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

Given , power of the lamp , P = 100 W
Wavelength of light , `lamda=589 nm`
`=589xx10^(-9)m`
(a) Energy per photon is given by
`E=hv = (hc)/lamda`
`=(6.62xx10^(-34)xx3xx10^8)/(589xx10^(-9))`
`=3.38xx10^(-19)J`
`=(3.38xx10^(-19))/(1.6xx10^(-19))=2.11eV`.
(b) Number of photons incident per second is
`n=p/E=(100)/(3.38xx10^(-19))`
`2.96xx10^(20)`
`=3xx10^(20)` photons/s .