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. $4.4 \times 10^{5} \,m / s$
• 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

Answer: (B)

Work function $W =4 eV =4 \times 1.6 \times 10^{-19} J $
$=6.4 \times 10^{-19} J$
Wavelength of incident radiation
$\lambda=0.2 \mu m =0.2 \times 10^{-6} m$
Maximum KE of liberated electron
$( KE )_{\max }=\frac{h c}{\lambda}-W $
$\frac{1}{2} m v_{\max }^{2}=\frac{h c}{\lambda}-W $
$\frac{1}{2} \times 9.1 \times 10^{-31} v_{\max }^{2} $
$=\frac{6.6 \times 10^{-34} \times 3 \times 10^{8}}{0.2 \times 10^{-6}}-6.4 \times 10^{-19} $
$=9.9 \times 10^{-19}-6.4 \times 10^{-19}=3.5 \times 10^{-19} $
$\therefore v_{\max }=\sqrt{\frac{3.5 \times 10^{-19} \times 2}{9.1 \times 10^{-31}}}=\sqrt{\frac{7}{9.1} \times 10^{12}} $
$=8.8 \times 10^{5} m / s$