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:

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

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

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