A 100W light bulb giving monochromatic light of wavelength `6000A^(@)` is placed at the centre of a spherical chamber of radius 0.20m. Assume that 50% of the energy supplied to the bulb is converted into light and that the surface of the chamber is perfectly absorbing. Find (i) the energy and momentum of each photon in the light beam.
(ii) How many photons per second, on the average arrive at the surface of spherical chamber, and
(iii) The pressure exerted by the light on the surface of the chamber. Given, `h=6.6xx10^(-34)Js`.

Explanation

Here, `lambda=6000A^(@)=6000xx10^(-10)m=6xx10^(-7)m, r=0.20m`
(i) Energy of each photon `=(hc)/lambda=((6.63xx10^(-34))xx(3xx10^(8)))/(6xx10^(-7))=3.3xx10^(-19)J`
Momentum of each photon `=h/lambda=(6.6xx10^(-34))/(6xx10^(-7))=1.1xx10^(-24)kgms^(-1)`
(ii) Energy of light emitted by the bulb per second `E=100xx50/100=50watt`
Number of photons reaching the surface per second =`("light en ergy falli ng per second")/("energy of each photon")=50/(3.3xx10^(-19))=1.51xx10^(20)`
(iii) Momentum of light falling per second on the surface of sphere `=E/c`
As the light is completely absorbed, the momentum per sec. of the reflected light is zero. The force exerted by light on the surface is equal to change in momentum of light per second
`=E/c-0=E/c`
Pressure on surface `=force /area=(E//c)/(4pir^(2))=(50//(3xx10^(8)))/(4xx(22//7)xx(0.2)^(2))=3.31xx10^(-7)Pa`