A light source of wavelength λ illuminates a metal surface and...

A light source of wavelength

\lambda

illuminates a metal surface and electrons are ejected with maximum kinetic energy of 2 eV . If the same surface is illuminated by a light source of wavelength

\frac{\lambda}{2}

, then the maximum kinetic energy of ejected electrons will be (The work function of metal is 1 eV )

Options

A3 eV
B2 eV
C6 eV
D5 eV

Correct answer

D. 5 eV

Step-by-step solution

Einstein's photoelectric equation

\begin{aligned} & \mathrm{KE}=\frac{h c}{\lambda}=\phi_0 \\ & 2 \mathrm{eV}=\frac{h c}{\lambda}-1 \mathrm{eV} \\ & \frac{h c}{\lambda}=3 \mathrm{eV} \\ & \mathrm{KE}^{\prime}=\frac{h c}{(\lambda / 2)}-\phi_0=6 \mathrm{eV}-1 \mathrm{eV} \end{aligned}

=5 \mathrm{eV}$

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