First slide

Photoelectric effect and study of photoelectric effect

Question

Threshold frequency for a certain metal is v₀. When light of frequency 2v₀ is incident on it, the maximum velocity of photoelectrons is 4 x 10⁸ cm s^-1. If frequency of incident radiation is increased to 5v₀, then the maximum velocity of photoelectrons, in cm s^-1, will be

Moderate

A

$(4 / 5) \times 10^{8}$
B

$2 \times 10^{8}$
C

$8 \times 10^{8}$
D

$20 \times 10^{8}$

Solution

Einstein's equation for photoelectric effect is
$\begin{array}{l} h v - h v_{0} = \frac{1}{2} m v_{max}^{2} \\ When v = 2 v_{0}, v_{max} = 4 \times 10^{8} {cms}^{- 1} \\ 2 h v_{0} - h v_{0} = (1 / 2) m {(4 \times 10^{8})}^{2} \\ h v_{o} = \frac{1}{2} m {(4 \times 10^{8})}^{2} . . . . . . . (i) \end{array}$
$\begin{array}{l} v = 5 v_{0}, v_{max} = v^{'} \\ h (5 v_{0}) - h v_{0} = \frac{1}{2} m v^{' 2} . . . . . . (i i) \end{array}$
Dividing Eq. (ii) by Eq. (i), we get
$v^{'} = 8 \times 10^{8} {cms}^{- 1}$

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