Question 11.7: A 100 W 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 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?

Hint: \(E = {hc \over \lambda}\)

Step 1: Find the energy per photon.
The energy per photon associated with the sodium light is given as:

E=hcλ=6.626×1034×3×108589×109=3.37×1019J=3.37×10101.6×1019= 2.11eV

P = nE
Step 1: Find the number of photons.
Number of photons delivered to the sphere = n.
The equation for power can be written as: P = nE
\(\Rightarrow~n=\frac{P}{E} =\frac{100}{3.37\times 10^{-19}}=2.96\times10^{20}~per~ sec.\)