A small paddle wheel in a cathode ray tube turns when the rays hit it. This shows cathode rays:

Carry momentum, so they have mass

Structure of the Atom | HSC Physics Module 8

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.

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

$\frac{q}{m} = \frac{v}{B r}$

His value, about $1.76 \times 1 0^{11}$ 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.

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:

$q E = m g \Rightarrow q = \frac{m g d}{V}$

He found that every drop's charge was a whole number multiple of $1.6 \times 1 0^{- 19}$ 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 $\frac{q}{m}$ gave the electron's mass: $9.1 \times 1 0^{- 31}$ 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.

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 12Limits 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:

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.
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 $3.2 \times 1 0^{- 19}$ , $4.8 \times 1 0^{- 19}$ and $8.0 \times 1 0^{- 19}$ C, the largest value that divides all of them a whole number of times is $1.6 \times 1 0^{- 19}$ C (2, 3 and 5 times).

How many electrons? Find the drop's charge from $q = \frac{m g d}{V}$ , then divide by $e$ . A drop of mass $3.0 \times 1 0^{- 15}$ kg held by 460 V across 5.0 mm has $q = 3.2 \times 1 0^{- 19}$ 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 $m = \frac{e}{e / m}$ from an $e$ that is 6% high and an $\frac{e}{m}$ that is 3% low gives a mass about 9% too high.

Fields from plates. $E = \frac{V}{d}$ : 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 $v_{y} = \frac{q E}{m} t$ .

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 $\frac{2 m}{m + M} u$ . A neutron (about a proton's mass) can give a proton almost all its speed, but gives a nitrogen nucleus ( $M = 14 m$ ) 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 ( $q / m = v / B r$ ) to find the electron's charge-to-mass ratio.
Millikan's oil drops showed charge is quantised, in multiples of $1.6 \times 1 0^{- 19}$ 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.

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Cathode rays bend towards a positive plate. This shows they are:
1. A Uncharged
2. B Negatively charged
3. C Positively charged
4. D Waves
Show answer
B: Negatively charged
Opposite charges attract, so the rays are negative.
A small paddle wheel in a cathode ray tube turns when the rays hit it. This shows cathode rays:
1. A Are light
2. B Carry momentum, so they have mass
3. C Are positive
4. D Travel in curves
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B: Carry momentum, so they have mass
Only something with mass and momentum can push the wheel round.
Thomson's experiment discovered the:
1. A Electron
2. B Proton
3. C Neutron
4. D Nucleus
Show answer
A: Electron
His charge-to-mass ratio showed cathode rays were tiny particles: electrons.

Structure of the Atom

Cathode rays

Thomson measures the charge-to-mass ratio

Millikan measures the charge

Rutherford's nuclear model

Chadwick finds the neutron

Quick summary

Quiz

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