Chapter 12 · Introduction

Chapter 12 — Atoms

Almost all of an atom's mass sits in a nucleus a hundred-thousandth of its size, and its electrons may only have certain energies. Both facts were read from experiments — a beam of alpha particles bouncing off gold foil, and the sharp coloured lines in the light of glowing hydrogen.

Switch on a sodium street lamp and it glows a deep yellow; a neon sign glows orange-red; a tube of hydrogen in a school laboratory glows a soft pink. Pass each light through a prism and you do not get a rainbow. You get a handful of sharp, bright lines of colour on a dark background — and every element has its own pattern, as personal as a fingerprint. Astronomers use these fingerprints to find out what distant stars are made of; helium was discovered in the spectrum of the Sun in 1868, decades before anyone found it on Earth. Forensic laboratories, steel plants and pollution monitors identify metals in the same way. But why should an atom emit only certain colours?

To answer that question we first need to know what an atom looks like inside. In this chapter you follow the experiments that settled it. In 1909 Hans Geiger and Ernest Marsden fired alpha particles at a thin gold foil and found that a few of them bounced almost straight back — impossible if the atom's positive charge were spread out thinly, as J. J. Thomson had proposed. Ernest Rutherford concluded that the positive charge and nearly all the mass are packed into a tiny central nucleus, with electrons far outside. That nuclear atom, however, should collapse in a fraction of a microsecond according to classical physics. In 1913 Niels Bohr rescued it with three bold postulates: electrons move only in certain stationary orbits, with fixed energies, and light is emitted only when an electron jumps from one orbit to another. His model predicts the wavelengths of the hydrogen lines to a fraction of a percent, and ten years later Louis de Broglie's matter waves explained why only those orbits are allowed.

Thomson's atom→Alpha scattering→Nuclear atom→Line spectra→Bohr's postulates→$E_n=-13.6/n^2$ eV→de Broglie waves

🎯 By the end of this chapter you can…

describe the Geiger–Marsden alpha-particle scattering experiment, its observations, and why they rule out Thomson's model in favour of a nuclear atom;
explain the role of the impact parameter and calculate the distance of closest approach, and use it to put an upper limit on the size of a nucleus;
describe emission and absorption line spectra and use the Rydberg formula for the Lyman, Balmer and Paschen series of hydrogen;
state Bohr's postulates and derive the radius, speed and energy of the electron in the $n$th orbit of hydrogen;
draw and use the energy-level diagram of hydrogen to find photon wavelengths, ionisation and excitation energies, and the number of spectral lines;
explain Bohr's quantisation of angular momentum with de Broglie's standing waves, and state the limits of the model;
solve board, JEE Main, JEE Advanced and NEET problems on all of the above.

Light from the chosen source passes through a slit and a prism, which spreads it out by wavelength onto the strip below (visible range, $380$–$700$ nm). Each dot is a little packet of light travelling to its place on the strip, and the strip brightens as they arrive. A hot filament gives a continuous band; glowing hydrogen gives only a few sharp lines; white light that has passed through a hot hydrogen atmosphere loses exactly those colours. The hydrogen wavelengths are computed from the formula you will meet in Section 12.2, $\tfrac1\lambda=R\left(\tfrac14-\tfrac1{n^2}\right)$. Click the strip to read a wavelength.

Source:

spectrum type—

lines in view—

clicked wavelength—

Sections in this chapter

12.1

Alpha-Particle Scattering and Rutherford's Nuclear Model

Thomson's model, the Geiger–Marsden experiment, the impact parameter, the distance of closest approach and electron orbits in the nuclear atom.

$d_0=\dfrac{1}{4\pi\varepsilon_0}\dfrac{2Ze^2}{K}$

Open section →12.2

Atomic Spectra and Bohr's Model of the Hydrogen Atom

Emission and absorption line spectra, the spectral series of hydrogen, Bohr's postulates and the radius, speed and energy of each orbit.

$r_n=0.53\,n^2$ Å, $\ E_n=-\dfrac{13.6}{n^2}$ eV

Open section →12.3

The Line Spectra of Hydrogen and de Broglie's Explanation

Energy-level diagrams, emission and absorption of photons, ionisation and excitation, the Rydberg constant from theory, and standing electron waves.

$h\nu=E_i-E_f$, $\ 2\pi r_n=n\lambda$

Open section →

✅ Before you start

You need Coulomb's law and the constant $k=\dfrac{1}{4\pi\varepsilon_0}$ (Section 1.1), electrostatic potential energy, the electron volt and the energy method for the distance of closest approach (Section 2.1 and Section 2.2), and the electromagnetic spectrum (Section 8.2). From Chapter 11 — Dual Nature of Radiation and Matter you need the photon energy $E=h\nu=\dfrac{hc}{\lambda}$ (with $hc=1240$ eV nm) and the de Broglie wavelength $\lambda=\dfrac hp$. From Class 11 Physics you need uniform circular motion and centripetal force, angular momentum $L=mvr$, and conservation of energy and momentum (Class 11 Physics, Chapters 4–6). No calculus is needed in this chapter.

← 11.3 The Wave Nature of Matter 12.1 Alpha-Particle Scattering and Rutherford's Nuclear Model →