41.3 Content
41.3.1 Cathode Ray Experiments
Key observations that proved cathode rays are particles:
| Observation | Evidence For |
|---|---|
| Deflection by electric field | Rays are charged |
| Deflection by magnetic field | Rays are charged particles with mass |
| Same properties regardless of cathode material | Rays are fundamental (not atoms) |
| Cause paddle wheel to rotate | Rays have momentum (mass × velocity) |
| Travel in straight lines | Rays are particles, not waves |
41.3.2 Interactive: Cathode Ray Tube
41.3.3 Thomson’s Charge-to-Mass Experiment (1897)
Thomson measured the charge-to-mass ratio of electrons by balancing electric and magnetic forces:
\[\frac{q}{m} = \frac{v}{Br}\]
where: - \(q/m\) = charge-to-mass ratio (C/kg) - \(v\) = electron velocity (m/s) - \(B\) = magnetic field strength (T) - \(r\) = radius of circular path (m)
Thomson’s Method:
- Velocity selector: Balance electric and magnetic forces so only electrons with \(v = E/B\) pass through undeflected
- Magnetic deflection: Remove electric field; electrons curve in a circle
- Measure radius: From the curvature, calculate \(r\)
- Calculate q/m: Use \(q/m = v/(Br)\)
Thomson found \(q/m = 1.76 \times 10^{11}\) C/kg for cathode rays—about 1800 times larger than for hydrogen ions. This meant electrons were either very light or very highly charged (or both). Later work showed electrons are very light.
41.3.4 Interactive: Thomson’s Experiment
41.3.5 Millikan’s Oil Drop Experiment (1909)
Millikan determined the charge of a single electron by suspending charged oil drops in an electric field:
\[q = \frac{mg}{E}\]
where: - \(q\) = charge on droplet (C) - \(m\) = mass of droplet (kg) - \(g\) = 9.8 m/s² - \(E\) = electric field strength (V/m)
Key Finding: All measured charges were integer multiples of a fundamental unit:
\[e = 1.6 \times 10^{-19}\ \text{C}\]
Millikan found charges like 3.2 × 10⁻¹⁹ C, 4.8 × 10⁻¹⁹ C, 6.4 × 10⁻¹⁹ C—always multiples of e. This proved charge is quantised in discrete units, not continuous.
41.3.6 Interactive: Millikan Oil Drop
41.3.7 Geiger-Marsden Experiment (1909-1911)
Also called the “gold foil experiment” or “alpha scattering experiment”:
Setup: Alpha particles fired at thin gold foil
Observations:
| Result | Percentage | Implication |
|---|---|---|
| Passed straight through | ~99% | Atom is mostly empty space |
| Deflected at small angles | ~1% | Some positive charge present |
| Scattered back (>90°) | ~0.01% | Concentrated positive charge |
41.3.8 Interactive: Rutherford Scattering
41.3.9 Rutherford’s Nuclear Model (1911)
From the scattering data, Rutherford concluded:
- Nucleus: Tiny, dense, positively charged centre (~10⁻¹⁵ m)
- Electrons: Orbit at relatively large distances (~10⁻¹⁰ m)
- Mostly empty space: Atom is ~100,000× larger than nucleus
Closest approach formula (all kinetic energy → potential energy):
\[r_{min} = \frac{kZe \cdot 2e}{KE}\]
where Z is the atomic number and 2e is the alpha particle charge.
41.3.10 Chadwick’s Discovery of the Neutron (1932)
The Problem: Nuclei were heavier than protons alone could explain. Rutherford predicted “neutral particles” in 1920.
Chadwick’s Experiment: 1. Bombard beryllium with alpha particles 2. Observe highly penetrating radiation that wasn’t deflected by fields 3. This radiation could knock protons from paraffin wax 4. From momentum conservation, Chadwick calculated the mass
\[m_n \approx 1.008665\ \text{u} \approx 1.67 \times 10^{-27}\ \text{kg}\]
Paraffin (wax) is rich in hydrogen. When neutrons collide with protons (similar mass), they transfer maximum momentum—like billiard balls. This made detection possible.