First slide

Radiation

Question

A black body radiates maximum energy at wavelength $λ$ when its temperature is T. Now temperate of the black body is increased by 50%. Then the percentage change in wavelength at which the black body will radiate maximum energy is

Moderate

A

17.67%
B

33.33%
C

23.12%
D

25%

Solution

(2)
By Wien's displacement Law,
$\begin{array}{l} T^{'} λ^{'} = T λ \Rightarrow λ^{'} = \frac{T}{T^{'}} . λ = \frac{T}{1.5 T} \times λ = \frac{2 λ}{3} . \\ ∴ D e c r e a s e i n w a v e l e n g t h = \frac{λ - λ^{'}}{λ} \times 100 % = 33.33 % \end{array}$

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