, shape aur (many-electron atoms mein) energy ka kuch hissa; $m_{l}$ orientation; $m_{s}$ spin.

Compare

Orbit ya orbital?

Bohr orbit

nucleus ke chaaron taraf ek definite circular path
har pal exact position aur velocity chahiye, jise uncertainty principle mana karta hai
iska koi asli matlab nahi aur ise kabhi observe nahi kiya ja sakta
ek number, $n$ , se label kiya jaata hai

Atomic orbital

ek one-electron wave function $ψ$
yeh batata hai ki electron kahan hone ki sambhaavna hai, koi path nahi
$∣ ψ ∣^{2}$ ek probability density hai: probability per unit volume
teen numbers, $n$ , $l$ aur $m_{l}$ , se label kiya jaata hai

Kyunki $∣ ψ ∣^{2}$ jagah-jagah badalta hai, kisi region mein probability nikaalne ke liye chhote volumes $Δ V$ , jinmein yeh lagbhag constant hai, par $∣ ψ ∣^{2} Δ V$ ko jodte hain.

Example 2.17NCERT Problem 2.17

N shell mein orbitals aur electrons

$n = 4$ wale shell mein kitne orbitals hain, aur usmein kitne electrons aa sakte hain?

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Example 2.18NCERT Problem 2.18

Subshells ka naam batana

In subshells ke naam batao: (a) $n = 3$ , $l = 1$ ; (b) $n = 5$ , $l = 2$ ; (c) $n = 4$ , $l = 3$ ; (d) $n = 6$ , $l = 0$ .

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Quick check

3 mein se 1

Quantum numbers ka kaun sa set allowed nahi hai?

n = 3

l = 2

m_{l} = - 2

n = 4

l = 0

m_{l} = 0

n = 1

l = 0

m_{l} = 0

n = 2

l = 2

m_{l} = 0

Answer dekho

Answer (D) $n = 2$ , $l = 2$ , $m_{l} = 0$

l

sirf

n - 1

tak jaata hai, isliye

n = 2

mein

l = 0

ya 1 ho sakta hai, kabhi 2 nahi.

2.6.2 Atomic Orbitals ke Shapes

Nucleus se distance $r$ ke against plot karne par $ψ$ har orbital ke liye alag hota hai (Fig. 2.16). 1s ke liye yeh nucleus par sabse bada hai aur smoothly girta hai; 2s ke liye yeh girta hai, zero cross karta hai, negative ho jaata hai aur dheere-dheere wapas zero ki taraf aata hai.

Max Born ne dikhaya ki $∣ ψ ∣^{2}$ hi maayne rakhne wali quantity hai, yaani probability density. 1s ke liye yeh nucleus par sabse zyada hai aur tezi se girti hai; 2s ke liye yeh ek distance par zero tak girti hai, ek chhote maximum tak badhti hai aur phir fade ho jaati hai. Zero probability density wali surface node hai (nodal surface, नोड); ns orbital mein $n - 1$ spherical nodes hote hain.Entrance papers radial probability, $4 π r^{2} ψ^{2}$ , bhi use karte hain, yaani distance $r$ par ek patle shell mein electron milne ka chance. 1s ke liye yeh nucleus par zero hai aur $r = 52.9$ pm, yaani Bohr ke radius, par peak karti hai.

3/3Square karne par dono positive hain; node par 2s probability density zero hai.

Fig. 2.162s wave function ek baar sign badalta hai, isliye uski probability density ek distance par zero ho jaati hai: ek node.NCERT Fig. 2.12 · p. 57

Do graphs ek hi distance axis share karte hain. Step 1 mein upar wala graph 1s ke liye psi dikhata hai, nucleus par ooncha aur smoothly girta hua. Step 2 mein ek 2s curve judta hai jo node mark wale point par axis cross karta hai aur wapas upar uthne se pehle zero se neeche jaata hai. Step 3 mein neeche wala graph psi squared dikhata hai: 1s curve lagaataar girta hai, jabki 2s curve node par zero ko chhoota hai aur phir ek chhota doosra hump banata hai.

