Question

A monochromatic source of light operating at 198 W emits $4\times {10}^{20}$ photons per second. Find the wavelength of light in nm.(Take $h=6.6\times {10}^{-34}Js$)

Answer 1

Energy of single photon $=\frac{hc}{\lambda }$
If there are n photons, total energy $=\frac{nhc}{\lambda }$
power, $P=\frac{E}{t}=198W$
$E=energy$, $t=time$
since $t=1s$, $P=E$ (total )
Total energy emitted = 198 W
Equating
$\frac{nhc}{\lambda }=198$
$n=\frac{198\lambda }{hc}$
By substituting values:
$4\times {10}^{20}=\frac{198\times \lambda }{6.6\times {10}^{-34}\times (3\times {10}^8)}$
$\lambda =400\text{nm}$