(A) According to Einstein's photoelectric equation,the maximum kinetic energy $K_{\max}$ is given by $K_{\max} = hf - \phi$,where $\phi = hf_0$ is the

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(A) According to Einstein's photoelectric equation,the maximum kinetic energy $K_{\max}$ is given by $K_{\max} = hf - \phi$,where $\phi = hf_0$ is the work function.For incident frequency $f = 2f_0$:$\frac{1}{2}mv_1^2 = h(2f_0) - hf_0 = hf_0$ --- $(1)$For incident frequency $f = 5f_0$:$\frac{1}{2}mv_2^2 = h(5f_0) - hf_0 = 4hf_0$ --- $(2)$Dividing equation $(1)$ by equation $(2)$:$\frac{\frac{1}{2}mv_1^2}{\frac{1}{2}mv_2^2} = \frac{hf_0}{4hf_0}$$\frac{v_1^2}{v_2^2} = \frac{1}{4}$Taking the square root on both sides:$\frac{v_1}{v_2} = \frac{1}{2}$

Class 12 Physics Dual Nature of Radiation and Matter Einstein's Photoelectric Equation and Energy Quantum of Radiation

Medium

The threshold frequency of a metal is $f_0$. When light of frequency $2f_0$ is incident on the metal plate,the maximum velocity of the photoelectrons is $v_1$. When the frequency of the incident radiation is increased to $5f_0$,the maximum velocity of the photoelectrons emitted is $v_2$. The ratio of $v_1$ to $v_2$ is:

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A
$v_1/v_2 = 1/2$
B
$v_1/v_2 = 1/8$
C
$v_1/v_2 = 1/16$
D
$v_1/v_2 = 1/4$

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Dual Nature of Radiation and Matter

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Einstein's Photoelectric Equation and Energy Quantum of Radiation

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