Quantum physics summary
Quantum: smallest possible amount of a physical quantity.
Photon: quantum of electromagnetic radiation $$E=hf=\frac{hc}{\lambda}$$
Photoelectric effect: 1 photon hitting the metal=1 photoelectron emitted
Threshold frequency $$(f_{0})$$ minimal frequency of a photon to trigger the photoelectric effect (depends on the metal).
Work function : minimal energy of the photon $$\phi=hf_{0}$$
Einstein's photoelectric equation $$$K_\text{max}=\frac{1}{2}mv_{\text{max}}^{2}=hf\phi$$$
Photoelectric current between an emitter and a collector: $$I=\frac{ne}{t}$$
Intensity $$ =\frac{P}{A}=\frac{N(hf)/t}{A}$$
$$n\propto N \quad \Rightarrow \quad I\propto \text{Intensity}$$
Stopping potential $$(V_{\text{s}})$$: potential difference required to stop a photoelectron with the maximum possible kinetic energy exactly at the collector's surface. $$$ V_{\text{s}}=\left (\frac{h}{e}\right )f\frac{\phi}{e} $$$
Waveparticle duality (observable at quantum scales) all matter is both a wave and a particle.
de Broglie relation:
$$$\lambda=\frac{h}{p}$$$Electrons are in atomic levels around the atom.
Photons emitted by the deexcitation of an atom (electronic change to a lower level): emission spectrum (coloured parallel spectral lines on a dark background)
Photons absorbed excite an atom (electronic change to a higher level): absorption spectrum (dark parallel lines on a coloured background)
Difference between the energy levels : $$hf=E_{2}E_{1}$$
Xray spectrum:
 intensity spikes : excited metal atoms return to their ground state (discrete energies).

continuous spectrum : electrons decelerating on a metal surface (bremsstrahlung).
Minimum wavelength: $$$h\left(\frac{c}{\lambda_{\text{min}}}\right)=\frac{1}{2}mv^{2}$$$
Heisenberg uncertainty principle :
$$$\Delta x\Delta p\geq\frac{\hbar}{2} \qquad \Delta E\Delta t\geq\frac{\hbar}{2}$$$Wave function $$\psi$$ (Schrödinger model): carries all the waveparticle information.
$$\vert\psi\vert^{2}=$$ probability density: probability of finding a particle at particular a point.
Potential barrier : region in space where the potential energy of a particle is higher than its surroundings.
Barrier height : minimum energy to pass through the barrier.
Quantum tunnelling : quantum phenomenon of passing through a potential barrier without sufficient energy.
Transmission coefficient $$(T)$$ probability of tunnelling $$$ T=e^{2kd} \qquad k=\sqrt{\frac{8\pi^{2}(UE)}{h^{2}}}$$$
Reflection coefficient $$(R)$$ : $$R+T=1$$
Scanning tunnelling microscope (STM) : device that gives atomicscale images of surface by using quantum tunnelling.
Symbol  Meaning 

$$h$$  Planck constant 
$$c$$  Speed of light 
$$f$$  Frequency 
$$v$$  Velocity 
$$\lambda$$  Wavelength 
$$m$$  Mass of an electron 
$$K_{\text{max}}$$  Maximum kinetic energy of a photoelectron 
$$N$$  Number of incident photons 
$$n$$  Number of emitted photoelectrons 
$$p$$  Momentum 
$$e$$  Charge of an electron 
$$\hbar=h/2\pi$$  Reduced Planck constant 
$$d$$  Barrier width 
$$h$$  Barrier height 
$$E$$  Energy 