Question

When a metal surface is illuminated by light of wavelengths $400\, nm$ and $250\,nm$, the maximum velocities of the photoelectrons ejected are $V$ and $2 V$ respectively. The work function of the metal is

• A. $2 h c \times 10^{6}\, J$
• B. $1.5 hc \times 10^{6} \,J$
• C. $hc \times 10^{6}\, J$
• D. $0.5 hc \times 10^{6} \,J$

Answer 1

Answer: (A)

$2 h c \times 10^{6}\, J$

Answer 2

Let the work function of metal be W,
Case $1, \frac{ hc }{200\, nm }-2 W = mv ^{2}...1$
Case $2, \frac{ hc }{250 \,nm }- W =2 mv ^{2}...2$
From 1 and 2,
$\Rightarrow \frac{ hc }{200 \,nm }-2 W =\frac{- W }{2}+\frac{ hc }{500 \,nm }$
$\Rightarrow 2 w -\frac{ W }{2}= hc \left(\frac{1}{200}-\frac{1}{500}\right) \frac{1}{ nm }$
$\frac{3 W }{2}= hc \left(\frac{300}{1000}\right) \times 10^{9}$
$\Rightarrow W = hc \frac{2}{3} \times \frac{3}{1000} \times 10^{6}$
$\Rightarrow W =2 hc \times 10^{6}\, J$