MCQ on Wien’s Law

The following question on Wien’s law is a typical one and is of the type often found in Medical and Engineering Entrance test papers:

A black body emits radiations of maximum intensity for the wave length of 7000Ǻ, when the temperature of the body is 3927ºC. If the temperature of the body is increased by 1000ºC, the maximum intensity would be observed at nearly

(a) 3650Ǻ (b) 4650Ǻ (c) 5650Ǻ

(d) 6000Ǻ (e) 6650Ǻ

The wave length λ_m corresponding to the maximum intensity emission from a black body at a temperature T is given by Wien’s law,

λ_mT = constant [= 0.29 cm K, if you express λ_m in cm].

In other words, λ_m1T₁ = λ_m2T₂

[Remember, you have to substitute the absolute (Kelvin) temperatures in this equation].

Therefore, 7000×4200 = λ_m2×5200, from which λ_m2 =5650Ǻ, nearly.

[For question setters: When a question is set using Wien’s law, it should be remembered that the product λ_mT satisfies the condition, λ_mT = 0.29 cmK, if λ_m is expressed in cm. I write this because I have seen questions in which this point is ignored]