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 X-rays to the number density of photons of the visible light of the given wavelengths is :
Correct Option: 1
(1) Given,
Wavelength of X-rays, $\lambda_{1}=1 \mathrm{~nm}=1 \times 10^{-9} \mathrm{~m}$
Wavelength of visible light, $\lambda_{2}=500 \times 10^{-9} \mathrm{~m}$
The number of photons emitted per second from a source of monochromatic radiation of wavelength $\lambda$ and power $P$ is given as
$n=\frac{P}{E}=\frac{P}{h v}=\frac{P \lambda}{h c}$ $\left(\because \mathrm{E}=\right.$ h $v$ and $\left.v=\frac{\mathrm{c}}{\lambda}\right)$
$\Rightarrow$ Clearly $n \propto \lambda$
$\Rightarrow \frac{n_{1}}{n_{2}}=\frac{\lambda_{1}}{\lambda_{2}}=\frac{1}{500}$
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