A parallel beam of uniform, monochromatic light of wavelength $2640Å$ has an intensity of $100 {\mathrm{Wm}}^{-2}$. The number of photons in $1m{m}^3$ of this radiation is

If there are n photons in a portion of the light beam of length $l$ and cross sectional area $A$, then intensity i.e., energy flowing through per unit time per unit cross sectional area, is

  $I=\frac{n\left({\displaystyle \frac{hc}{\lambda }}\right)}{A\left({\displaystyle \frac{l}{c}}\right)}=\frac{nh{c}^2}{Al\lambda }$.

Hence number of photons per unit volume

$\frac{n}{Al}=\frac{I\lambda }{h{c}^2}=\frac{\left(100\right)\times \left(2640\times {10}^{-10}\right)}{\left(6.63\times {10}^{-34}\right)\times {\left(3\times {10}^8\right)}^2}=4.42\times {10}^{11} {\mathrm{m}}^{-3}=442 {\mathrm{mm}}^{-3}$.