When light of frequency twice the threshold frequency is incident on the metal plate, the maximum velocity of emitted electron is V1. When the frequency of incident radiation is increase to ten times the threshold value, the maximum velocity of emitted electron becomes V2. If V2 = x V1, the value of x will be____

Case- I : h(2υ0)=hυ0+12mv12 hυ0=12mv12 ……(1)Case - II : h(10υ0)=hυ0+12mv12 ∴9hυ0=12mv12 ……(2)Divide (2) and (1) 9hυ0hυ0=(V2V1)2 ∴V2V1=9 ∴V2=3V1 But V2=xV1 ∴x=3

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When light of frequency twice the threshold frequency is incident on the metal plate, the maximum velocity of emitted electron is V₁. When the frequency of incident radiation is
increase to ten times the threshold value, the maximum velocity of emitted electron becomes V₂. If V₂ = $x$ V₁, the value of $x$ will be____

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answer is 3.

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Detailed Solution

Case- I : $h (2 υ_{0}) = h υ_{0} + \frac{1}{2} m v_{1}^{2}$
$h υ_{0} = \frac{1}{2} m v_{1}^{2}$ ……(1)
Case - II : $h (10 υ_{0}) = h υ_{0} + \frac{1}{2} m v_{1}^{2}$
$∴ 9 h υ_{0} = \frac{1}{2} m v_{1}^{2}$ ……(2)
Divide (2) and (1)
$\frac{9 h υ_{0}}{h υ_{0}} = {(\frac{V_{2}}{V_{1}})}^{2} ∴ \frac{V_{2}}{V_{1}} = \sqrt{9} ∴ V_{2} = 3 V_{1}$
But $V_{2} = x V_{1}$ $∴ x = 3$