Structure of Atom: Class 11 Chemistry · Chapter 2

Why does sodium burst into flame in water while neon reacts with nothing at all? Why is copper a shiny metal and sulphur a brittle yellow solid? Push any question in chemistry far enough and the answer lies inside the atom.

The idea of a smallest, uncuttable particle is old. In India the Vaisheshika school, linked with the sage Kanad, spoke of the paramanu (परमाणु); in Greece, Leucippus and Democritus called it atomos, 'uncuttable'. These were inspired guesses that nobody could test.

John Dalton made atoms testable in 1808: each element has its own kind of atom with its own mass, and compounds form when atoms join in small whole-number ratios. That explained the laws of chemical combination (Chapter 1), but not why a plastic comb pulled through dry hair picks up scraps of paper. If atoms were featureless balls, where would electric charge come from? Experiments at the end of the 1800s gave the answer: atoms have parts.

2.1 Discovery of Sub-atomic Particles

The parts of the atom were found by passing electricity through gases. One rule runs through everything that follows: like charges repel, and opposite charges attract.

2.1.1 Discovery of Electron

The first hint came from solutions. In the 1830s Michael Faraday showed that a given quantity of charge passed through a dissolved or molten salt always deposits the same amount of substance at an electrode (you will study his laws in Class 12). Electricity, it seemed, might come in particles too.

From the 1850s Faraday and others passed electricity through sealed glass tubes with most of the gas pumped out and a metal electrode at each end. At very low pressure and high voltage a current flows, carried by something that leaves the negative electrode (the cathode) and travels towards the positive one (the anode). These streams were named cathode rays. If the anode has a hole and the far end of the tube is coated with zinc sulphide, the rays that pass through the hole make a bright spot there (Fig. 2.1).

What are these rays? Experiments with many such tubes settled it:

• They are negative particles. An electric field pulls the beam towards the positive plate, and a magnet swings it just as it would swing negative charges moving away from the cathode. The particles were named electrons.
• Every atom has them. Change the electrode metal or the gas in the tube and the rays behave the same, so electrons are part of every element's atoms.
• They fly in straight lines. Away from fields, a metal object in their path casts a sharp shadow.
• We see only their effects. The rays are invisible, but fluorescent coatings glow where they land, which is how the picture tube of an old (CRT) television worked.

2.1.2 Charge to Mass Ratio of Electron

In 1897 J. J. Thomson measured how strongly cathode rays are bent, using an electric field and a magnetic field at right angles to each other and to the beam. The deflection of a moving charged particle depends on three things: a bigger charge feels a bigger force, a lighter particle is easier to deflect, and a stronger field (a higher voltage on the plates or a larger current in the coils) pushes harder.

Each field alone moves the spot, in opposite directions. Thomson adjusted the two until the spot returned to its undeflected position, and from the field strengths needed, together with the deflection by one field alone, he found the ratio of the electron's charge to its mass. The modern value is

Since the electron is negative, its charge is written $-e$; $e$ itself is always positive.11Per kilogram, electrons carry about 1800 times more charge than hydrogen ions do: an early sign that the electron is far lighter than any atom.

2.1.3 Charge on the Electron

Robert Millikan measured the charge itself between 1909 and 1913 with his oil-drop experiment (Fig. 2.2). Tiny oil drops falling between two horizontal plates reach a steady speed that reveals their size and mass. X-rays ionise the air, and some drops pick up charge from the ions. A voltage across the plates can then slow, stop or even lift a charged drop. Measuring the field needed, drop after drop, Millikan found that every charge $q$ was a whole-number multiple of one smallest amount, $e$:

That smallest charge belongs to a single electron. Millikan's value was close to $1.6\times {10}^{-19}\mathrm{C}$; since 2019 the elementary charge has been fixed by definition at exactly $e=1.602176634\times {10}^{-19}\mathrm{C}$. Combining $e$ with Thomson's ratio gives the mass of the electron:

2.1.4 Discovery of Protons and Neutrons

Atoms are neutral, so something positive must balance the electrons. In 1886 Eugen Goldstein used a tube with holes in its cathode and saw rays streaming back through the holes, opposite to cathode rays. These canal rays behaved very differently:

• fields bend them the way positive charges bend;
• their mass and charge-to-mass ratio change with the gas in the tube: they are positive ions of that gas, formed when electrons are knocked off its atoms;
• some ions carry two or more units of charge, always a whole multiple of $e$.

