Photoelectric Effect

\text{Einstein's Equation:} \quad KE_{\max} = h\nu - \phi \quad [ML^2$T^{-2}$] \quad \text{(J or eV)}

\text{Stopping Potential:} \quad eV_0 = h\nu - \phi \implies V_0 = \frac{h\nu - \phi}{e} \quad [ML^2$T^{-3}A^{-1}$] \quad \text{(V)}$$

\text{Threshold Frequency:} \quad \nu_0 = \frac{\phi}{h} \quad [$T^{-1}$] \quad \text{(Hz)}

$\text{Threshold Wavelength:} \quad \lambda_0 = \frac{hc}{\phi} \quad [L] \quad \text{(m)}$

\text{KE in terms of wavelength:} \quad KE_{\max} = hc\left(\frac{1}{\lambda} - \frac{1}{\lambda_0}\right) \quad [ML^2$T^{-2}$]

Photon Properties

\text{Photon Energy:} \quad E = h\nu = \frac{hc}{\lambda} \quad [ML^2$T^{-2}$] \quad \text{(J or eV)}

\text{Photon Momentum:} \quad p = \frac{h}{\lambda} = \frac{E}{c} = \frac{h\nu}{c} \quad [M$LT^{-1}$] \quad \text{(kg m/s)}

\text{Planck's constant:} \quad h = 6.63 \times 10^{-34} \text{ J s} \quad [ML^2$T^{-1}$]

$\text{Energy conversion:} \quad 1 \text{ eV} = 1.6 \times 10^{-19} \text{ J}$

de Broglie Wavelength

$\text{General:} \quad \lambda = \frac{h}{mv} = \frac{h}{p} \quad [L] \quad \text{(m)}$

$\text{From KE:} \quad \lambda = \frac{h}{\sqrt{2m \cdot KE}} \quad [L]$

$\text{Electron through potential V:} \quad \lambda = \frac{h}{\sqrt{2m_e eV}} = \frac{1.227}{\sqrt{V}} \text{ nm} \quad \text{(electrons ONLY)}$

$\text{Thermal wavelength:} \quad \lambda = \frac{h}{\sqrt{3mkT}} \quad [L] \quad \text{(k = Boltzmann constant)}$

$\text{Mass ratio at same V:} \quad \frac{\lambda_1}{\lambda_2} = \sqrt{\frac{m_2}{m_2}} \implies \frac{\lambda_e}{\lambda_p} = \sqrt{\frac{m_p}{m_e}} \approx 42.8$

Key Constants