First slide

Photoelectric effect and study of photoelectric effect

Question

When radiation of wavelength $λ$ is used to illuminate a metallic surface, the stopping potential is V. When the same surface is illuminated with radiation of wavelength 3 $λ$ , the stopping potential is $\frac{V}{4}$ . If the threshold wavelength for the metallic surface is $n λ$ ,then value of n will be

Moderate

Solution

$\begin{array}{l} \begin{array}{l} e V = \frac{h c}{λ} - ϕ \\ \frac{e V}{4} = \frac{h c}{3 λ} - ϕ \end{array}\} solving \\ \frac{h c}{λ} - ϕ = 4 (\frac{h c}{3 λ} - ϕ) \\ \Rightarrow ϕ = \frac{h c}{9 λ} \\ \Rightarrow \frac{h c}{λ_{0}} = \frac{h c}{9 λ} \\ \Rightarrow λ_{0} = 9 λ \end{array}$

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