Ncert Exercises & Solutions

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

Hint: The energy of photons depends on the wavelength of the rays.

Step 1: Find the ratio of photons.

Suppose the wavelength of X-rays is $λ_{1}$ , and the wavelength of visible light is $λ_{2}$ .

$G i v e n, P = 100 W$
$λ_{1} = 1 n m$
$a n d λ_{2} = 500 n m$

Also, $n_{1} a n d n_{2}$ represents the number of photons of X-rays and visible light emitted from the two sources per sec.

$\begin{array}{l} S o, \frac{E}{t} = P = n_{1} \frac{h c}{λ_{1}} = n_{2} \frac{h c}{λ_{2}} \\ \Rightarrow \frac{n_{1}}{λ_{1}} = \frac{n_{2}}{λ_{2}} \\ \Rightarrow \frac{n_{1}}{n_{2}} = \frac{λ_{1}}{λ_{2}} = \frac{1}{500} \end{array}$

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