PX156 - A4 - the photoelectric effect

the emission of electrons from a metal surface due to incident electromagnetic radiation
lenard's experimental observations:
- not all electrons emerge with the same kinetic energy
- the maximum kinetic energy is independent of the intensity of light, but dependent on the frequency
- no electrons are emitted if the frequency of light is lower than a critical value, the threshold frequency

K E_{e^{-}} = h f - ϕ

where, $ϕ =$ work function energy: energy required to remove the electron

for a photon with $λ = 700 n m$ , $f = 430 T H z :$

E = h f = 3 \times 10^{- 19} J

considering photon as a particle:

\begin{aligned} E_{t o t} & = K E + m_{0} c^{2} \\ = (γ - 1) m_{0} c^{2} + m_{0} c^{2} \\ = γ m_{0} c^{2} \\ = \frac{1}{\sqrt{1 - \frac{u^{2}}{c^{2}}}} m_{0} c^{2} \end{aligned}

where, $γ =$ lorentz factor

for $u \to c : E \to \infty$ if $m_{0} \neq 0$

E_{t o t}^{2} = (m_{0} c^{2})^{2} + (p c)^{2}

for $m_{0} = 0 : E = p c = h f :$

p = \frac{E}{c} = \frac{h}{λ}