## Photoelectric effect
+![](graphics/photoelectric-effect.png)
+
### Planck's equation
$$E=hf,\quad f={c \over \lambda}$$
- 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
+![](graphics/standing-wave-electrons.png)
+
### Photon momentum
$$\rho = {hf \over c} = {h \over \lambda}$$
- Black lines in spectrum show light not reflected
### Emission
+
+![](graphics/energy-levels.png)
+
- 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
- EMR is absorbed/emitted when $E_{\operatorname{K-in}}=\Delta E_{\operatorname{shells}}$ (i.e. $\lambda = {hc \over \Delta E_{\operatorname{shells}}}$)
## Light sources
+
+![](graphics/synchrotron.png)
+
- **incandescent:** <10% efficient, broad spectrum
- **LED:** semiconducting doped-Si diodes
- - most electrons in *valence band* (energy level)