Two sources of light emit X-rays of wavelength
Question:

Two sources of light emit X-rays of wavelength $1 \mathrm{~nm}$ and visible light of wavelength $500 \mathrm{~nm}$, respectively. Both the sources emit light of the same power $200 \mathrm{~W}$. The ratio of the number density of photons of $\mathrm{X}$-rays to the number densitty of photons of the visible light of the given wavelengths is :

1. $\frac{1}{500}$

2. 500

3. 250

4. $\frac{1}{250}$

Correct Option: 1

Solution:

$P=\frac{n h c}{\lambda t}$

$\therefore \frac{\mathrm{n}_{1}}{\mathrm{n}_{2}}=\frac{\lambda_{1}}{\lambda_{2}}=\frac{1}{5}$