Answer to Question #114217 in Quantum Mechanics for jay

Question

⦁ Photons of wavelength (i) 5000 Å and (ii) 2000 Å are incident on the surface of silver (Work Function = 4.7 eV). Explain whether electrons are able to come out of the surface or not. If not, why not

Answer 1

Kinetic energy of the emitted electron is given by

$T_e=\frac{\hbar c}{\lambda}-4.7>0$ $\lambda=2000 \colon T_e=1.58 \cdot 10^{-19} \frac{kg \cdot m^2}{s^2}-4.7 \cdot 1.6 \cdot 10^{-19} \frac{kg \cdot m^2}{s^2}\\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,=(1.58-7.52)\cdot 10^{-19} J<0$

Obviously, for $\lambda=5000 \colon T_e<0$.

Hence, the energy of photons is too low for electrons to leave the surface.