JEE (Advanced) 2017 Paper-2 Question 3

Question 3

A photoelectric material having work-function $$\phi_{0}$$ is illuminated with light of wavelength $$\lambda (\lambda < \frac{hc}{\phi_{0}})$$. The fastest photoelectron has a de Broglie wavelength $$\lambda_{d}$$. A change in wavelength of the incident light by $$\triangle \lambda$$ results in a change $$\triangle \lambda_{d}$$ in $$\lambda_{d}$$. Then the ratio $$\frac{\triangle\lambda_{d}}{\triangle\lambda}$$ is proportional to

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