Chapter 11 - Dual Nature of Radiation and Matter

Metals have free electrons that move inside but cannot easily leave. To get them out you need extra energy called work function phi0. It is like water in a well - need energy to pull bucket out.

Four ways: Thermionic emission - heat metal filament glows electrons come out like steam from hot water. Field emission - very strong electric field pulls electrons. Photoelectric emission - light shines and knocks electrons out. Secondary emission - fast electron hits and knocks more out.

Work function phi0 = h nu0 where nu0 threshold frequency. Different metals different phi0. Cesium low ~2 eV easy, platinum high ~5.6 eV hard. 1 eV = 1.6x10^-19 J.

When light of enough frequency falls on metal, electrons fly out instantly. This is photoelectric effect. Observed in vacuum tube with cathode and anode, light on cathode current flows.

Key surprises that wave theory could not explain: No delay even for dim light - electron comes out immediately. Exists threshold frequency nu0 below which no electron even if intense light for hours. Kinetic energy of electrons depends on frequency not intensity. Number of electrons depends on intensity.

Wave theory expected more intense light should give faster electrons and any frequency should work if waited long. Experiment showed opposite. So light must be particle.

First law: For any metal there is threshold frequency nu0 and wavelength lambda0 = c/nu0. Below nu0 no photoelectric even if intensity huge.

Second: Number of photoelectrons per second proportional to intensity, at fixed frequency above threshold. So current increases with brightness.

Third: Maximum kinetic energy Kmax independent of intensity, depends on frequency linearly. Stopping potential Vs needed to stop fastest electrons Vs proportional to Kmax.

Graph Vs vs nu is straight line slope h/e, intercept -phi0/e on Vs axis. Graph Kmax vs nu also straight line slope h. Graph photocurrent vs intensity straight line through origin.

Einstein said light comes as packets photons energy E = h nu. One photon gives full energy to one electron. Part used to free electron work function phi0, remaining becomes kinetic energy.

So h nu = phi0 + Kmax. If Kmax = 1/2 mv_max^2 = e Vs where Vs stopping potential. So Kmax = h nu - phi0 = h (nu - nu0). At threshold nu=nu0 Kmax zero.

Vs = (h/e) nu - phi0/e. This matches straight line experiment. So photon picture explains all laws.

If nu less than nu0, h nu less than phi0 cannot free electron. Intensity means more photons, so more electrons but each still h nu energy.

Photon is particle of light but also wave. Energy E = h nu = hc / lambda. Momentum p = h / lambda = h nu / c. Rest mass zero, moves at c. When photon collides it behaves like billiard ball transferring energy and momentum.

Intensity of light means number of photons per second per area. More intense beam more photons but each photon same energy if frequency same.

Photon is neutral, spin 1, travels at light speed, energy depends only on frequency colour. Red photon less energy ~1.8 eV, blue ~3 eV, UV more.

Daily picture: sunlight is rain of photons, each colour different energy packet.

de Broglie said if light can be particle, particle can be wave. Every moving particle has wavelength lambda = h / p = h / mv where p momentum. If particle accelerated through voltage V, lambda = h / sqrt(2 m e V) = 12.27 / sqrt(V) angstrom for electron.

Heavier particle same speed smaller wavelength. For cricket ball mass 150 g speed 20 m/s lambda ~2e-34 m too tiny cannot see. Electron mass tiny so lambda ~1 angstrom comparable to atoms so visible as diffraction.

Faster particle smaller wavelength. Energy larger momentum larger wavelength smaller.

This idea means matter also dual nature particle plus wave.

Davisson and Germer fired electrons at nickel crystal. Electrons scattered and showed diffraction peaks where 2d sin theta = n lambda Bragg law. Measured lambda matched de Broglie prediction. So electrons are waves confirmed.

Application electron microscope: uses electron waves with tiny lambda ~0.01 angstrom when accelerated 100 kV, so can see much smaller details than light microscope whose lambda ~5000 angstrom. Resolution much higher.

Other uses photocell, photodiode, solar cell - all photoelectric based.

Photocell: light on cathode makes current, used in automatic doors counting, street light auto on off, burglar alarm.

Solar panel: photons free electrons in semiconductor generate electricity.

Photodiode and camera light meter exposure control using photoelectric.

Heisenberg uncertainty principle: cannot know position and momentum both exact at same time Delta x Delta p >= h/4pi, arises from wave nature.

Summary dual nature: light and matter both wave and particle. At low intensity particle picture photon counting, high intensity wave interference visible.