When photons of wavelength λ₁ are incident on an isolated sphere, the… | JEE Main 2016 (9 Apr, Shift 1)

Q144JEE Main 2016 · 9 APR · SHIFT 1Difficult

Photoelectric Effect: Einstein's Equation

When photons of wavelength $\lambda_1$ are incident on an isolated sphere, the corresponding stopping potential is found to be V. When photons of wavelength $\lambda_2$ are used, the corresponding stopping potential was thrice that of the above value. If light of wavelength $\lambda_3$ is used then find the stopping potential for this case:

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Answer: (c)

$eV = \frac{hc}{\lambda_1} - \phi$ and $3eV = \frac{hc}{\lambda_2} - \phi$ .
Subtract: $eV = \frac{hc}{2}\left(\frac{1}{\lambda_2} - \frac{1}{\lambda_1}\right)$ , so $\phi = \frac{hc}{\lambda_1} - eV = hc\left(\frac{3}{2\lambda_1} - \frac{1}{2\lambda_2}\right)$ .
$V_3 = \frac{1}{e}\left(\frac{hc}{\lambda_3} - \phi\right) = \frac{hc}{e}\left[\frac{1}{\lambda_3} + \frac{1}{2\lambda_2} - \frac{3}{2\lambda_1}\right]$
So the answer is (c).

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Photoelectric Effect: Einstein's Equation question from JEE Main 2016 (9 Apr, Shift 1)

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