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Question:

The black body spectrum of an object O1 is such that its radiant intensity (i.e., intensity per unit wavelength interval) is maximum at a wavelength of 200 nm. Another object O2 has the maximum radiant intensity at 600 nm. The ratio of power emitted per unit area by source O1 to that of source O2 is?

81 : 1

9 : 1

1 : 81

1 : 9

Solution:

The wavelength of peak of blackbody spectrum is related to the temperature by:
λmaxT=k
where k is a constant.
Hence
λ1T1=k and λ2T2=k
Power emitted per unit area ∝T⁴
Therefore
I1/I2 = T⁴₁/T⁴₂ = λ⁴₂/λ⁴₁ = (600/200)⁴ = 3⁴ = 81