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?

Options

A. `(1)/(200)`
B. `(1)/(300)`
C. `(1)/(400)`
D. `(1)/(500)`

Answer

D

Explanation

Power of a source `=P=` Nhv where N is the number of photons emitted. Let `N_(1)` and `N_(2)` be the number of photons of X-rays and visible light, emitted from the two sources . For both sources P is the same.
`:.` For X-rays, `P=N_(1)hv_(1)=(N_(1)h*C)/(lambda_(1))`
and for visible light, `P=(N_(2)hC)/(lambda_(2))`
`:.(N_(1)hc)/(lambda_(1))=(N_(2)hC)/(lambda_(2))`
`:.(N_(1))/(N_(2))=(lambda_(1))/(lambda_(2))=(1nm)/(500nm)=(1)/(500)`