MHT CET · Physics · Dual Nature of Matter
When a metal surface is illuminated by light of wavelength \(\lambda_1\) and \(\lambda_2\), the maximum velocities of photoelectrons ejected are V and 2 V respectively. The work function of the metal is ( \(h=\) Planck's constant, \(c=\) velocity of light, \(\left.\lambda_1>\lambda_2\right)\)
- A \(\frac{\mathrm{hc}}{2 \lambda_1 \lambda_2}\left(\lambda_1-\lambda_2\right)\)
- B \(\frac{\mathrm{hc}}{\lambda_1 \lambda_2}\left(\lambda_1-\lambda_2\right)\)
- C \(\frac{\mathrm{hc}}{\lambda_1 \lambda_2}\left(\lambda_1+\lambda_2\right)\)
- D \(\frac{\mathrm{hc}}{3 \lambda_1 \lambda_2}\left(4 \lambda_2-\lambda_1\right)\)
Answer & Solution
Correct Answer
(D) \(\frac{\mathrm{hc}}{3 \lambda_1 \lambda_2}\left(4 \lambda_2-\lambda_1\right)\)
Step-by-step Solution
Detailed explanation
\(\frac{hc}{\lambda_1} = \phi + \frac{1}{2}mV^2\) \(\frac{hc}{\lambda_2} = \phi + \frac{1}{2}m(2V)^2 = \phi + 2mV^2\)
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