The black body spectrum of an object `O_(1)` is such that its radiant intensity (i.e. intensity per unit wavelength interval) is maximum at a wavelength of 200 nm. Another object `O_(2)` has the maximum radiant intensity at 600 nm. The ratio of power emitted per unit area by source `O_(1)` to that of source `O_(2)` is

Options

A. `1 : 81`
B. `1 : 9`
C. `9 : 1`
D. `81 : 1`

Answer

D

Explanation

From Wien's Displacement law,
`lambda_(m) T=b=` constant or `lambda_(m) =(b)/(T)`
From stefa's law, `E prop T^(4)` ltbgt `:. (E_(1))/(E_(2)) = (T_(1)^(4))/(T_(2)^(4)) = (lambda_(m2)^(4))/(lambda_(m1)^(4)) = ((600)^(4))/((2000)^(4)) = (81)/(1)`