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 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 x 10^-9 m

Planck’s constant, h = 6.626 x 10^–34Js

Speed of light, c = 3 x 10⁸ m/s

Ans (a).

The energy per photon associated with the sodium light is given as:

E = hc/λ = (6.626 x 10^–34) x (3 x 10⁸) /(589 x 10^-9)  = 3.37 x 10^-¹⁹J

= (3.37 x 10^-¹⁹)/(1.6 x 10⁻¹⁹ )

=2.11 eV

Ans (b).
Number of photons delivered to the sphere = n.

The equation for power can be written as: P = nE

=> n = P/E= (100)/ (3.37 x 10^-¹⁹) = 2.96 x 10²⁰photons/s

Therefore, every second, 2.96 x 10²° photons are delivered to the sphere.