The lightest positive ion comes from hydrogen. Around 1919 Rutherford showed that this particle can be knocked out of other nuclei too, and it was named the proton (प्रोटॉन). Its charge is equal and opposite to the electron's, but it is about 1836 times heavier.

The masses still did not add up: helium is about four times as heavy as hydrogen yet has only two protons. In 1932 James Chadwick bombarded beryllium with alpha particles and detected uncharged particles slightly heavier than protons: neutrons (न्यूट्रॉन). Table 2.1 compares the three particles.

2.2 Atomic Models

By the early 1900s scientists knew that atoms contain electrons and something positive. A good model of how these are arranged had to explain why atoms are stable, why elements differ in their physical and chemical behaviour, how atoms join into molecules, and why each kind of atom absorbs and emits its own particular radiation. We follow two early attempts.

2.2.1 Thomson Model of Atom

Thomson pictured the atom as a sphere about ${10}^{-10}\mathrm{m}$ in radius, filled evenly with positive charge, with electrons embedded where the arrangement is electrically most stable: like raisins in a laddoo. In English it is called the plum-pudding model. It gives a neutral atom with its mass spread evenly through the sphere, and that second feature is what the next experiment tested. (Thomson won the 1906 Nobel Prize in Physics for his work on how gases conduct electricity.)

2.2.2 Rutherford's Nuclear Model of Atom

If Thomson was right, a fast, heavy alpha particle should pass through a gold atom like a bullet through a cloud, swerving by at most a fraction of a degree. In 1909 Hans Geiger and Ernest Marsden, in Ernest Rutherford's laboratory, fired alpha particles from a radioactive source at gold foil less than a micrometre thick and counted the flashes they made on a zinc sulphide screen at different angles (Fig. 2.3). They found:

• almost all the alpha particles went straight through, as if nothing were there;
• a small fraction were turned aside, mostly through small angles;
• a very few, roughly one in many thousands, came almost straight back.

Rutherford reasoned that if most particles feel nothing, most of the atom is empty space; and that turning back a heavy, fast alpha particle needs a huge repulsion, possible only if the atom's positive charge, with nearly all its mass, is packed into a tiny region, the nucleus. Its radius is about ${10}^{-15}\mathrm{m}$, against ${10}^{-10}\mathrm{m}$ for the atom: a factor of 100 000. Shrink a nucleus to a mustard seed on the centre spot of a cricket ground, and the atom's edge would lie near the boundary rope.

Rutherford's nuclear model (1911): the positive charge and nearly all the mass are concentrated in a tiny central nucleus; electrons move round it at high speed in circular orbits, as planets circle the Sun; and electrostatic attraction holds the electrons and nucleus together.

2.2.3 Atomic Number and Mass Number

The charge of a nucleus comes from its protons. Their number is the atomic number, $Z$ (परमाणु क्रमांक): every carbon nucleus has 6, every iron nucleus 26. A neutral atom has as many electrons as protons, so

Protons and neutrons are together called nucleons, and they carry almost all the mass. Their total is the mass number, $A$ (द्रव्यमान संख्या):

2.2.4 Isobars and Isotopes

A nucleus, or its atom, is written ${\phantom{X}}_{\phantom{\mathrm{Z}}}^{\phantom{\mathrm{A}}}{\phantom{X}}_{\phantom{2}\mathrm{Z}}^{\phantom{2}\mathrm{A}}\mathrm{X}$: the element symbol with the mass number as a left superscript and the atomic number as a left subscript. Uranium-235 is ${\phantom{X}}_{\phantom{92}}^{\phantom{235}}{\phantom{X}}_{\phantom{2}92}^{\phantom{2}235}\mathrm{U}$, with 92 protons and $235-92=143$ neutrons. Since the symbol already fixes $Z$, the subscript is often dropped: ${\phantom{X}}_{\phantom{}}^{\phantom{235}}{\phantom{X}}_{\phantom{2}}^{\phantom{2}235}\mathrm{U}$ or 'U-235'.

