From 11af55e709f1dc4efff07536b767b9e3800c8a74 Mon Sep 17 00:00:00 2001
From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Tue, 21 Aug 2018 08:54:52 +1000
Subject: [PATCH] photoelectric effect

---
 physics/light-matter.md | 112 ++++++++++++++++++++++++++++++++++++----
 1 file changed, 103 insertions(+), 9 deletions(-)

diff --git a/physics/light-matter.md b/physics/light-matter.md
index 04a90a4..fd6828c 100644
--- a/physics/light-matter.md
+++ b/physics/light-matter.md
@@ -4,25 +4,119 @@
 
 ### Planck's equation
 
-$$E=hf$$
+$$E=hf,\quad f={c \over \lambda}$$
+$$\therefore E={hc \over \lambda}$$
 
 where  
 $E$ is energy of a quantum of light (J)  
-$f$ is frequency of EM radiation
+$f$ is frequency of EM radiation  
 $h$ is Planck's constant ($6.63 \times 10^{-34}\operatorname{J s}$)
 
+### Electron-volts
 
-### Electron diffraction patterns
+$$ 1 \operatorname{eV} = 1.6 \times 10^{-19} \operatorname{J}$$
 
-$$W=qV$$
+*Amount of energy an electron gains when it moves through a potential difference of 1V*
 
-(work for accelerating electon of charge $q$ with voltage $V$)
+- equivalent unit is Joule seconds (e.g. $h$)
 
-$$\lambda = {h \over mv}$$
+### Photoelectric effect
+
+- some metals becomes positively charged when hit with EM radiation
+- this is due to e- being ejected from surface of metal
+- *photocurrent* - flow of e- due to photoelectric effect
+- causes increase in current in a circuit
+- $V_{\operatorname{supply}}$ does not affect photocurrent
+- if $V_{\operatorname{supply}} \gt 0$, e- are attracted to collector anode.
+- if $V_{\operatorname{supply}} \lt 0$, e- are attracted to illuminated cathode, and $I\rightarrow 0$
+
+#### Wave / particle (quantum) models
+wave model:  
+- cannot explain photoelectric effect
+- $f$ is irrelevant to photocurrent
+- predicts that there should be a delay between incidence of radiation and ejection of e-
+
+particle model:  
+- explains photoelectric effect
+- rate of photoelectron release is proportional to intensity of incident light
+- shining light on a metal "bombards" it with photons
+- no time delay
+
+#### Work function and threshold frequency
+
+- *threshold frequency* $f_0$ - minimum frequency for photoelectrons to be ejected
+- if $f \lt f_0$, no photoelectrons are detected
+
+- Einstein: energy required to eject photoelectron is constant for each metal
+- *work function* $\phi$ - minimum energy required to release photoelectrons
+- $\phi$ is determined by strength of bonding
+
+$$\phi=hf_0$$
+
+#### $E_K$ of photoelectrons
+
+$$E_{\operatorname{k-max}}=hf - \phi$$
+
+where  
+$E_k$ is max energy of an emmitted photoelectron  
+$f$ is frequency of incident photon (**not** emitted electron)  
+$\phi$ is work function ("latent" energy)
+
+Gradient of a frequency-energy graph is equal to $h$  
+y-intercept is equal to $\phi$
+
+## Wave-particle duality
+
+### Double slit experiment
+Particle model allows potential for photons to interact as they pass through slits. However, an interference pattern still appears when a dim light source is used so that only one photon can pass at a time.
+
+## De Broglie's theory
+- theorised that matter may display both wave- and particle-like properties like light
+- predict wavelength of a particle with $\lambda = {h \over \rho}$ where $\rho = mv$
+- impossible to confirm de Broglie's theory of matter with double-slit experiment, since wavelengths are much smaller than for light, requiring an equally small slit ($< r_{\operatorname{proton}}$)
+- confirmed by Davisson and Germer's apparatus (diffraction pattern like double-slit)
+- also confirmed by Thomson - e- diffraction pattern resembles x-ray (wave) pattern
+- electron is only stable in orbit if $mvr = n{h \over 2\pi}$ where $n \in \mathbb{Z}$
+- rearranging this, $2\pi r = n{h \over mv}$ (circumference)
+- therefore, stable orbits are those where circumference = whole number of e- wavelengths
+- if $2\pi r \ne n{h \over mv}$, interference occurs when pattern is looped and standing wave cannot be established
+
+### Photon momentum
+- if a massy particle (e.g. electron) has a wavelength, then anything with a wavelength must have momentum
+- therefore photons have (theoretical) momentum
+- to solve photon momentum, rearrange $\lambda = {h \over mv}$
+
+## Spectral analysis
+
+
+### Absorption
+- Black lines in spectrum show light not reflected  
+
+### Emission
+- Coloured lines show light being ejected from e- shells  
+- Energy change between ground / excited state: $\Delta E = hf = {hc \over \lambda}$  
+- Bohr's model describes discrete energy levels
+- Energy is conserved (out = in)
+- Ionisation energy - minimum energy required to remove an electron
+- EMR is absorbed/emitted when $E_{\operatorname{K-in}}=\Delta E_{\operatorname{shells}}$ (i.e. $\lambda = {hc \over \Delta E_{\operatorname{shells}}}$)
+
+## Light sources
+- **incandescent:** <10% efficient, broad spectrum
+- **LED:** semiconducting doped-Si diodes
+- - most electrons in *valence band* (energy level)
+- - provided energy, electrons can jump to *conduction band* and move through Si as current
+- - colour determined by $\Delta E$ between bands (shells), and type of doping
+- **laser:** gas atoms are excited
+- - *popular inversion* - most gas atoms are excited
+- - photons are released if stimulated by another photon of the right wavelength
+- **synchrotron:** - magnetically accelerates electrons
+- - extremely bright
+- - highly polarised
+- - emitted in short pulses
+- - broad spectrum
+
+## Quantum mechanics
 
-(de Broglie's equation)
 
-Solving wavelength of electrons from gun:
-1.
 
 774 abc melbourne
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