where
$E$ is energy of a quantum of light (J)
$f$ is frequency of EM radiation
-$h$ is Planck's constant ($6.63 \times 10^{-34}\operatorname{J s}$)
+$h$ is Planck's constant ($6.63 \times 10^{-34}\operatorname{J s}=4.12 \times 10^{-15} \operatorname{eV s}$)
### Electron-volts
Gradient of a frequency-energy graph is equal to $h$
y-intercept is equal to $\phi$
+#### Stopping potential $V_0$
+$$V_0 = {E_{K \operatorname{max}} \over q_e} = {{hf - \phi} \over q_e}$$
+
## 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
+
+$$\lambda = {h \over \rho} = {h \over mv}$$
+
- 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 ($< r_{\operatorname{proton}}$)
- if $2\pi r \ne n{h \over mv}$, interference occurs when pattern is looped and standing wave cannot be established
### Photon momentum
+
+$$\rho = {hf \over c} = {h \over \lambda}$$
- 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 $\lambda = {h \over mv}$