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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