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A black body at $1227^\circ C$ emits radiations with maximum intensity at a wavelength of 5000 Å. If the temperature of the body is increased by $1000^\circ C$, the maximum intensity will be observed at :-
A
4000 Å
B
5000 Å
C
6000 Å
D
3000 Å
Detailed Solution
By Wien's displacement law, $\lambda_m T = b$ (constant), with $T$ in kelvin.
Initial temperature: $T_1 = 1227 + 273 = 1500$ K
Final temperature: $T_2 = 1500 + 1000 = 2500$ K (a rise of $1000^\circ C$ is a rise of 1000 K)
$\lambda_m T_1 = \lambda'_m T_2$
$(5000)(1500) = (\lambda'_m)(1500 + 1000)$
$\Rightarrow \lambda'_m = \dfrac{(5000)(1500)}{2500}$
$\lambda'_m = 3000$ Å
Initial temperature: $T_1 = 1227 + 273 = 1500$ K
Final temperature: $T_2 = 1500 + 1000 = 2500$ K (a rise of $1000^\circ C$ is a rise of 1000 K)
$\lambda_m T_1 = \lambda'_m T_2$
$(5000)(1500) = (\lambda'_m)(1500 + 1000)$
$\Rightarrow \lambda'_m = \dfrac{(5000)(1500)}{2500}$
$\lambda'_m = 3000$ Å