First slide

Photoelectric effect and study of photoelectric effect

Question

The surface of a metal is illuminated alternately with photons of energies $E_{1}$ = 4 eV and $E_{2}$ = 2.5 eV respectively. The ratio of maximum speeds of the photoelectrons emitted in the two cases is 2. The work function of the metal in (eV) is _____.

Moderate

Solution

$\begin{array}{l} C a s e (i) : \frac{1}{2} m v_{1}^{2} = 4 - ϕ \\ C a s e (i i) : \frac{1}{2} m v_{2}^{2} = 2.5 - ϕ \\ a n d \\ G i v e n : \frac{v_{1}}{v_{2}} = \frac{2}{1} \\ \Rightarrow \sqrt{\frac{4 - ϕ}{2.5 - ϕ}} = 2 \\ \Rightarrow 4 - ϕ = 10 - 4 ϕ \\ \Rightarrow ϕ = 2 e V \end{array}$

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