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 2v respectively. The work function of the metal is (h = Planck’s constant, c = velocity of light in air)

• 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

The correct option is A

$2hc\times {10}^{6}J$

By using $\frac{hc}{\lambda }=W_0+\frac{1}{2}m{v}^2$
$\Rightarrow \frac{hc}{400\times {10}^{-9}}=W_0+\frac{1}{2}m{v}^2\cdots \left(i\right)$
$and\frac{hc}{250\times {10}^{-9}}=W_0+\frac{1}{2}m(2v{)}^2\cdots (ii)$
On solving (i) and (ii)
$\frac{1}{2}m{v}^2=\frac{hc}{3}[\frac{1}{250\times {10}^{-9}}-\frac{1}{400\times {10}^{-9}}]\cdots \left(iii\right)$
From equation (i) and (iii) $W_0=2hc\times {10}^{6}J$