Question

The work function of a metal is 4.2 eV. If radiations of 2000 A${}^o$ on the metal, then the kinetic energy of the fastest photoelectron is:

• A. 1.6 $\times$ 10${}^{-19}$ J
• B. 16 $\times$ 10${}^{10}$ J
• C. 3.2 $\times$ 10${}^{-19}$ J
• D. 6.4 $\times$ 10${}^{-10}$ J

Answer 1

The correct option is C 3.2 $\times$ 10${}^{-19}$ J

The energy of radiation is $E=\frac{hc}{\lambda }$

Where,

h = Planck’s constant

c = speed of light

$E=\frac{6.626\times {10}^{-34}\times 3\times {10}^8}{2000\times {10}^{-16}}=9.939\times {10}^{-19}J$.

The work function is $\psi =4.2eV=4.2\times 1.602\times {10}^{-19}J=6.728\times {10}^{-19}J$.

The kinetic energy of the fastest photon is

$=E-\psi$

$=9.939\times {10}^{-19}J-6.728\times {10}^{-19}J=3.2\times {10}^{-19}J$.

Hence, the correct option is $C$