JEE Main 2021 · Physics · Atoms, Nuclei and Dual Nature of Radiation · medium

Light of wavelength 200 nm falling on a metal produces photoelectrons whose maximum kinetic energy is three times that obtained with light of…

Numerical answer

Light of wavelength

200\ \mathrm{nm}

falling on a metal produces photoelectrons whose maximum kinetic energy is three times that obtained with light of wavelength

400\ \mathrm{nm}

. Taking

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

, the work function of the metal is

x\times10^{-2}\ \mathrm{eV}

. The value of

x

Show answer and solution

Answer: 155

Photon energies:

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

and

\dfrac{1240}{400}=3.1\ \mathrm{eV}

. Einstein's equation:

6.2-\phi=3(3.1-\phi)\Rightarrow 2\phi=9.3-6.2=3.1\Rightarrow\phi=1.55\ \mathrm{eV}=155\times10^{-2}\ \mathrm{eV}

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