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 $E=W_0+K_{max}\Rightarrow \frac{hc}{\lambda }=W_0+\frac{1}{2}m{v}^2\frac{hc}{400\times {10}^{-9}}=W_0+\frac{1}{2}m{v}^2$ ……(i) and
$\frac{hc}{250\times {10}^{-9}}=W_0+\frac{1}{2}m(2v{)}^2$
……(ii)
From equation (i) and (ii) $W_0=2hc\times {10}^{6}J$.