Question

The photoelectric work function for a metal is $4.2eV$. If the stopping potential is $3V$, find the threshold wavelength and maximum kinetic energy of emitted electrons.
(Velocity of light in air $=3\times {10}^{8}m/s$, Planck's constant $=6.63\times {10}^{-34}J-s$, Charge on electron $=1.6\times {10}^{-19}C$)

Answer 1

Given : $e=1.6\times {10}^{-19}C$, $c=3\times {10}^{8}m/s$
$\varphi =4.2eV$, $h=6.63\times {10}^{-34}J.s$, $V_S=3V$
$\varphi =4.2\times 1.6\times {10}^{-19}J$
$=6.72\times {10}^{-19}J$
(a) Threshold wavelength $={\lambda }_0=\frac{hc}{\varphi }$
$=\frac{6.63\times {10}^{-34}\times 3\times {10}^8}{6.72\times {10}^{-19}}$
$=2.960\times {10}^{-7}m$
$=2960\mathring{A}$
(b) Maximum kinetic energy,
${KE}_{max}=e{V}_S=1.6\times {10}^{-19}\times 3$
$=4.8\times {10}^{-19}J$