Hydrogen shows isotopes (समस्थानिक) most clearly. About 99.985% of its atoms are protium, ${\phantom{X}}_{\phantom{1}}^{\phantom{1}}{\phantom{X}}_{\phantom{2}1}^{\phantom{2}1}\mathrm{H}$, with no neutron; about 0.015% are deuterium, ${\phantom{X}}_{\phantom{1}}^{\phantom{2}}{\phantom{X}}_{\phantom{2}1}^{\phantom{2}2}\mathrm{H}$ or D, with one; and a trace is radioactive tritium, ${\phantom{X}}_{\phantom{1}}^{\phantom{3}}{\phantom{X}}_{\phantom{2}1}^{\phantom{2}3}\mathrm{H}$ or T, with two. Natural chlorine is roughly three parts ${\phantom{X}}_{\phantom{}}^{\phantom{35}}{\phantom{X}}_{\phantom{2}}^{\phantom{2}35}\mathrm{C}\mathrm{l}$ to one part ${\phantom{X}}_{\phantom{}}^{\phantom{37}}{\phantom{X}}_{\phantom{2}}^{\phantom{2}37}\mathrm{C}\mathrm{l}$, and carbon includes ${\phantom{X}}_{\phantom{}}^{\phantom{12}}{\phantom{X}}_{\phantom{2}}^{\phantom{2}12}\mathrm{C}$, ${\phantom{X}}_{\phantom{}}^{\phantom{13}}{\phantom{X}}_{\phantom{2}}^{\phantom{2}13}\mathrm{C}$ and the radioactive ${\phantom{X}}_{\phantom{}}^{\phantom{14}}{\phantom{X}}_{\phantom{2}}^{\phantom{2}14}\mathrm{C}$ used in dating. Isobars (समभारिक) belong to different elements, so they behave quite differently.

Why do isotopes react alike? Chemistry is about electrons, and their number is fixed by the number of protons. Neutrons add mass but leave the electron count unchanged, so isotopes have practically identical chemical properties. Small differences show up in rates and physical properties, most of all for hydrogen, since D is twice as heavy as H: heavy water, $\mathrm{D}{\phantom{X}}_2\mathrm{O}$, freezes at 3.8 °C.

2.2.5 Drawbacks of Rutherford Model

Rutherford's picture borrows the solar system. A planet held by gravity, $F=G{m}_1{m}_2\mathrm{/}{r}^2$, follows a steady orbit that Newton's mechanics predicts precisely, and the electrical attraction between electron and nucleus, $F=k{q}_1{q}_2\mathrm{/}{r}^2$, has the same form. So electrons ought to orbit just as smoothly.

The catch: anything moving in a circle is accelerating, because its direction keeps changing. Maxwell's theory says an accelerating charge radiates electromagnetic waves (planets have no net charge, so they escape this). An orbiting electron should lose energy, spiral inwards and fall into the nucleus in well under a microsecond (Fig. 2.5); the usual estimate is about ${10}^{-8}\mathrm{s}$. Real atoms last indefinitely. Nor can electrons stand still, since the nucleus would then pull them straight in, collapsing the atom into a tiny Thomson-like one.

The model also says nothing about how the electrons are arranged or what energies they have, which is exactly what chemistry needs.

2.3 Developments Leading to the Bohr's Model of Atom

In 1913 Niels Bohr rescued Rutherford's atom by combining two lines of evidence: electromagnetic radiation behaves both as a wave and as a stream of particles, and atoms emit and absorb light only at sharply defined wavelengths. We take them in turn.

2.3.1 Wave Nature of Electromagnetic Radiation

Newton thought light was a stream of tiny particles (corpuscles), but experiments on interference in the early 1800s convinced most physicists that it is a wave. In the 1860s and 1870s James Clerk Maxwell showed what kind: an accelerating charge creates changing electric and magnetic fields, each regenerating the other, so the disturbance travels outwards as an electromagnetic wave. Heinrich Hertz made and detected such waves in 1887–88, and their speed matched that of light. The thermal radiation given out by hot objects turned out to be electromagnetic waves too.

