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

Answer: (B)

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