(A) According to Einstein's photoelectric equation,$K_{max} = h\nu - W_0 = \frac{1}{2}mv^2$,where $W_0 = h\nu_0$.For frequency $2\nu_0$:$h(2\nu_0) = h

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(A) According to Einstein's photoelectric equation,$K_{max} = h\nu - W_0 = \frac{1}{2}mv^2$,where $W_0 = h\nu_0$.For frequency $2\nu_0$:$h(2\nu_0) = h\nu_0 + \frac{1}{2}mv_1^2$$h\nu_0 = \frac{1}{2}mv_1^2$ ..... $(i)$For frequency $5\nu_0$:$h(5\nu_0) = h\nu_0 + \frac{1}{2}mv_2^2$$4h\nu_0 = \frac{1}{2}mv_2^2$ ..... $(ii)$Dividing equation $(i)$ by $(ii)$:$\frac{h\nu_0}{4h\nu_0} = \frac{\frac{1}{2}mv_1^2}{\frac{1}{2}mv_2^2}$$\frac{1}{4} = \frac{v_1^2}{v_2^2}$Taking the square root on both sides:$\frac{v_1}{v_2} = \frac{1}{2}$Thus,the ratio is $1:2$.

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

Medium

When the light of frequency $2v_0$ (where $v_0$ is threshold frequency) is incident on a metal plate,the maximum velocity of electrons emitted is $v_1$. When the frequency of the incident radiation is increased to $5v_0$,the maximum velocity of electrons emitted from the same plate is $v_2$. The ratio of $v_1$ to $v_2$ is

NEET 2018 All NEET

A
$1:2$
B
$1:4$
C
$2:1$
D
$4:1$

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Class 12

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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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