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 at $500nm$. Find the ratio of number of photons of $X-rays$ to the photons of visible light of the given wavelength?

Answer 1

Given, power of the source, $P=100W$
Wave length of $X-rays$, ${\lambda }_1=1nm$
Wavelength of visible light, ${\lambda }_1=500nm$
Let $n_1$ be the number of photons of X-ray and $n_2$ be the number of photons of visible region.
Since we know, each photon has energy
$E=\frac{hc}{\lambda }$
As power is constant, so total energy will be constant.
$n_1{E}_1=n_2{E}_2$
$\frac{n_{1}hc}{{\lambda }_1}=\frac{n_{2}hc}{{\lambda }_2}$
$\frac{n_1}{n_2}=\frac{{\lambda }_1}{{\lambda }_2}=\frac{1}{500}$
Final Answer: $\frac{1}{500}$