A black body is at a temperature of `5760 K`. The energy of radiation emitted by the body at wavelength `250 nm` is `U_(1)` at wavelength `500 nm` is `U_(2)` and that at `1000 nm` is `U_(3)`. Wien's consant, `b = 2.88 xx 10^(6) nmK`. Which of the following is correct?

Options

A. `U_(3)` = 0
B. `U_(1)gtU_(2)`
C. `U_(2)gtU_(1)`
D. `U_(1) = 0`

Answer

C

Explanation

c) Given, temperature , `T_(1)=57600K`
Since, it is given that energy of radiation emitted by the body at wavelength 250 nm is `U_(1)`, at wavelength 500nm is `U_(2)` and that at 1000 nm is `U_(3)`.
`therefore`According to Wien's law, we get
`lambda_(m)T`=b
where, b = Wien's constant = `2.88 xx 10^(6)` nmK
`rArr lambda_(m)=b/T` `rArr lambda_(m) = (2.88 xx 10^(6)nmK)/(5760K)rArr lambda_(m)`=500 nm
`therefore lambda_(m)=b/T rArr lambda_(m) = (2.88 xx 10^(6))/(5760K)` `rArr lambda_(m)` = 500 nm
`therefore` `lambda_(m)` = wavelength corresponding to maximum energy, so, `U_(2)gtU_(1)`.