JEE Main 2022 · Physics · Atoms, Nuclei and Dual Nature of Radiation · medium

Light of wavelength 300 nm incident on a metal surface gives photoelectrons with maximum kinetic energy K1. When wavelength 200 nm is used, the…

Single correct option

Light of wavelength

300\ \mathrm{nm}

incident on a metal surface gives photoelectrons with maximum kinetic energy

K_1

. When wavelength

200\ \mathrm{nm}

is used, the maximum kinetic energy is

K_2=2K_1

. Taking

hc=1240\ \mathrm{eV\,nm}

, the work function of the metal is nearly

Show answer and solution

Answer: (B) $2.07\ \mathrm{eV}$

Photon energies:

E_1=\dfrac{1240}{300}=4.133\ \mathrm{eV}

and

E_2=\dfrac{1240}{200}=6.2\ \mathrm{eV}

. Einstein's equation gives

K_1=E_1-\phi

and

K_2=E_2-\phi

. With

K_2=2K_1

6.2-\phi=2(4.133-\phi)=8.267-2\phi

, so

\phi=8.267-6.2=2.067\ \mathrm{eV}

. This equals

\dfrac{1240}{600}

, i.e. the threshold wavelength is

600\ \mathrm{nm}

. The check

K_1=2.07\ \mathrm{eV}

K_2=4.13\ \mathrm{eV}

confirms the ratio.

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