Charge-cloud picture wahan dots ki bheed dikhati hai jahan density zyada hai. Shape ko ek boundary surface zyada saaf dikhati hai, jo constant $∣ ψ ∣^{2}$ ki hoti hai aur lagbhag 90% probability ko gherti hai. 100% nahi, kyunki $∣ ψ ∣^{2}$ kabhi bilkul zero tak nahi pahunchta, isliye aisi surface infinite hogi.

s orbitals ki boundary surfaces nucleus par centred spheres hoti hain: probability sirf is par depend karti hai ki tum nucleus se kitne door ho, direction par nahi. Yeh $n$ ke saath badhte hain: 1s < 2s < 3s < 4s.

p orbitals ( $l = 1$ , $n \geq 2$ ) ke nucleus ke opposite sides par do lobes hote hain, aur unke beech ek nodal plane (Fig. 2.17). Ek subshell ke teen p orbitals size, shape aur energy mein ek jaise hain lekin perpendicular axes ke along point karte hain: $p_{x}$ , $p_{y}$ , $p_{z}$ (in labels aur $m_{l}$ = −1, 0, +1 ke beech koi simple match nahi hai). Yeh $n$ ke saath size aur energy mein badhte hain (4p > 3p > 2p) aur inmein $n - 2$ spherical nodes hote hain.

d orbitals ( $l = 2$ , $n \geq 3$ ) paanch hain: $d_{x y}$ , $d_{y z}$ , $d_{x z}$ , $d_{x^{2} - y^{2}}$ aur $d_{z^{2}}$ . Pehle chaar mein clover leaf jaise chaar lobes hain; $d_{z^{2}}$ mein z ke along do lobes aur beech mein ek ring hai. Free atom ke paanchon 3d orbitals ki energy barabar hoti hai; 4d aur 5d dikhne mein milte-julte hain lekin bade aur zyada energy wale hain.

2/3Teen p orbitals x, y aur z ke along point karte hain, har ek mein nucleus se guzarta ek nodal plane.

Fig. 2.17s orbitals spheres hain; p orbitals x, y aur z ke along lobes ke pairs hain; zyaadatar d orbitals mein chaar lobes hain.NCERT Fig. 2.14 · p. 58

Step 1 1s aur bade 2s ki boundary surfaces ko nucleus ke chaaron taraf circles ki tarah dikhata hai. Step 2 px, py aur pz dikhata hai, har ek ek axis ke along lobes ka pair, pz ka nodal plane dashed. Step 3 axes ke beech lobes wala d xy, axes ke along lobes wala d x squared minus y squared, aur z ke along do lobes aur ek ring wala d z squared dikhata hai.

Radial nodes spheres hote hain (jaise 2s aur 3p mein); angular nodes nucleus se guzarte planes ya cones hote hain, jaise $p_{z}$ ka xy plane ya $d_{x y}$ ke xz aur yz planes. Kul milakar:

nodes ki sankhya

\begin{aligned} angular & = l \\ radial & = n - l - 1 \\ total & = n - 1 \end{aligned}

Quick check

3 mein se 1

4d orbital mein kitne radial nodes hote hain?

node

Answer dekho

Answer 1 node

n - l - 1 = 4 - 2 - 1 = 1

, plus

l = 2

angular nodes: kul 3.

2.6.3 Orbitals ki Energies

Hydrogen atom mein orbital ki energy sirf $n$ par depend karti hai (Eq. 2.13), isliye order hai

\begin{aligned} 1s < 2s = 2p \\ < 3s = 3p = 3d \\ < 4s = 4p \\ = 4d = 4f < \dots \end{aligned}

2s aur 2p shape mein alag hain lekin energy mein nahi: barabar energy wale orbitals degenerate (अपभ्रष्ट) hote hain. 1s mein electron, jo sabse zor se pakda hai, ground state mein hai; 2s, 2p ya usse upar woh excited state mein hai (Fig. 2.18, left).

Many-electron atom mein energy $l$ par bhi depend karti hai: ek shell ke andar s < p < d < f, aur shells overlap kar sakte hain: 4s 3d se neeche hai, 6s 4f aur 5d se neeche, aur 4f 6p se neeche.

