A 100 W 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 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?
Power of the sodium lamp, P = 100 W
Wavelength of the emitted sodium light, λ = 589 nm = 589 × 10−9 m
Planck’s constant, h = 6.626 × 10−34 Js
Speed of light, c = 3 × 108 m/s
(a)The energy per photon associated with the sodium light is given as:
$E=\frac{h c}{\lambda}$
$=\frac{6.626 \times 10^{-34} \times 3 \times 10^{8}}{589 \times 10^{-9}}=3.37 \times 10^{-19} \mathrm{~J}$
$=\frac{3.37 \times 10^{-19}}{1.6 \times 10^{-19}}=2.11 \mathrm{eV}$
(b)Number of photons delivered to the sphere = n
The equation for power can be written as:
$P=n E$
$\therefore n=\frac{P}{E}$
$=\frac{100}{3.37 \times 10^{-19}}=2.96 \times 10^{20}$ photons $/ \mathrm{s}$
Therefore, every second, $2.96 \times 10^{20}$ photons are delivered to the sphere.