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There are two sources of light, each emitting with a power of $100 W .$ One emits $X - rays$ of wavelength $1 nm$ and the other visible light of $500 nm .$ The ratio of number of photons of $X - rays$ to the photons of visible light of the given wavelength is

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$1 : 500$

$1 : 400$

$1 : 300$

$1 : 200$

answer is A.

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Detailed Solution

Here, $P = 100 W, λ_{1} = 1 nm, λ_{2} = 500 nm$

Let $n_{1} a n d n_{2}$ be the number of photons of $X - rays$ and visible light emitted from the two sources:

$∴ n_{1} \frac{h c}{λ_{1}} = n_{2} \frac{h c}{λ_{2}} \Rightarrow \frac{n_{1}}{λ_{1}} = \frac{n_{2}}{λ_{2}} \Rightarrow \frac{n_{1}}{n_{2}} = \frac{λ_{1}}{λ_{2}} = \frac{1}{500}$

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