Example: 

the microwave radiation has a frequency of 12 gigahertz.

a)   What will be the energy of the photon corresponding to this radiation?

b)   Compute the wavelength of the radiation.

(h = 6.626 × 10 ^-34 J s   and 1 gigahertz = 10⁹ Hz)

Solution:

The energy of radiation is related to the frequency as,

E = hν

Substituting the values of frequency and Planck's constant, we get

E = 6.626 ×10^-34 Js ×1.2 ×10¹⁰ s^-1 = 7.95 ×10^-24 J

∴The energy of the photon having a frequency of 12 gigahertz = 7.95 × 10 ^-24 J

Further, since  E = h( c/λ) we can rearrange the equation to get

λ = E/hc

Substituting the values of E, h and c we get

λ =       7.95 × 10^-24 J/6.626 × 10^-34 J s × 3.0 × 10⁸ m s ^-1 =  400 nm

∴The wavelength of the radiation = 400 nm