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(A) The power of radiation is given by $P = \frac{n h c}{t \lambda}$,where $n$ is the number of photons emitted in time $t$.Let $n'$ be the number of

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$1:500$

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(A) The power of radiation is given by $P = \frac{n h c}{t \lambda}$,where $n$ is the number of photons emitted in time $t$.Let $n'$ be the number of photons emitted per unit time,so $n' = \frac{n}{t}$.Thus,$P = n' \frac{h c}{\lambda}$,which implies $n' = \frac{P \lambda}{h c}$.Since $P$,$h$,and $c$ are constant for both sources,we have $n' \propto \lambda$.Therefore,the ratio of the number of photons is $\frac{n'_1}{n'_2} = \frac{\lambda_1}{\lambda_2}$.Given $\lambda_1 = 1 \, nm$ and $\lambda_2 = 500 \, nm$.Substituting the values,$\frac{n'_1}{n'_2} = \frac{1 \, nm}{500 \, nm} = \frac{1}{500}$.

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 at $500 \, nm$. Find the ratio of the number of photons of $X$-rays to the photons of visible light of the given wavelength.

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