Question

If a surface has a work function 4.0 eV, 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. $4.4\times {10}^{5}m{s}^{-1}$
• B. $8.8\times {10}^{7}m{s}^{-1}$
• C. $8.8\times {10}^{5}m{s}^{-1}$
• D. $4.4\times {10}^{7}m{s}^{-1}$

Answer 1

The correct option is C $8.8\times {10}^{5}m{s}^{-1}$

The Einstein's equation for photoelectric effect is given by , $K_{max}=h\nu -W$

or $\frac{1}{2}m{v}^2=\frac{hc}{\lambda }-W$

or $v=\sqrt{\frac{2(hc/\lambda -W)}{m}}=\sqrt{\frac{2\left[\right(6.62\times {10}^{-34}\times 3\times {10}^8\left)/\right(0.2\times {10}^{-6})-(4\times 1.6\times {10}^{-19}\left)\right]}{9.1\times {10}^{-31}}}$

$=8.8\times {10}^{5}m/s$ (where mass of electron $m=9.1\times {10}^{-31}kg$)