Question

A $600W$ mercury lamp emits monochromatic radiation of wavelength $331.3nm$. 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 $\lambda =331.3nm=331.3\times {10}^{-9}m$
$h=6.626\times {10}^{-34}J$
$c=3\times {10}^{8}m{s}^{-1}$
$t=1s$
$Power=\frac{energy}{time}$
$=\frac{nhv}{t}=\frac{nhc}{\lambda t}$
or $n=\frac{power\times \lambda t}{hc}$
$=\frac{600\times 331.3\times {10}^{-9}\times 1}{6.626\times {10}^{-34}\times 3\times {10}^8}$
$n=1\times {10}^{21}$