Revise Structure of the atom for IB Physics (E.1)

Before 1911 the accepted 'plum pudding' model imagined the atom as a diffuse cloud of positive charge with electrons dotted through it. Under Ernest Rutherford's direction, Hans Geiger and Ernest Marsden fired a beam of alpha particles (helium nuclei, $^{4}_{2}He^{2+}$) at a very thin gold foil, surrounded by a zinc-sulphide screen that flashed wherever a particle struck. If the plum-pudding picture were right, the fast, massive alpha particles should have sailed through with only tiny deflections.

Most did pass almost straight through — but a small fraction were deflected through large angles, and about 1 in 8000 bounced almost straight back towards the source. A diffuse charge could never turn a fast alpha particle around; only a concentrated charge could. Rutherford's own words capture the shock: it was 'almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you.'

The nucleus is built from nucleons — protons and neutrons — and is surrounded by electrons. The proton number $Z$ fixes which element you have; the number of neutrons can vary. Any specific nucleus (a nuclide) is written in standard notation.

$^{A}_{Z}X$

$X$ is the chemical symbol, $Z$ is the proton number (number of protons), and $A$ is the nucleon number (total protons + neutrons). The number of neutrons follows from $N = A - Z$. A neutral atom has as many electrons as protons, so it also has $Z$ electrons. Isotopes are nuclides of the same element — the same $Z$ — but with different $A$, and therefore a different number of neutrons; because they share the same electron count they are chemically identical but differ in mass and nuclear stability.

The electrons around the nucleus cannot take any energy they please. Each is restricted to a set of allowed energy levels, like rungs on a ladder with nothing permitted in between. The levels are labelled with negative energies because a bound electron has less energy than a free one (the free state at rest is the $0$ eV reference); the ground state is the most negative, and higher levels lie closer to $0$ eV. The strongest evidence for these discrete rungs comes from the light atoms give out.

Heat a low-density gas until it glows and split its light with a prism or diffraction grating, and you do not get a smooth rainbow. You get a few sharp bright lines at particular wavelengths — an emission line spectrum — with darkness in between. Each line is produced when an electron falls from a higher level to a lower one and the atom releases a single photon carrying exactly the energy gap. Pass white light through the same gas when it is cool and you see the reverse: a continuous spectrum crossed by dark absorption lines at exactly the same wavelengths, where electrons have absorbed photons to jump up. The pattern of lines is unique to each element — a light 'barcode' — and the very existence of sharp lines is only possible if the energy gaps, and hence the levels, are fixed and discrete.

Light is emitted and absorbed in discrete packets called photons. The energy of one photon depends only on its frequency, through Planck's relation.

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

Here $h = 6.63 \times 10^{-34}$ J s is the Planck constant, $f$ is the frequency, and the second form uses $c = f\lambda$ with $c = 3.0 \times 10^{8}$ m s⁻¹ to bring in the wavelength $\lambda$. A higher frequency (shorter wavelength) always means a more energetic photon: blue-light photons carry more energy than red-light ones. Because atomic energies in joules are awkwardly small, physicists use the electronvolt (eV) — the energy an electron gains crossing a potential difference of one volt: $1\ \text{eV} = 1.60 \times 10^{-19}$ J. Energy levels are usually quoted in eV, but $E = hf$ needs SI units, so you must convert any eV value to joules before substituting.

When an electron drops from a higher level $E_{\text{high}}$ to a lower level $E_{\text{low}}$, the photon released carries an energy equal to the difference between the levels — never the value of a single level. This is the single most common conceptual error in the topic.

$\Delta E = E_{\text{high}} - E_{\text{low}} = hf = \frac{hc}{\lambda} \quad\Rightarrow\quad \lambda = \frac{hc}{\Delta E}$

In Paper 2 the marks are analytic: each is tied to a specific line of working — a method mark (M) or an answer mark (A) — and error-carried-forward (ECF) means one wrong number early on does not have to cost you the marks that follow. But that protection only exists if the method is written down. Study how each mark below is earned by a specific line.

The discrete-level, photon picture built here underpins the rest of the unit. The same $E = hf$ governs the photoelectric effect, where photons eject electrons from a metal, and the same idea of quantised energy carries into the nucleus, where discrete nuclear energy states explain gamma emission. The eV, introduced here as a convenience, becomes the natural energy unit for nuclear reactions and mass–energy calculations. Master the habit — photon energy is the gap between levels, convert to joules, then use $E = hf = hc/\lambda$ — and the quantum physics that follows becomes variations on a method you already own.