Question

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

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

Answer 1

Answer: (A)

Here, $P = 100 W , \lambda_{1}=1\,nm, \lambda_{2}=500\,nm$
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 $\frac{n_{1}}{n_{2}}=\frac{\lambda_{1}}{\lambda_{2}}=\frac{1}{500}$