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?

Solution

Given,
Power, P (power) = 100 W
Wavelength of sodium light, λ = 589 x 10^–9 m

(a) Energy of each photon assosciated with the sodium light,
$E = hv = \frac{hc}{λ} = \frac{6.63 \times 10^{- 34} \times 3 \times 10^{8}}{589 \times 10^{- 9}} J$

$\Rightarrow$ $E = 3.38 \times 10^{- 19} J$

(b) Number of photons delivered to sphere per second,
As, P= nE

$n = \frac{Energy radiated per second}{Energy of each proton}$

$n = \frac{100}{3.38 \times 10^{- 19}} = 3 \times 10^{20} photon / s .$

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