(B) According to Einstein's photoelectric equation,the maximum kinetic energy ${K_{\max }}$ is given by ${K_{\max }} = h\nu - h{\nu _0}$,where ${\nu _

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$\frac{{k\nu _1 - \nu _2}}{{k - 1}}$

(B) According to Einstein's photoelectric equation,the maximum kinetic energy ${K_{\max }}$ is given by ${K_{\max }} = h\nu - h{\nu _0}$,where ${\nu _0}$ is the threshold frequency.For frequency ${\nu _1}$,${K_1} = h({\nu _1} - {\nu _0})$.For frequency ${\nu _2}$,${K_2} = h({\nu _2} - {\nu _0})$.Given the ratio of maximum kinetic energies is ${K_1}:{K_2} = 1:k$,we have $\frac{{{K_1}}}{{{K_2}}} = \frac{1}{k}$.Substituting the expressions,we get $\frac{{h({\nu _1} - {\nu _0})}}{{h({\nu _2} - {\nu _0})}} = \frac{1}{k}$.$k({\nu _1} - {\nu _0}) = {\nu _2} - {\nu _0}$.$k{\nu _1} - k{\nu _0} = {\nu _2} - {\nu _0}$.$k{\nu _1} - {\nu _2} = k{\nu _0} - {\nu _0} = {\nu _0}(k - 1)$.Therefore,the threshold frequency is ${\nu _0} = \frac{{k{\nu _1} - {\nu _2}}}{{k - 1}}$.

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

Medium

Photoelectric emission is observed from a metallic surface for frequencies ${\nu _1}$ and ${\nu _2}$ of the incident light rays $({\nu _1} > {\nu _2})$. If the maximum values of kinetic energy of the photoelectrons emitted in the two cases are in the ratio of $1:k$,then the threshold frequency of the metallic surface is

A
$\frac{{\nu _1 - \nu _2}}{{k - 1}}$
B
$\frac{{k\nu _1 - \nu _2}}{{k - 1}}$
C
$\frac{{k\nu _2 - \nu _1}}{{k - 1}}$
D
$\frac{{\nu _2 - \nu _1}}{k}$

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Class 12

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Chapter

Dual Nature of Radiation and matter

Subtopic

Einstein's Photoelectric Equation and Energy Quantum of Radiation

$A$ Hydrogen-like atom has atomic number $Z$. Photons emitted in the electronic transitions from level $n=4$ to level $n=3$ in these atoms are used to perform a photoelectric effect experiment on a target metal. The maximum kinetic energy of the photoelectrons generated is $1.95 \ eV$. If the photoelectric threshold wavelength for the target metal is $310 \ nm$,the value of $Z$ is:

MediumIIT 2023

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The stopping potential for photoelectrons emitted from a surface illuminated by light of wavelength $6630 \; \mathring{A}$ is $0.42 \; V$. If the threshold frequency is $x \times 10^{13} \; s^{-1}$,where $x$ is ... (nearest integer).
(Given: speed of light $= 3 \times 10^{8} \; m/s$,Planck's constant $= 6.63 \times 10^{-34} \; J \cdot s$)

MediumJEE MAIN 2022

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The energy of a photon with wavelength $\lambda$ is $2 \ eV$. When it strikes a metal surface,the maximum velocity of the emitted photoelectrons is $v$. If the value of $\lambda$ is decreased by $25\%$ and the maximum velocity is doubled,the work function of the metal becomes ...... $eV$.

Medium

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Photoelectric emission is observed from a metallic surface for frequencies $v_1$ and $v_2$ of the incident light $(v_1 > v_2)$. If the maximum values of kinetic energy of the photoelectrons emitted in the two cases are in the ratio $1: n$,then the threshold frequency of the metallic surface is

MediumTS EAMCET 2010

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Light of wavelength $488 \;nm$ is produced by an argon laser which is used in the photoelectric effect. When light from this spectral line is incident on the emitter, the stopping (cut-off) potential of photoelectrons is $0.38 \;V$. Find the work function (in $eV$) of the material from which the emitter is made.

Medium

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The energy of a photon with wavelength $\lambda$ is $2 \ eV$. When it strikes a metal surface,the maximum velocity of the emitted photoelectrons is $v$. If the value of $\lambda$ is decreased by $25\%$ and the maximum velocity is doubled,the work function of the metal becomes ...... $eV$.

Photoelectric emission is observed from a metallic surface for frequencies $v_1$ and $v_2$ of the incident light $(v_1 > v_2)$. If the maximum values of kinetic energy of the photoelectrons emitted in the two cases are in the ratio $1: n$,then the threshold frequency of the metallic surface is

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