Three properties matter here (Fig. 2.6):

• the electric and magnetic fields oscillate at right angles to each other and to the direction of travel;
• no medium is needed: sound needs air, but sunlight crosses empty space;
• wavelengths span an enormous range, the electromagnetic spectrum (Fig. 2.7), and our eyes respond only to a narrow band from about 400 nm (violet) to 750 nm (red).

A wave has a wavelength $\lambda$, the distance from one crest to the next (in m, nm, pm or the older ångström, 1 Å = ${10}^{-10}$ m), and a frequency $\nu$, the number of crests passing a point each second (in hertz, 1 Hz = 1 s⁻¹). In a vacuum every electromagnetic wave travels at $c=2.998\times {10}^8\mathrm{m}{\mathrm{s}}^{-1}$, usually rounded to $3.0\times {10}^8\mathrm{m}{\mathrm{s}}^{-1}$. Each second $\nu$ crests pass, each $\lambda$ long, so

Spectroscopists also use the wavenumber $\bar{\nu }$: how many wavelengths fit into one metre (SI unit m⁻¹) or, more often in practice, into one centimetre (cm⁻¹).

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

The wave picture explains interference and diffraction (the bending of waves round obstacles). Yet by 1900 several observations refused to fit it: the light given out by hot objects (black-body radiation), the release of electrons from metals by light (the photoelectric effect), the fall in the heat capacity of solids at low temperature, and the line spectra of atoms. All pointed to one strange conclusion: energy changes hands only in fixed amounts.

An electric heater's coil glows dull red as it warms, then orange, then yellow-white, and stars hotter than the Sun look blue-white: a hot body's light shifts to shorter wavelengths as its temperature rises. To study this cleanly, physicists imagined a black body, an ideal object that absorbs every wavelength and reflects none; in equilibrium it emits as much as it absorbs, and its radiation depends only on its temperature. Soot comes close, and a hollow box with a tiny hole is almost perfect, because light entering the hole is absorbed before it can escape. At a fixed temperature the intensity rises with wavelength to a peak and then falls; a hotter body emits more at every wavelength and peaks at a shorter one (Fig. 2.8).

Wave theory could not reproduce these curves. In 1900 Max Planck found a formula that fitted them perfectly by assuming that the vibrating atoms in the walls can absorb or emit energy only in whole packets, which he called quanta (singular quantum). The energy of one quantum is proportional to the frequency:

An oscillator of frequency $\nu$ can hold energy $0,h\nu ,2h\nu ,\dots$ but nothing in between, rather like paying only with ₹1 coins: ₹7 or ₹8, never ₹7.50. Because $h$ is so tiny, the steps go unnoticed in daily life; for atoms they decide everything.

Photoelectric effect

In 1887 Heinrich Hertz noticed that ultraviolet light helped sparks jump between electrodes. The reason, found later, is that light falling on a clean metal can knock electrons out of it: the photoelectric effect. Caesium and potassium respond even to visible light; zinc and copper need ultraviolet. Experiments in evacuated tubes (Fig. 2.9) showed four things:

• No delay. Electrons leave the moment the light arrives, however dim it is.
• A threshold. Each metal has a minimum frequency ${\nu }_0$, its threshold frequency (देहली आवृत्ति); below it no electrons escape, however bright or long the light.
• Brightness sets the number. Above ${\nu }_0$, brighter light ejects more electrons per second.
• Frequency sets the energy. The electrons' maximum kinetic energy rises with frequency and does not depend on brightness.

Wave theory predicts the opposite at almost every point: bright red light should eventually free electrons, dim light should need time, and brighter light should give faster electrons. Instead, potassium gives off no electrons in red light of any brightness, while even faint violet light ejects them at once.

In 1905 Albert Einstein took Planck's idea literally: light travels as packets of energy $h\nu$, now called photons (फोटॉन). One photon gives all its energy to one electron at once. At least $h{\nu }_0$ is needed to pull the electron out; this minimum is the metal's work function, $W_0$ (कार्यफलन). The rest becomes kinetic energy:

Every observation follows. Below threshold no single photon can free an electron, and an electron cannot pool energy from several photons. Above it, the surplus $h(\nu -{\nu }_0)$ becomes kinetic energy, which therefore rises with frequency. Brighter light means more photons, hence more electrons, each with the same maximum energy. One photon acts at once, so there is no delay.22Electrons from deeper inside the metal lose some energy on the way out, so Eq. (2.7) gives the maximum kinetic energy.

