A 100 W sodium lamp radiates energy uniformly in all directions .The lamp located at the centre of a large sphere the absorbs all the sodium light which is incident on it.The wavelength of the sodium light 589 nm.(a) what is the energy per photo assosciated with the sodium light? (b)At what rate are the photons delivered to the sphere.

Explanation

Here P=100 W, `lambda=589 nm=589xx10^(-9)m`
`h=6.63xx1-^(-34)Js,c=3xx10^(8)ms^(-1)`
(a) Energy of each photon,
E=hv
`therefore E=(hc)/(lambda)=(6.63xx10^(-34)xx3xx10^(8))/(589xx10^(-9))`
`therefore E=0.033769xx10^(-17)`
`E~~3.38xx10^(-19)J`
`therefore E=(3.38xx10^(-19))/(1.6xx10^(-19))eV`
`therefore` E=2.11 eV
(b)Rate of photon incident on sphere.
`N=(P)/(E)=(100)/(3.38xx10^(-19))`
`therefore N=29.58xx10^(+19)`
`therefore N~~3.0xx10^(20)`photon/second