The power radiated by a black body is 'P' and it radiates maximum energy around the wavelength `lmbda_(0)` If the temperature of the black body is now changed so that it raddiates maximum energy around a wavelength
`lambda_(0)//2` the power radiated becomes .

Options

A. `(3)/(4)`
B. `(4)/(3)`
C. `(256)/(81)`
D. `(81)/(256)`

Answer

C

Explanation

From Wien.s law, `lamda_("max")T`= constant
So, `lamda_("max"_(1)) T_(1) = lamda_("max"_(2)) T_(2)`
`rArr lamda_(0) T = (3 lamda_(0))/(4)T. rArr (T.)/(T) = (4)/(3)` …(i) According to Stefan.-Boltzmann law, energy emitted per unit time by a black body is `A e sigma T^(4)` , i.e, power radiated.
`:. P prop T^(4)`
So, `(P_(2))/(P_(1)) = ((T.)/(T))^(4) rArr n = ((4)/(3))^(4) = (256)/(81)`