Question

If a surface has a work function $4.0eV$, what is the maximum velocity of electrons liberated from the surface when it is irradiated with ultraviolet radiation of wavelength $0.2\mu m$?

• A. $4.4\times {10}^{5}m/s$
• B. $8.8\times {10}^{7}m/s$
• C. $8.8\times {10}^{5}m/s$
• D. $4.4\times {10}^{7}m/s$

Answer 1

The correct option is C $8.8\times {10}^{5}m/s$

Given : $\varphi =4eV$ $\lambda =0.2\mu m=200$ $nm$

Using $K.E_{max}=\frac{hc}{\lambda }-\varphi$ where $K.E_{max}=\frac{1}{2}m{v}^2$ and $hc=1240$ $eV$

$\therefore$ $K.E_{max}=\frac{1240}{200}-4=2.2eV=2.2\times 1.6\times {10}^{-19}=3.53\times {10}^{-19}$ $J$

Maximum velocity $v=\sqrt{\frac{2K.E_{max}}{m}}$

$\therefore$ $v=\sqrt{\frac{2\times 3.52\times {10}^{-19}}{9.1\times {10}^{-31}}}=8.8\times {10}^5$ $m/s$