First slide

Photo Electric Effect

Question

The threshold wavelength of a metal surface is 500 nm. V is the maximum velocity of photo electrons when the wavelength of incident light is 400 nm. If the maximum velocity of photo electrons from the same metal surface is 2V, the wavelength of incident light is

Moderate

A

350 nm
B

300 nm
C

250 nm
D

200 nm

Solution

$\begin{array}{l} \frac{1}{2} m V^{2} = h c (\frac{1}{λ} - \frac{1}{λ_{0}}) \\ \begin{array}{l} {(\frac{V_{1}}{V_{2}})}^{2} = \frac{(\frac{1}{λ_{1}} - \frac{1}{λ_{0}})}{(\frac{1}{λ_{2}} - \frac{1}{λ_{0}})} \\ {(\frac{1}{2})}^{2} = \frac{(\frac{1}{400} - \frac{1}{500})}{(\frac{1}{λ_{2}} - \frac{1}{500})} \\ \frac{1}{λ_{2}} = \frac{1}{100} - \frac{3}{500} \\ λ_{2} = 250 nm \end{array} \end{array}$

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