E.1 Structure of the atom

UNIT SYLLABUS

SL/HL 6 hours SL + 3 hours HL

Three experiments built the modern atom. Geiger and Marsden fired alpha particles at gold foil and watched a few bounce back — Rutherford's conclusion: nearly all the mass and all positive charge sit in a tiny nucleus. Atomic spectra showed that each element emits and absorbs only specific wavelengths — evidence that electron energies are quantised into discrete levels, with photons of energy $E = hf$ carrying the differences. At HL, Bohr's model makes hydrogen quantitative ($E_n = -13.6/n^2$ eV, from quantised angular momentum), and high-energy scattering probes where Rutherford's picture bends: the nucleus has a measurable radius growing as $A^{1/3}$.

Guiding Questions

? What experimental evidence supports our current model of the atom?
? How do atomic spectra reveal the quantisation of energy in atoms?

Hydrogen energy levels in the Bohr model: transitions down to n = 2 emit the visible Balmer series; the photon energy equals the gap between levels.

✓ What the IB expects you to master

Describe the Geiger–Marsden–Rutherford experiment and how its results imply a small, dense, positive nucleus.
Use nuclear notation $^A_Z X$ with nucleon number $A$ , proton number $Z$ .
Explain emission and absorption spectra as evidence for discrete atomic energy levels.
Relate photon energy to transitions: $E = hf = \frac{hc}{\lambda}$ , and identify elements from their spectra.
HL: use the nuclear radius relation $R = R_0A^{1/3}$ and deduce the near-constant density of nuclear matter.
HL: explain deviations from Rutherford scattering at high energy, and use the distance of closest approach.
HL: apply the Bohr model for hydrogen: $E_n = -\frac{13.6}{n^2}\ \text{eV}$ , from quantised angular momentum $mvr = \frac{nh}{2\pi}$ .

1 Key Formulas

Photon energy

E = hf = \frac{hc}{\lambda}

Hydrogen energy levels (HL)

E_{n} = -\frac{13.6}{n^{2}}\ \text{eV}

Quantised angular momentum (HL)

mvr = \frac{nh}{2\pi}

Nuclear radius (HL)

R = R_{0}A^{\frac{1}{3}}

2 Exam Preparation & Topic Explanations

Spectra questions decoded

Energy-level diagrams are read with one rule: photon energy = level gap. Downward arrows emit, upward arrows absorb; the biggest gap gives the shortest wavelength. Convert eV to joules ( $\times 1.6\times10^{-19}$ ) before using $E = hc/\lambda$ .

Negative level energies mean bound electrons — zero is the ionisation threshold, and $-13.6$ eV is hydrogen's ionisation energy from the ground state.

Pro Exam Strategy

More lines exist than levels: $n$ levels give $n(n-1)/2$ possible transitions.
The Geiger–Marsden results and conclusions must be paired precisely: most pass straight (empty space), few bounce back (tiny massive positive nucleus).
Closest-approach = energy conservation between kinetic and electric potential energy.
HL: deviations from Rutherford scattering at high energy reveal the strong force taking over — the alpha "touches" the nucleus.

3 MCQ Practice

Q1. In the Geiger–Marsden experiment, the observation that a small fraction of alpha particles deflected through more than 90° implies that:

Atoms are mostly empty space
Electrons orbit the nucleus
The positive charge is concentrated in a tiny, massive nucleus
Alpha particles are positively charged

Q2. An electron in hydrogen falls from $n = 3$ ( $-1.51$ eV) to $n = 2$ ( $-3.40$ eV). The emitted photon has energy:

1.89 eV
4.91 eV
3.40 eV
1.51 eV

Q3. Nucleus A has 8 times as many nucleons as nucleus B. The ratio of their radii $R_A/R_B$ is:

8
4
2
$\sqrt{8}$

4 Short Answer Questions

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