The emission spectrum of a black body at two different temperatures are shown by curves `P` and `Q` (as shown in figure). The ratio of the areas under the two curves `P` and `Q` will be

Options

A. `1 : 16`
B. `4 : 9`
C. `81 : 256`
D. `16 : 81`

Answer

D

Explanation

Absolute temperature of the black body corresponding to curve `P` and `Q` are in the inverse ratio `lambda_(m)` (Wein's displament law).
`i.e., (T_P)/(T_Q) = (1987)/(2980)`
Area under curves represent the total power radiated by a body and is proportional of the fourth power of absolute temperature (Stefan'slaw)
`:. (A_P)/(A_Q) = ((T_P)/(T_Q))^(4) = 16/81`.