A 100W 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 the sodium light is 589nm. (a) What is energy associated per photon with the sodium light? (b) At what rate are photons delivered to the sphere?

Explanation

Power of the sodium lamp, P=100 W
Wavelength of the emitted sodium light , `lambda`=589 nm = `589xx10^(-9)`m
Planck's constant, h=`6.626xx10^(-34) Js`
Speed of light, `c=3xx10^8` m/s
(a)The energy per photon associated with the sodium light is given as : `E=(hc)/lambda`
`=(6.626xx10^(-34)xx3xx10^8)/(589xx10^(-9))=3.37xx10^(-19) J`
`=(3.37xx10^(-19))/(1.6xx10^(-19))=2.11 eV`
(b)Number of photons delivered to the sphere = n
The equation for power can be written as : P=nE
`therefore n=P/E`
`=100/(3.37xx10^(-19))=2.96xx10^20` photons/s
Therefore, every second, `2.96xx10^20` photons are delivered to the sphere.