Question

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

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

Answer 1

Answer: (A)

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