Dual Nature Of Light Question 235

Question: There are $ n_{1} $ photons of frequency $ {\gamma_{1}} $ in a beam of light. In an equally energetic beam, there are $ n_{2} $ photons of frequency $ {\gamma_{2}} $ . Then the correct relation is [KCET 2003]

Options:

A) $ \frac{n_{1}}{n_{2}}=1 $

B) $ \frac{n_{1}}{n_{2}}=\frac{{\gamma_{1}}}{{\gamma_{2}}} $

C) $ \frac{n_{1}}{n_{2}}=\frac{{\gamma_{2}}}{{\gamma_{1}}} $

D) $ \frac{n_{1}}{n_{2}}=\frac{\gamma _{1}^{2}}{\gamma _{2}^{2}} $

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Answer:

Correct Answer: C

Solution:

$ E=nh\nu \Rightarrow \nu \propto \frac{1}{n}\Rightarrow \frac{n_{1}}{n_{2}}=\frac{{\gamma_{2}}}{{\gamma_{1}}} $ .