A body emits maximum energy at 4253 `Å` and the same body at some other temperature emits maximum energy at 2342 `Å`. Find the ratio of the maximum energy radiated by the body in a short wavelength range.

Explanation

If `E_(1)` and `E_(2)`are the maximum energy radiated by the body in short wavelength interval at temperature `T_(1)` and `T_(2)` then according to Wein's fifth power law, we have
`(E_(1))/(E_(2))=((T_(1))/(T_(2)))^(5)` ….(4.67)
According to Wein's displacement law, we have
`lambda_(m1)T_(1) = lambda_(m2)T_(2)`
or `(T_(1))/(T_(2)) =(lambda_(m2))/(lambda_(m1))` ...(4.68)
Here `lambda_(m1)` and `lambda_(m2)` are the wavelength at temperatures `T_(1)` and `T_(2)` at which the energy radiated in a small internal of wavelength is maximum.
Now from equation-(4.67) and (4,68), we have
`(E_(1))/(E_(2))=((lambda_(m2))/(lambda_(m1)))^(5)`
or `(E_(1))/(E_(2)) =((234 xx 10^(-10))/(4253 xx 10^(-10)))^(5) = 0.0506`