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Question

The energy radiated by a black body at 2300 K is found to have maximum intensity at wavelength 1260 nm, its emissive power being 8000 W/m2. When the body is cooled to a temperature T K, the emissive power is found to decrease to 500 W/m2. Find the wavelength at which intensity of emission is maximum at the temperature T.

A
1575 nm
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B
2520 nm
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C
1260 nm
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D
5040 nm
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Solution

The correct option is B 2520 nm
λmax=1260×109 m at T1=2300 K
Also, T2=T K

We know that ET4
E1E2=(T1T2)4T2=T1[E2E1]1/4
T2=2300×[5008000]1/4
T2=2300×12=1150 K
By Wein's law,
T1λ1=T2λ2
λ2=T1λ1T2=2300×1260×1091150
λ2=2520 nm

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