The power radiated by a black body is P, and it radiates maximum energy around the wavelength `lambda_(0)`. If the temperature of the black body is now changed so that it radiates maximum energy around a wavelength `3lambda_(0)//4`, the power radiated by it will increase by a factor of

Options

A. `256/81 P`
B. `27/64 P`
C. `64/27 P`
D. 81/256 P`

Answer

A

Explanation

According to Wien,s law,
`lambda_(m)T` = constant
or `T alpha 1/(lambda_(m))`
`lambda_(m)` has become `3/4` times.
`therefore` Temperature will have become `4/3` times.
Now, according to Stefan's law, power `PalphaT^(4)`.
Therefore new power will be
`(4/3)^(4)P= 256/81P`