Iska kaaran electron–electron repulsion hai, jo hydrogen mein nahi hota. Andar ke electrons bahar wale electron ko nucleus se kuch had tak shield karte hain, isliye use kam charge mehsoos hota hai, yahi effective nuclear charge $Z_{e f f} e$ (प्रभावी नाभिकीय आवेश) hai. Phir bhi uska attraction nuclear charge ke saath badhta hai, isliye $Z$ badhne par orbital energies aur zyada negative hoti jaati hain.

Shielding shape par depend karti hai. Ek shell mein s electron p electron se zyada samay nucleus ke paas bitata hai, aur p, d se zyada. Isliye s electrons p se behtar shield karte hain, aur p, d se behtar; aur ek shell ke andar $Z_{e f f}$ s se p se d tak girta hai, isliye s sabse kas ke pakda hota hai aur sabse neeche hota hai. Isse har shell subshells mein bat jaata hai (Fig. 2.18, right).

Fig. 2.18Hydrogen mein energy sirf

n

par depend karti hai; many-electron atoms mein subshells split hote hain, aur 4s 3d se neeche aa jaata hai.NCERT Fig. 2.16 · p. 60

Do energy ladders saath-saath khadi hain, energy upar ki taraf badhti hai. Left wali ladder, hydrogen ke liye, mein sabse neeche 1s hai, phir 2s aur 2p ek hi line par, 3s, 3p aur 3d ek hi line par, aur 4s, 4p, 4d aur 4f ek aur line par, jo dikhata hai ki same n wale orbitals degenerate hain. Right wali ladder, many-electron atom ke liye, mein 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p order mein alag lines hain, 4s ki line 3d ki line se neeche, jo dikhata hai ki subshells split hote hain aur 4s 3d se neeche hai.

Koi simple formula nahi hai, lekin ek kaam ka rule of thumb (n + l) rule hai: $n + l$ ki value jitni kam, energy utni kam; jab do orbitals ka $n + l$ same ho, to kam $n$ wale ki energy kam hoti hai (Table 2.5).

Table 2.5n + l ke hisaab se grouped orbitals (har group mein kam n pehle aata hai)

$n + l$	Orbitals, badhti energy ke order mein
1	1s
2	2s
3	2p, 3s
4	3p, 4s
5	3d, 4p, 5s
6	4d, 5p, 6s
7	4f, 5d, 6p, 7s

Nuclear charge badhne par koi bhi orbital energy mein neeche bhi aata hai: helium ka 1s hydrogen ke 1s se kaafi neeche hai, aur lithium ka aur bhi neeche.

2.6.4 Atom mein Orbitals ki Filling

Atom ke electrons asal mein kaun se orbitals mein rehte hain? Upar wale energy order ke saath teen rules yeh tay karte hain.

PrincipleAufbau principle

Atom ki ground state mein electrons badhti energy ke order mein orbitals bharte hain: har naya electron abhi bache sabse kam energy wale orbital mein jaata hai.

Aufbau German mein 'building up' (banaate jaana) hai. Orbital energies har atom mein thodi badalti hain, isliye koi ek order saare atoms ke liye sahi nahi hai, lekin sabse bahar wale electrons ke liye (n + l) order kamaal ka kaam karta hai:

\begin{aligned} 1s, 2s, 2p, 3s, 3p, \\ 4s, 3d, 4p, 5s, 4d, \\ 5p, 6s, 4f, 5d, 6p, \\ 7s, 5f, 6d \end{aligned}

Yeh Table 2.5 ko row by row padhna hai. Potassium ka aakhri electron 4s mein jaata hai, 3d mein nahi, kyunki 4s ka $n + l$ kam hai (4 vs 5). Jahan do subshells energy mein bahut paas hote hain, wahan exceptions hote hain (Section 2.6.6).

PrinciplePauli exclusion principle

Ek atom ke andar har electron ka chaar quantum numbers $n$ , $l$ , $m_{l}$ aur $m_{s}$ ka apna unique combination hota hai. Doosre shabdon mein, ek orbital mein zyada se zyada do electrons hote hain, aur unke spins opposite hone chahiye.

