Question

Ultraviolet beam of wavelength $280nm$ is incident on lithium surface of work function $2.5eV$. The maximum velocity of electron emitted from metal surface is

• A. $8.2\times 10^{5}m/s$
• B. $10^{6}m/s$
• C. $7\times 10^{5}m/s$
• D. $6\times 10^{5}m/s$

Answer 1

Answer: (A)

According to Einstein's photoelectric equation
$\frac{hc}{\lambda }={\varphi }_0+\frac{1}{2}m{v}_{\max }^2$
$\therefore v_{\max }=\sqrt{\frac{2\left(\frac{hc}{\lambda }-{\varphi }_0\right)}{m}}=\sqrt{\frac{2\left(\frac{1240}{280}-2.5\right)}{9.1\times 10^{-31}}}$
( Using $hc=1240eVnm)$
$=\sqrt{\left(\frac{2\times 1.9\times 1.6\times 10^{-19}}{9.1\times 10^{-31}}\right)}$
$=8.2\times 10^{5}m/s$