Question

A 100W sodium lamp radiates energy uniformly in all directions. The lamp is located at the center of a large sphere that absorbs all the sodium light which is incident on it. The wavelength of the sodium light is 589 nm.

(a) What is the energy per photon associated with the sodium light?

(b) At what rate are the photons delivered to the sphere?

Answer 1

(a) $\lambda =589\times {10}^{-9}m$

Energy per photon is given by, $E=\frac{hc}{\lambda }$

$E=\frac{6.6\times {10}^{-34}\times 3\times {10}^{-8}}{589\times {10}^{-9}}$

$=3.37\times {10}^{-19}J$ or $2.11eV$.

(b) $P=100W$

Let $n$ no. of photons delievered to this sphere.

So, $P=nE$

$\Rightarrow n=\frac{100}{3.37\times {10}^{-19}}=2.96\times {10}^{20}photon/second$