Question

A $100W$ sodium lamp radiates energy uniformly in all directions. The lamp is located at the centre of a large sphere that absorbs all the sodium light which is incident on it. The wavelength of the sodium light is $589nm$. The number of photons delivered per second to the sphere is

• A. $3\times {10}^{15}$
• B. $3\times {10}^{10}$
• C. $3\times {10}^{20}$
• D. $3\times {10}^{19}$

Answer 1

The correct option is C $3\times {10}^{20}$

Here, $\lambda =589\times {10}^{-9}m,h=6.63\times {10}^{-34}Js$
$P=100W$
Energy of a photon,
$E=\frac{hc}{\lambda }=\frac{6.63\times {10}^{-34}\times 3\times {10}^8}{589\times {10}^{-9}}$

Number of photons deliverved per second
$n=\frac{P}{E}=\frac{100}{3.38\times {10}^{-19}}=3\times {10}^{20}$