Wolfgang Pauli ne ise 1925 mein diya. Ek orbital ke do electrons ke $n$ , $l$ aur $m_{l}$ same hote hain, isliye woh $m_{s}$ mein alag hote hain. Isliye s, p, d aur f subshells mein 2, 6, 10 aur 14 electrons aate hain, aur ek shell mein zyada se zyada $2 n^{2}$ .

PrincipleHund's rule of maximum multiplicity

Barabar energy wale orbitals (ek subshell) mein aane wale electrons tab tak pair nahi karte jab tak subshell ke har orbital mein ek electron na aa jaaye, aur single electrons ke spins parallel hote hain.

Isliye pairing p subshell mein 4th electron se shuru hoti hai, d mein 6th se aur f mein 8th se, jaise khaali bus mein passengers pehle ek-ek karke double seat par akele baithte hain, uske baad hi koi kisi anjaan ke bagal mein baithta hai.

2.6.5 Atoms ka Electronic Configuration

Atom ke electrons uske orbitals mein jis tarah baante hote hain, woh uska electronic configuration (इलेक्ट्रॉनिक विन्यास) hai. Ise do tarah likha ja sakta hai:

spdf notation: har bhare subshell ko $n$ aur uske letter se likhte hain, aur electrons ki sankhya superscript mein; nitrogen $1 s^{2} 2 s^{2} 2 p^{3}$ hai;
orbital (box) diagram: har orbital ek box hai aur har electron ek arrow, $m_{s} = + \frac{1}{2}$ ke liye ↑ aur $m_{s} = - \frac{1}{2}$ ke liye ↓; kyunki yeh spins dikhata hai, isme chaaron quantum numbers ki jaankaari hoti hai.

Hydrogen $1 s^{1}$ hai aur helium $1 s^{2}$ , jiske do electrons opposite spin ke hain. 1s bhar jaane par lithium ka teesra electron 2s mein jaata hai ( $1 s^{2} 2 s^{1}$ ) aur beryllium use bhar deta hai ( $1 s^{2} 2 s^{2}$ ). Boron se neon tak 2p Hund's rule se bharta hai: carbon ( $2 p^{2}$ ) mein do unpaired electrons hain, nitrogen ( $2 p^{3}$ ) mein teen, aur pairing oxygen ( $2 p^{4}$ ) se shuru hoti hai. Neon, $1 s^{2} 2 s^{2} 2 p^{6}$ , doosra shell poora karta hai.

Sodium se argon tak yahi 3s aur 3p ke saath dohraaya jaata hai. Bhare hue andar ke shells ko matching noble gas se likhte hain: sodium $[N e] 3 s^{1}$ hai, argon $[N e] 3 s^{2} 3 p^{6}$ . Andar ke shell ke electrons core electrons hain; sabse bahar wale shell ke electrons valence electrons hain, jo chemistry tay karte hain.

Potassium $[A r] 4 s^{1}$ hai aur calcium $[A r] 4 s^{2}$ ; phir 4p se pehle scandium se zinc tak 3d bharta hai. Do pattern todte hain: chromium $[A r] 3 d^{5} 4 s^{1}$ hai, $3 d^{4} 4 s^{2}$ nahi, aur copper $[A r] 3 d^{10} 4 s^{1}$ , $3 d^{9} 4 s^{2}$ nahi, kyunki half-filled aur filled subshells khaas taur par stable hote hain (Section 2.6.6).

Gallium se krypton tak 4p bharta hai; rubidium se xenon tak 5s, 4d aur 5p ke saath yahi pattern dohraaya jaata hai. Caesium aur barium 6s bharte hain; lanthanum se mercury tak 4f aur 5d bharte hain; phir 6p, 7s, 5f aur 6d aate hain. Uranium ke baad ke lagbhag saare elements artificial aur short-lived hain; saare 118 known elements ke ab naam hain. Tables mein diye configurations zyaadatar spectroscopy se aate hain.

