# Structure of the Atom

> Cathode rays, Thomson's charge-to-mass ratio, Millikan's oil drops, Rutherford's gold foil and Chadwick's neutron.

From HSC Physics on WhizzNotes, free study notes for NSW students: https://whizznotes.com/physics/structure-of-the-atom/. Updated 2 November 2026.
Year 11 and Year 12 boxes go deeper than the Year 10 text around them.

### Story time: The cannonball and the tissue paper
In 1909, two of Ernest Rutherford's students, Hans Geiger and Ernest Marsden, fired tiny alpha particles at a sheet of gold foil thinner than a hair. Almost all of them went straight through, as expected.

But about one in eight thousand bounced back towards the source. Rutherford later said it was "quite the most incredible event" of his life, as if a cannonball fired at tissue paper had bounced straight back at you.

The only way to explain it was that nearly all of an atom's mass is packed into a tiny, dense, positive centre: the **nucleus**. Atoms, it turned out, are mostly empty space.

**In short:** An atom has a tiny, dense, positive nucleus with electrons around it, and is mostly empty space. Thomson found the electron, Millikan measured its charge, Rutherford's gold foil experiment found the nucleus, and Chadwick found the neutron.

## Cathode rays

In the late 1800s, scientists sealed metal plates (electrodes) in glass tubes, pumped out most of the air, and connected a high voltage. A glow appeared, streaming from the negative electrode (the **cathode**). These were called **cathode rays**.

| Observation | What it showed |
|---|---|
| A metal object in the path casts a sharp shadow | Cathode rays travel in **straight lines** |
| They turn a small paddle wheel | They carry **momentum**, so they are particles with mass |
| They bend towards a positive plate | They are **negatively charged** |
| They bend in a magnetic field | They are moving charges |
| They are the same whatever the cathode metal | They are part of **every** atom |

## Thomson measures the charge-to-mass ratio

In 1897, J.J. Thomson used crossed electric and magnetic fields on cathode rays.

1. **Velocity:** He adjusted the fields until the beam went straight through. Then the electric and magnetic forces balanced: $qE = qvB$, so $v = \dfrac{E}{B}$.
2. **Charge-to-mass ratio:** He switched the electric field off. The magnetic field alone bent the beam into a circle: $qvB = \dfrac{mv^2}{r}$, so

$$\frac{q}{m} = \frac{v}{Br}$$

His value, about $1.76 \times 10^{11}$ C/kg, was about **1800 times bigger** than for a hydrogen ion. Either the particles had a huge charge or a tiny mass. They were the first subatomic particles found: **electrons**.

Thomson's **plum pudding model**: the atom is a ball of positive charge with electrons scattered through it, like plums in a pudding.

### Worked example: Thomson's method
Fields of $E = 2.0 \times 10^4$ V/m and $B = 1.0 \times 10^{-3}$ T let a beam pass straight through. With E off, the beam curves with radius 0.11 m.

- $v = \dfrac{2.0 \times 10^4}{1.0 \times 10^{-3}} = 2.0 \times 10^7$ m/s
- $\dfrac{q}{m} = \dfrac{2.0 \times 10^7}{1.0 \times 10^{-3} \times 0.11} = 1.8 \times 10^{11}$ C/kg

## Millikan measures the charge

In 1909, Robert Millikan sprayed tiny oil drops between two horizontal charged plates. Some drops picked up extra electrons. He adjusted the voltage until a drop **hung still**, with the electric force up balancing its weight down:

$$qE = mg \quad\Rightarrow\quad q = \frac{mgd}{V}$$

He found that every drop's charge was a **whole number multiple** of $1.6 \times 10^{-19}$ C. Charge comes in packets: it is **quantised**. The smallest packet is the charge of one electron, $e$.

Combining Millikan's $e$ with Thomson's $\dfrac{q}{m}$ gave the electron's mass: $9.1 \times 10^{-31}$ kg.

## Rutherford's nuclear model

Geiger and Marsden fired **alpha particles** (positive, fairly heavy) at thin gold foil.

| Observation | Conclusion |
|---|---|
| Most went straight through | The atom is **mostly empty space** |
| A few were deflected by large angles | There is a concentrated **positive** charge |
| About 1 in 8000 bounced back | The positive charge and almost all the mass are in a **tiny nucleus** |

**Rutherford's model**: a tiny, dense, positive **nucleus** with electrons orbiting far away around it. The nucleus is about 100 000 times smaller than the atom.

## Chadwick finds the neutron

The nucleus had more mass than its protons could account for. In 1932, James Chadwick studied a strange radiation that came from beryllium when it was hit by alpha particles.

- It was **not deflected** by electric or magnetic fields, so it had **no charge**.
- It knocked **protons** out of paraffin wax at high speed. Gamma rays could not do that, but a neutral particle with about the **same mass as a proton** could, just like one snooker ball hitting another.