Work functions are usually given in electron volts: 1 eV, the energy an electron gains crossing 1 V, is $1.602\times {10}^{-19}\mathrm{J}$. A handy shortcut: photon energy in eV ≈ 1240 ÷ wavelength in nm (Table 2.2).

So is light a wave or a stream of particles? It shows dual behaviour: it interferes and diffracts like a wave as it travels, but is absorbed or emitted in whole photons, like particles. Which face we see depends on the experiment, and in Section 2.5.1 you will see that electrons, too, behave like waves.

2.3.3 Evidence for the Quantized Electronic Energy Levels: Atomic Spectra

A glass prism spreads white light into a band of colours. Light slows down in glass, shorter wavelengths more, so violet bends most and red least. Every colour from red to violet is present, merging into the next: a continuous spectrum, like a rainbow.

Atoms can also emit light. Heat them in a flame or pass a discharge through a gas and they are excited to higher-energy states; dropping back, they give out the energy as radiation, forming an emission spectrum. Shine continuous light through a cool sample instead, and the atoms absorb certain wavelengths, leaving dark gaps: an absorption spectrum, like a photographic negative of the emission spectrum. The study of spectra is spectroscopy (Fig. 2.11).

The crucial clue: free atoms emit only certain sharp wavelengths, seen as bright lines with darkness between, a line spectrum or atomic spectrum (रेखा स्पेक्ट्रम). An element's absorption lines fall exactly where its emission lines are. Each element's pattern is as personal as a fingerprint: the yellow of sodium street lamps and the red of neon signs are two familiar examples. Around 1860 Robert Bunsen and Gustav Kirchhoff discovered caesium and rubidium from new lines in spectra, and thallium, indium, gallium and scandium were also first noticed this way.

Line spectrum of hydrogen

Hydrogen, with one electron, has the simplest spectrum. A discharge splits $\mathrm{H}{\phantom{X}}_2$ into excited atoms, which emit light at a set of separate frequencies. In 1885 Johann Balmer, a Swiss schoolteacher, found that hydrogen's visible lines, written as wavenumbers, fit

These form the Balmer series. Johannes Rydberg then showed that every series of hydrogen lines fits one expression:

where $n_1=1,2,3,\dots$ and $n_2=n_1+1,n_1+2,\dots$; $109677\mathrm{c}{\mathrm{m}}^{-1}$ is the Rydberg constant for hydrogen. Each $n_1$ gives one series (Table 2.3). Every element's line spectrum is unique and regular, but why should whole numbers appear at all? Bohr gave the answer.

2.4 Bohr's Model for Hydrogen Atom

In 1913 Niels Bohr accepted that classical physics fails inside atoms and laid down new rules, chosen to fit hydrogen's spectrum while keeping Rutherford's nucleus. It is not modern quantum mechanics, but its numbers for hydrogen are still right. His postulates:

1. The electron moves only in certain circular orbits of fixed radius and energy, the stationary states or allowed energy levels (स्थिर अवस्था), arranged concentrically round the nucleus.
2. In a stationary state the electron neither gains nor loses energy, so the atom does not radiate or collapse.
3. The electron can jump between states, absorbing exactly the energy difference $\mathrm{\Delta }E$ to move up and emitting it as one photon on dropping down, with frequency given by Bohr's frequency rule, Eq. (2.10).
4. Only orbits in which the angular momentum is a whole-number multiple of $h\mathrm{/}2\pi$ are allowed, Eq. (2.11).

The fourth postulate is the new physics: orbits in between are forbidden, and Maxwell's rule that orbiting charges radiate is set aside. Its consequences (derived below) are three. The orbits are numbered by the principal quantum number $n=1,2,3,\dots$ (Section 2.6.1). The radii grow as $n^2$:

so the electron normally sits $52.9\mathrm{p}\mathrm{m}$ from the nucleus, and the second and third orbits are 4 and 9 times as far out. The energies are negative and crowd together as $n$ grows:

The ground state has $E_1=-2.18\times {10}^{-18}\mathrm{J}$, and $E_2=-5.45\times {10}^{-19}\mathrm{J}$. Drawn as lines, these make an energy-level diagram (Fig. 2.12). As $n\to \mathrm{\infty }$ the energy rises to zero: the electron is free and the atom ionised.