InteractiveElectron configuration builder

1s se 4p tak orbital boxes ki rows filling order mein bani hain. Tum slider ya previous aur next buttons se hydrogen se krypton tak koi element chunte ho, ya Add electron dabakar electrons ek-ek karke rakhte ho. Arrows pairing se pehle boxes ko akele-akele bharte hain. Readouts element, poora aur noble-gas configuration, aur unpaired aur outer-shell electrons ki sankhya batate hain, aur ek message us rule ka naam batata hai jisne aakhri electron rakha, chromium aur copper exceptions ke liye note ke saath.

Fig. 2.19Hydrogen se krypton tak elements mein step karo, ya ek-ek karke electrons jodo, aur aufbau principle, Pauli's principle aur Hund's rule ko kaam karte dekho.

Configurations samjhaate hain ki atoms kyun judte hain, kuch elements metals kyun hain, aur helium inert kyun hai jabki halogens behad reactive, aise sawaal jinhe Dalton ke atoms chhoo bhi nahi sakte the. Tum inhe aage ke har chapter mein use karoge, Chapter 3 ke periodic table se shuru karke.

2.6.6 Completely Filled aur Half Filled Subshells ki Stability

Ground state sabse kam total energy wala configuration hai. Jab do subshells energy mein bahut paas hon, jaise chromium aur copper mein 4s aur 3d, to ek electron 4s se 3d mein chala jaata hai agar isse 3d theek half full ( $d^{5}$ ) ya full ( $d^{10}$ ) ho jaaye. Do effects in subshells ko extra stable banaate hain.

Symmetry. Electrons saare orbitals mein barabar faile hote hain. Ek subshell ke electrons space ke alag-alag regions mein hote hain, isliye ek doosre ko kam shield karte hain aur zyada zor se pakde jaate hain.

Exchange energy. Degenerate orbitals mein same spin wale electrons jagah badal sakte hain, aur har possible exchange energy kam karta hai (exchange energy). $k$ parallel-spin electrons $k (k - 1) / 2$ exchanges dete hain: $d^{4}$ ke liye 6, $d^{5}$ ke liye 10 (Fig. 2.20). Half-filled aur filled subshells ise maximum karte hain, aur Hund's rule ke peeche bhi yahi hai.

2/3Paanch parallel spins: 4 + 3 + 2 + 1 = 10 exchanges.

Fig. 2.20Paanch parallel spins 10 exchanges dete hain jabki chaar sirf 6, isiliye chromium

3 d^{5} 4 s^{1}

pasand karta hai.NCERT Fig. 2.18 · p. 65

Paanch boxes ek d subshell dikhate hain. Step 1 mein chaar boxes mein up arrows hain jo chhe curved links se pairs mein jude hain. Step 2 mein paanchva arrow links ko das tak le jaata hai (chaar plus teen plus do plus ek). Step 3 mein chromium ke do configurations compare kiye gaye hain: chhe exchanges wala 3d four 4s two, aur das wala tick kiya hua 3d five 4s one.

To half-filled aur filled subshells ko kam shielding, kam repulsion aur zyada exchange energy ka fayda milta hai. Aise hi exceptions mein molybdenum ( $4 d^{5} 5 s^{1}$ ) aur silver ( $4 d^{10} 5 s^{1}$ ) bhi hain, lekin har case itna simple nahi hota.

Quick check

4 mein se 1

Chromium (

Z = 24

) ka ground-state configuration kaun sa hai?

[A r] 3 d^{4} 4 s^{2}

[A r] 3 d^{5} 4 s^{1}

[A r] 3 d^{6}

[A r] 4 s^{2} 4 p^{4}

Answer dekho

Answer (B) $[A r] 3 d^{5} 4 s^{1}$

Half-filled

d^{5}

subshell mein zyada exchange energy hoti hai; seedha aufbau order galti se

3 d^{4} 4 s^{2}

dega.

