First slide

Photoelectric effect and study of photoelectric effect

Question

At an incident radiation frequency of v₁, which is greater than the threshold frequency, the stopping potential for a certain metal is V₁. At frequency 2v₁, the stopping potential is 3V₁. If the stopping potential at frequency 4v₁ is n V₁, then n is ………

Moderate

Solution

According to Einstein's equation, $hv = {hv}_{0} + eV$
$\Rightarrow V = \frac{h}{e} (v - v_{0})$
Given $V_{1} = \frac{h}{e} (v_{1} - v_{0}) and 3 V_{1} = \frac{h}{e} (2 v_{1} - v_{0})$
$\begin{array}{l} \Rightarrow \frac{3 V_{1}}{V_{1}} = \frac{2 v_{1} - v_{0}}{v_{1} - v_{0}} \Rightarrow v_{1} = 2 v_{0} \\ ∴ V_{1} = \frac{h}{e} (2 v_{0} - v_{0}) = \frac{h}{e} v_{0} \end{array}$
At frequency $4 v_{1}, {nV}_{1} = \frac{h}{e} (4 v_{1} - v_{0})$
$= \frac{h}{e} (8 v_{0} - v_{0}) = 7 \times \frac{h}{e} v_{0}$
$\Rightarrow {nV}_{1} = 7 V_{1} \Rightarrow n = 7$

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