Question

A $600\, W$ mercury lamp emits monochromatic radiation of wavelength $331.3\, nm$. How many photons are emitted from the lamp per second? ( $ h=6.626\times {{10}^{-34}}Js; $ velocity of light $ =3\times {{10}^{8}}m{{s}^{-1}} $ )

• A. $ 1\times {{10}^{19}} $
• B. $ 1\times {{10}^{20}} $
• C. $ 1\times {{10}^{21}} $
• D. $ 1\times {{10}^{23}} $
• E. $ 1\times {{10}^{22}} $

Answer 1

Answer: (C)

Given, power = 600 W $ \lambda =331.3\text{ }nm=331.3\times {{10}^{-9}}m $
$ h=6.626\times {{10}^{-34}}J $
$ c=3\times {{10}^{8}}m{{s}^{-1}} $
$ t=1\text{ }s $
$ Power=\frac{energy}{time} $
$ =\frac{nhv}{t}=\frac{nhc}{\lambda t} $
or $ n=\frac{power\times \lambda t}{hc} $
$ =\frac{600\times 331.3\times {{10}^{-9}}\times 1}{6.626\times {{10}^{-34}}\times 3\times {{10}^{8}}} $
$ n=1\times {{10}^{21}} $