Recap

Summary aur key points

Discharge-tube experiments ne dikhaya ki atoms mein electrons ( $e / m_{e} = 1.76 \times 10^{11}$ C kg⁻¹; Millikan ki oil drops se charge $1.602 \times 10^{- 19}$ C), protons aur neutrons hote hain (Section 2.1).
Thomson ka barabar faila positive sphere alpha-scattering test mein fail hua; Rutherford ne nateeja nikaala ki positive charge aur lagbhag saara mass lagbhag $10^{- 15}$ m ke nucleus mein hai (Section 2.2.2).
$Z$ protons ki sankhya hai aur $A = Z + N$ ; isotopes ka $Z$ same hota hai, isobars ka $A$ , aur isotopes ki chemistry same hoti hai (Section 2.2.4).
Orbit karta electron radiate karke spiral karte hue nucleus mein gir jaata, isliye Rutherford ka model nahi samjha sakta ki atoms stable kyun hain (Section 2.2.5).
Electromagnetic waves $c = ν λ$ aur $\overset{ˉ}{ν} = 1 / λ$ follow karti hain (Section 2.3.1); black-body radiation ne dikhaya ki energy quanta mein aati hai, $E = h ν$ (Section 2.3.2).
Einstein ki equation $h ν = h ν_{0} + \frac{1}{2} m_{e} v^{2}$ photoelectric effect samjhaati hai: frequency electrons ki energy tay karti hai, brightness sirf unki sankhya (Photoelectric effect).
Free atoms line spectra dete hain; hydrogen ki lines $109 677$ cm⁻¹ ke saath Rydberg ke formula mein fit hoti hain (Section 2.3.3).
Bohr ka quantised angular momentum, $m_{e} v r = n h / 2 π$ , $r_{n} = 52.9 n^{2} / Z$ pm aur $E_{n} = - 2.18 \times 10^{- 18} Z^{2} / n^{2}$ J deta hai; har line levels ke beech ek jump hai (Section 2.4).
Matter ka wave character hota hai, $λ = h / m v$ , aur $Δ x Δ p_{x} \geq h / 4 π$ definite orbits ko rule out karta hai (Section 2.5.1, Section 2.5.2).
Quantum mechanical model mein orbital ek wave function hai jise $n$ , $l$ aur $m_{l}$ se label kiya jaata hai, $∣ ψ ∣^{2}$ probability density hai, aur spin $m_{s} = \pm \frac{1}{2}$ jodta hai (Section 2.6, Section 2.6.1).
s orbitals spheres hain, p orbitals mein do lobes aur zyaadatar d orbitals mein chaar; $n - l - 1$ radial aur $l$ angular nodes hote hain (Section 2.6.2).
Many-electron atoms mein energy $n$ aur $l$ par depend karti hai ((n + l) rule), aur orbitals aufbau principle, Pauli's principle aur Hund's rule se bharte hain (Section 2.6.3, Section 2.6.4).
Half-filled aur filled subshells extra stable hote hain, jisse Cr $3 d^{5} 4 s^{1}$ aur Cu $3 d^{10} 4 s^{1}$ milte hain (Section 2.6.5, Section 2.6.6).

Apna NCERT exercise question dhoondo

Hamare practice questions ncert.ai ke liye likhe gaye hain aur NCERT exercises ko follow karte hain. Apni textbook ke question se match karne wala question dhoondo; uska answer uske saath hai.

