The Einstein’s equation for photoelectric effect is given by, \( KE = hv – hv_{0} \)

where

KE= maximum kinetic energy of electron

\( KE= \frac{1}{2}mv^{2} \)

h= Planck’s constant

\( v_{0} \) = threshold frequency

v = frequency of incident light

In first case:

\( \frac{1}{2}mv_{1}^{2} \) \( \Rightarrow h (2 v_{0}) – h v_{0} = hv_{0} —[1] \)

In second case:

\( \frac{1}{2}mv_{2}^{2} \) \( \Rightarrow h (5 v_{0}) – h v_{0} = 4hv_{0} —[2] \)

From equations [1] and [2], we get,

\( \frac{1}{2}mv_{2}^{2} = 4 * \frac{1}{2}mv_{1}^{2} \)

OR

\( v_{2} = 2v_{1} \) \( \Rightarrow 2 * (4 * 10^{6}) \) \( \Rightarrow 8 * 10^{6} m/s \)

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