Chadwick had found the **neutron**. Using conservation of momentum and energy in these collisions, he worked out its mass.

**Mind map**

```text
Structure of the Atom
  Cathode rays
    Straight lines
    Negative charge
    Have momentum
  Thomson
    v = E / B
    q/m = v / Br
    Electron found
    Plum pudding model
  Millikan
    Oil drop balanced
    q = mgd / V
    Charge is quantised
  Rutherford
    Gold foil
    Mostly empty space
    Tiny positive nucleus
  Chadwick
    Neutral radiation
    Knocked out protons
    Neutron found
```

### Year 11: Building on what you know
In Year 11 you learned that atoms contain protons, neutrons and electrons. This chapter shows **how** we found out. Each discovery used physics already understood at the time: Thomson used forces on charges in fields (see Charged Particles in Electric and Magnetic Fields), Millikan balanced forces, and Chadwick used conservation of momentum.

### Year 12: Limits of the models
**Plum pudding:** could not explain the large-angle scattering of alpha particles. A spread-out positive charge would only nudge them slightly.

**Rutherford's model** had two big problems:

1. An orbiting electron is accelerating. Maxwell's theory says accelerating charges give off EM radiation, so the electron should lose energy and spiral into the nucleus in a tiny fraction of a second. Atoms would not be stable.
2. It could not explain why atoms give off light only at certain wavelengths (line spectra).

Bohr's model fixed both (see The Quantum Atom).

**Millikan's reasoning, tested:** if drops had charges of $3.2 \times 10^{-19}$, $4.8 \times 10^{-19}$ and $8.0 \times 10^{-19}$ C, the largest value that divides all of them a whole number of times is $1.6 \times 10^{-19}$ C (2, 3 and 5 times).

**How many electrons?** Find the drop's charge from $q = \dfrac{mgd}{V}$, then divide by $e$. A drop of mass $3.0 \times 10^{-15}$ kg held by 460 V across 5.0 mm has $q = 3.2 \times 10^{-19}$ C, which is 2 extra electrons. The same reasoning works for models: if boxes of coins differ by 6, 9, 15 and 3 g, the largest mass that divides them all is 3 g, the mass of one coin.

**Combining measurements.** When two measured values are divided, their percentage uncertainties add. Getting $m = \dfrac{e}{e/m}$ from an $e$ that is 6% high and an $\dfrac{e}{m}$ that is 3% low gives a mass about 9% too high.

**Fields from plates.** $E = \dfrac{V}{d}$: 150 V across 2.5 cm gives 6000 V/m. A beam crossing plates of length $L$ at speed $v$ spends $t = \frac{L}{v}$ between them and leaves with sideways speed $v_y = \dfrac{qE}{m}t$.

**Scattering counts.** The number of alpha particles scattered falls very steeply with angle, because only those passing very close to the tiny nucleus are turned through large angles. A few still bounce back near 180°, from near head-on approaches.

**Chadwick's collisions.** In a head-on elastic collision, a particle of mass $m$ gives a stationary target of mass $M$ a speed of $\dfrac{2m}{m + M}u$. A neutron (about a proton's mass) can give a proton almost all its speed, but gives a nitrogen nucleus ($M = 14m$) only $\frac{2}{15}$ of it. Comparing the two let Chadwick work out the neutron's mass.

**Why a vacuum?** Cathode rays (electrons) would collide with air molecules, scattering and slowing them, so the beam would not travel in clean straight lines or bend in a measurable way.

## Quick summary

- Cathode rays are streams of negative particles with mass: electrons.
- Thomson used balanced fields ($v = E/B$) and a magnetic field alone ($q/m = v/Br$) to find the electron's charge-to-mass ratio.
- Millikan's oil drops showed charge is quantised, in multiples of $1.6 \times 10^{-19}$ C.
- Rutherford's gold foil experiment showed atoms are mostly empty space with a tiny, dense, positive nucleus.
- Chadwick discovered the neutral neutron, with about the same mass as a proton.

## Quiz

Try these questions from the chapter quiz.

1. Cathode rays bend towards a positive plate. This shows they are:
   - A. Uncharged
   - B. Negatively charged
   - C. Positively charged
   - D. Waves
   - Answer: B. Negatively charged. Opposite charges attract, so the rays are negative.

2. A small paddle wheel in a cathode ray tube turns when the rays hit it. This shows cathode rays:
   - A. Are light
   - B. Carry momentum, so they have mass
   - C. Are positive
   - D. Travel in curves
   - Answer: B. Carry momentum, so they have mass. Only something with mass and momentum can push the wheel round.

3. Thomson's experiment discovered the:
   - A. Electron
   - B. Proton
   - C. Neutron
   - D. Nucleus
   - Answer: A. Electron. His charge-to-mass ratio showed cathode rays were tiny particles: electrons.

The whole chapter quiz is on the page, for signed-in students: https://whizznotes.com/physics/structure-of-the-atom/#quiz