Tumhari NCERT textbook mein	Yahan practice question
NCERT Exercises 2.1	Practice Q1
NCERT Exercises 2.2	Practice Q2
NCERT Exercises 2.3	Practice Q3
NCERT Exercises 2.4	Practice Q4
NCERT Exercises 2.5	Practice Q5
NCERT Exercises 2.6	Practice Q6
NCERT Exercises 2.7	Practice Q7
NCERT Exercises 2.8	Practice Q8
NCERT Exercises 2.9	Practice Q9
NCERT Exercises 2.10	Practice Q10
NCERT Exercises 2.11	Practice Q11
NCERT Exercises 2.12	Practice Q12
NCERT Exercises 2.13	Practice Q13
NCERT Exercises 2.14	Practice Q14
NCERT Exercises 2.15	Practice Q15
NCERT Exercises 2.16	Practice Q16
NCERT Exercises 2.17	Practice Q17
NCERT Exercises 2.18	Practice Q18
NCERT Exercises 2.19	Practice Q19
NCERT Exercises 2.20	Practice Q20
NCERT Exercises 2.21	Practice Q21
NCERT Exercises 2.22	Practice Q22
NCERT Exercises 2.23	Practice Q23
NCERT Exercises 2.24	Practice Q24
NCERT Exercises 2.25	Practice Q25
NCERT Exercises 2.26	Practice Q26
NCERT Exercises 2.27	Practice Q27
NCERT Exercises 2.28	Practice Q28
NCERT Exercises 2.29	Practice Q29
NCERT Exercises 2.30	Practice Q30
NCERT Exercises 2.31	Practice Q31
NCERT Exercises 2.32	Practice Q32
NCERT Exercises 2.33	Practice Q33
NCERT Exercises 2.34	Practice Q34
NCERT Exercises 2.35–2.37	Practice Q35
NCERT Exercises 2.38–2.39	Practice Q36
NCERT Exercises 2.40	Practice Q37
NCERT Exercises 2.41	Practice Q38
NCERT Exercises 2.42	Practice Q39
NCERT Exercises 2.43–2.44	Practice Q40
NCERT Exercises 2.45	Practice Q41
NCERT Exercises 2.46	Practice Q42
NCERT Exercises 2.47	Practice Q43
NCERT Exercises 2.48	Practice Q44
NCERT Exercises 2.49	Practice Q45
NCERT Exercises 2.50	Practice Q46
NCERT Exercises 2.51	Practice Q47
NCERT Exercises 2.52	Practice Q48
NCERT Exercises 2.53	Practice Q49
NCERT Exercises 2.54	Practice Q50
NCERT Exercises 2.55	Practice Q51
NCERT Exercises 2.56	Practice Q52
NCERT Exercises 2.57	Practice Q53
NCERT Exercises 2.58	Practice Q54
NCERT Exercises 2.59	Practice Q55
NCERT Exercises 2.60	Practice Q56
NCERT Exercises 2.61	Practice Q57
NCERT Exercises 2.62	Practice Q58
NCERT Exercises 2.63	Practice Q59
NCERT Exercises 2.64	Practice Q60
NCERT Exercises 2.65	Practice Q61
NCERT Exercises 2.66	Practice Q62
NCERT Exercises 2.67	Practice Q63

Quick check: MCQs

2.1.4 Protons aur Neutrons ki Discovery3 questions
2.2.4 Isobars aur Isotopes3 questions
2.2.5 Rutherford Model ki Kamiyan3 questions
2.3.1 Electromagnetic Radiation ka Wave Nature3 questions
Photoelectric effect3 questions
Hydrogen ka line spectrum3 questions
2.4.2 Bohr's Model ki Limitations4 questions
Bohr model ke fail hone ke kaaran3 questions
2.6.1 Orbitals aur Quantum Numbers3 questions
2.6.2 Atomic Orbitals ke Shapes3 questions
2.6.4 Atom mein Orbitals ki Filling4 questions
2.6.6 Completely Filled aur Half Filled Subshells ki Stability4 questions

Glossary · 15

Key terms (English + Hindi)

atomic numberपरमाणु क्रमांकparamanu kramank: Nucleus mein protons ki sankhya, $Z$ .Chapter mein pehli baar yahan aaya →
atomic orbitalकक्षकkakshak: One-electron wave function $ψ$ ; $∣ ψ ∣^{2}$ probability density deta hai.Chapter mein pehli baar yahan aaya →

de Broglie wavelengthदे ब्रॉग्ली तरंगदैर्ध्यde Broglie tarangdairghya: Chalte particle ki wavelength $λ = h / m v$ .Chapter mein pehli baar yahan aaya →
degenerate orbitalsअपभ्रष्ट कक्षकapabhrasht kakshak: Barabar energy wale orbitals, jaise teen 2p orbitals.Chapter mein pehli baar yahan aaya →