The theory works for any hydrogen-like species, an ion with one electron such as $\mathrm{H}\mathrm{e}{\phantom{X}}^{+}$, $\mathrm{L}\mathrm{i}{\phantom{X}}^{2+}$ or $\mathrm{B}\mathrm{e}{\phantom{X}}^{3+}$. For nuclear charge $Ze$:

A larger $Z$ binds the electron more tightly and closer in. The electron's speed rises with $Z$ and falls with $n$; in hydrogen's first orbit it is about $2.2\times {10}^6\mathrm{m}{\mathrm{s}}^{-1}$.

2.4.1 Explanation of Line Spectrum of Hydrogen

When the electron jumps from level $n_{\mathrm{i}}$ to level $n_{\mathrm{f}}$, the atom's energy changes by

Moving up ($n_{\mathrm{f}}>n_{\mathrm{i}}$), $\mathrm{\Delta }E$ is positive: energy is absorbed (an absorption line). Falling ($n_{\mathrm{i}}>n_{\mathrm{f}}$), $\mathrm{\Delta }E$ is negative: a photon is emitted (an emission line). The photon's frequency is set by the gap; writing $n_1$ for the lower level and $n_2$ for the upper:

Equation (2.21) is Rydberg's formula, since $109677\mathrm{c}{\mathrm{m}}^{-1}=1.097\times {10}^7{\mathrm{m}}^{-1}$, now derived rather than fitted: Bohr's triumph. Each line is one jump: jumps down to $n=1$ give the Lyman series, down to $n=2$ the Balmer series, and so on (Fig. 2.12). One atom makes one jump at a time, but a tube holds countless atoms making every possible jump, so all lines appear together; a line is bright when many atoms make that jump.

2.4.2 Limitations of Bohr's Model

Bohr's model explains hydrogen's stability and predicts the spectra of hydrogen and one-electron ions such as $\mathrm{H}\mathrm{e}{\phantom{X}}^{+}$ and $\mathrm{L}\mathrm{i}{\phantom{X}}^{2+}$ remarkably well. Beyond that it fails:

• it cannot predict the spectrum of any atom with two or more electrons, not even helium;
• seen at high resolution, many hydrogen lines are close pairs (doublets), a fine structure the model misses;
• it cannot account for the Zeeman and Stark effects, in which lines split when the atom sits in a magnetic or an electric field;
• it says nothing about how atoms bond into molecules.

2.5 Towards Quantum Mechanical Model of the Atom

Two discoveries of the 1920s showed why Bohr's model had to fail, and pointed to its replacement. Matter, like light, has a dual nature; and there is a basic limit to how precisely we can know both where a particle is and how it is moving.

2.5.1 Dual Behaviour of Matter

In 1924 Louis de Broglie turned the photon idea round: if light waves can act like particles with momentum, perhaps particles such as electrons can act like waves. A photon's momentum is $p=h\mathrm{/}\lambda$; de Broglie proposed the same link for any particle of mass $m$ and speed $v$:

In 1927 Clinton Davisson and Lester Germer in the USA, and George Paget Thomson in Scotland, found that electron beams are diffracted by crystals just as X-rays are. (G. P. Thomson was J. J. Thomson's son: the father showed the electron is a particle, the son that it is also a wave.) The electron microscope uses this wave behaviour; electron wavelengths are far shorter than those of light, so it reveals detail thousands of times finer, down to single atoms.

Every moving object has a de Broglie wavelength, but for everyday objects it is absurdly small: a cricket ball's is about ${10}^{-34}$ m (Example 2.12), far too small to detect. Only for very light particles such as electrons is it comparable to the size of atoms.

It also explains Bohr's condition. A wave running round an orbit survives only if it joins up with itself, so a whole number of wavelengths must fit the circumference, $2\pi r=n\lambda$ (Fig. 2.14). With $\lambda =h\mathrm{/}{m}_{\mathrm{e}}v$ this gives $m_{\mathrm{e}}vr=nh\mathrm{/}2\pi$, exactly Eq. (2.11).