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
B. 2.5
C. 4
D. 4.5

Answer

C

Explanation

Given `T_(A) = 4T_(B)` …(i)
`lamda_(m_(B)) - lamda_(m_(A)) = 3.0 mu m` ..(ii)
According to Wien.s law, `lamda_(m)T=` constant
`:. lamda_(m_(A)) T_(A) = lamda_(m_(B)) T_(B) or (lamda_(m_(A)))/(lamda_(m_(B))) = (T_(B))/(T_(A)) = (T_(B))/(4T_(B))` (Using (i))
or `lamda_(m_(A)) = (lamda_(m_(B)))/(4)`
Substituting this value in (ii), we get
`lamda_(m_(B))- (lamda_(m_(B)))/(4) = 3.0 mu m or (3)/(4) lamda_(m_(B)) = 3.0 mu m`
or `lamda_(m_(B)) = 4.0 mu m`