The absolute temperature of a body X is 4 times that of body Y. For X and Y, the difference in wavelength at which enrgy radiated is maximum is `3mum`. What is the wavelength (in `mum`) at which the body Y radiates maximum energy ?

Options

A. `2 mum`
B. `3 mum`
C. `4 mum`
D. `5 mum`

Answer

C

Explanation

Given : `T_(X)=4T_(Y)" "...(1)`
`(lamda_(m))_(Y)-(lamda_(m))_(X)=3mum" "...(2)`
`[becauseT_(X)gtT_(Y),(lamda_m)_(Y)gt(lamda_(m))_(X)]`
`(because` As per Wien's law `lamda_(m)`T = constant)
`therefore(lamda_(m))_(X)T_(X)=(lamda_(m))_(Y)T_(Y)`
`therefore(lamda_(m))_(X)/(lamda_(m))_(Y)=T_(Y)/T_(X)=T_(Y)/(4T_(Y))" "..."from"(1)`
`therefore(lamda_(m))_(X)=(lamda_(m))_(Y)/4" "...(3)`
Using (3) in (2), we get,
`(lamda_(m))_(Y)-(lamda_(m))_(Y)/4=3`
`therefore3/4(lamda_(m))_(Y)=3`
`therefore(lamda_(m))_(Y)=4mum`