The power radiated by a black body is P and it radiates maximum energy at wavelength` lambda_(0)`.If the temperature of the black body is now changed, so that it radiates maximum energy at wavelength `(3)/(4) lambda_(0)`, the power radiated by it becomes nP.The value of n is

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`