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

Answer: (A)

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

Answer 2

By using $E = W_{0} + K_{\max}$ ⇒ $\frac{hc}{\lambda} = W_{0} + \frac{1}{2}mv^{2}$

$\frac{hc}{400 \times 10^{- 9}} = W_{0} + \frac{1}{2}mv^{2}$ ……(i) and

$\frac{hc}{250 \times 10^{- 9}} = W_{0} + \frac{1}{2}m(2v)^{2}$ ……(ii)

From equation (i) and (ii) $W_{0} = 2hc \times 10^{6}J.$