effective nuclear chargeप्रभावी नाभिकीय आवेशprabhavi nabhikiya avesh: Shielding ke baad electron ko mehsoos hone wala net nuclear charge.Chapter mein pehli baar yahan aaya →
electronic configurationइलेक्ट्रॉनिक विन्यासelectronic vinyas: Atom ke electrons uske orbitals mein kaise baante hain.Chapter mein pehli baar yahan aaya →

isobarसमभारिकsambharik: Alag elements ke atoms jinka mass number same hai.Chapter mein pehli baar yahan aaya →
isotopeसमस्थानिकsamasthanik: Ek hi element ke atoms jinmein neutrons ki sankhya alag hai.Chapter mein pehli baar yahan aaya →

line spectrumरेखा स्पेक्ट्रमrekha spectrum: Kisi element ki khaas wavelengths par sharp lines wala spectrum.Chapter mein pehli baar yahan aaya →

nodeनोडnod: Zero probability density wali surface: radial (sphere) ya angular (plane ya cone).Chapter mein pehli baar yahan aaya →

photonफोटॉनphoton: Electromagnetic energy ka ek packet (quantum), $E = h ν$ .Chapter mein pehli baar yahan aaya →

quantum numbersक्वांटम संख्याएँquantum sankhyayen: $n$ , $l$ , $m_{l}$ aur $m_{s}$ , jo orbital aur electron ke spin ko label karte hain.Chapter mein pehli baar yahan aaya →

stationary stateस्थिर अवस्थाsthir avastha: Bohr's model mein fixed energy wala allowed orbit.Chapter mein pehli baar yahan aaya →

uncertainty principleअनिश्चितता सिद्धांतanishchitata siddhant: Position aur momentum dono exactly nahi jaane ja sakte: $Δ x Δ p_{x} \geq h / 4 π$ .Chapter mein pehli baar yahan aaya →

work functionकार्यफलनkaryaphalan: Metal se electron nikaalne ki minimum energy, $h ν_{0}$ .Chapter mein pehli baar yahan aaya →

Structure of Atom: Class 11 Chemistry Chapter 2 Hinglish mein

Is chapter mein aap kya seekhenge

2.1 Sub-atomic Particles ki Discovery

2.1.1 Electron ki Discovery

2.1.2 Electron ka Charge to Mass Ratio

2.1.3 Electron par Charge

2.1.4 Protons aur Neutrons ki Discovery

2.2 Atomic Models

2.2.1 Atom ka Thomson Model

2.2.2 Atom ka Rutherford Nuclear Model

2.2.3 Atomic Number aur Mass Number

2.2.4 Isobars aur Isotopes

2.2.5 Rutherford Model ki Kamiyan

2.3 Bohr's Model of Atom tak le jaane wale Developments

2.3.1 Electromagnetic Radiation ka Wave Nature

2.3.2 Electromagnetic Radiation ka Particle Nature: Planck's Quantum Theory

Photoelectric effect

2.3.3 Quantized Electronic Energy Levels ka Saboot: Atomic Spectra

Hydrogen ka line spectrum

2.4 Hydrogen Atom ke liye Bohr's Model

2.4.1 Hydrogen ke Line Spectrum ki Explanation

2.4.2 Bohr's Model ki Limitations

2.5 Atom ke Quantum Mechanical Model ki Taraf

2.5.1 Matter ka Dual Behaviour

2.5.2 Heisenberg's Uncertainty Principle

Bohr model ke fail hone ke kaaran

2.6 Atom ka Quantum Mechanical Model

2.6.1 Orbitals aur Quantum Numbers

2.6.2 Atomic Orbitals ke Shapes

2.6.3 Orbitals ki Energies

2.6.4 Atom mein Orbitals ki Filling

2.6.5 Atoms ka Electronic Configuration

2.6.6 Completely Filled aur Half Filled Subshells ki Stability

Summary aur key points

Exercises: answers ke saath

Practice questions answers ke saath (NCERT “Board aur entrance practice”)

Apna NCERT exercise question dhoondo

Quick check: MCQs

Key terms (English + Hindi)

Tum chapter ke end tak pahunch gaye