A black body at $1227^\circ ext{C}$ emits radiations with maximum intensity at a wavelength of $5000 ext{ \

Question

A black body at $1227^\circ	ext{C}$ emits radiations with maximum intensity at a wavelength of $5000 	ext{ \AA}$. If the temperature of the body is increased by $1000^\circ	ext{C}$, the maximum intensity will be observed at:

Accepted Answer

According to Wien's displacement law, the product of the wavelength corresponding to maximum intensity ($\lambda_m$) and the absolute temperature ($T$) is constant: $\lambda_m T = 	ext{constant}$.
Given initial temperature, $T_1 = 1227^\circ	ext{C} = 1227 + 273 = 1500 	ext{ K}$.
Initial wavelength, $\lambda_1 = 5000 	ext{ \AA}$.
The temperature is increased by $1000^\circ	ext{C}$, so the new absolute temperature is $T_2 = 1500 	ext{ K} + 1000 	ext{ K} = 2500 	ext{ K}$.
Using the relation $\lambda_1 T_1 = \lambda_2 T_2$:
$\lambda_2 = \frac{\lambda_1 T_1}{T_2} = \frac{5000 	imes 1500}{2500} = 2 	imes 1500 = 3000 	ext{ \AA}$.

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