Question

The work function of a metal is 4.2 $eV$. If a radiation of $2000\stackrel{o}{A}$ falls 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

$3.2\times {10}^{-19}J$

We know from Einstein's photoelectron equation,

KE = [Energy of radiation - Work function]

= $[h\nu -h{\nu }_0]$ = $[\frac{hc}{\lambda }-4.2\times 1.602\times {10}^{-19}J]$

= $[\frac{6.625\times {10}^{-34}Js\times 3\times {10}^{8}m}{2000\times {10}^{-10}m}-4.2\times 1.602\times {10}^{-19}]$

= $(9.9\times {10}^{-19}J)-(6.7\times {10}^{-19}J)$

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