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?
(a) Energy of photon E = hv = hc/λ
Where h = plank’s constant = 6.63 × 10-34 J. sec
ν = frequency of light
c = speed of light = 3 × 108 m/s
λ = wavelength of light
E = 6.63 × 10-34 × 3 x108 / 589 × 10-9
= 3.38 × 10-19 J
Energy of a photon is equal to 3.38 × 10-19 J.
(b) Rate of photon falling on the sphere = power of lamp/energy per photon
∴ Rate of photon = 100 / 3.38 × 10-19J = 3.0 × 1020 photons/sec.
Rate at which photons are falling on the sphere is equal to 3.0 × 1020 photons/sec.