How many photons/s are contained in a beam of electromagnetic radiation of total power 180 W if the source is (a) an AM radio station of 1100 kHz, (b) 8.0-nm x rays, and (c) 4.0-MeV gamma rays?

a) No. of photons/s = 246961 x

b) No. of photons/s = 72.43 x

c) No. of photons/s = 28.125 x

Explanation:

Given total power of electromagnetic radiation = 180 W = 180 j/s

a)Given source of frequency γ = 1100kHz

                                     =1100 x Hz

We know that, Energy of each photon E = hγ

where h = 6.626 x Js is planck's constant

E = 6.626 x x 1100 x

  = 7288.6 x J

Total energy of all photons = 180 j/s

No. of photons =

                         =

                         = 246961 x

b) Given wavelength λ = 8nm

We know that c= γλ

where c=3x m is velocity of light

Therefore, frequency γ = c/λ

                                       =

                                       = 0.375 x

Also we know that E = hγ

                                   = 6.626 x x 0.375 x

                                   = 2.485 x

Hence no. of photons =

                                     = 72.43 x

c) Given Energy of each photon = 4 MeV

We know that 1 Mev = 1.6 x J

Therefore Energy of each photon = 4 x 1.6 x J

                                                        = 6.4 x J

No. of photons =

                         = 28.125 x