Question

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

• A. $1:500$
• B. $1:400$
• C. $1:300$
• D. $1:200$

Answer 1

Answer: (A)

Here, $P=100W,{\lambda }_1=1nm,{\lambda }_2=500nm$
Let $n_1$ and $n_2$ be the number of photons of $X$-rays and visible light emitted from the two sources
$\therefore n_1\frac{hc}{{\lambda }_1}=n_2\frac{hc}{{\lambda }_2}$ or $\frac{n_1}{{\lambda }_1}=\frac{n_2}{{\lambda }_2}$ or $\frac{n_1}{n_2}=\frac{{\lambda }_1}{{\lambda }_2}=\frac{1}{500}$