A black body is at a temperature of $5760 ext{ K}$. The energy of radiation emitted by the body at a waveleng

Question

A black body is at a temperature of $5760	ext{ K}$. The energy of radiation emitted by the body at a wavelength of $250	ext{ nm}$ is $U_1$, at a wavelength of $500	ext{ nm}$ is $U_2$ and that at $1000	ext{ nm}$ is $U_3$. Given Wien's constant $b=2.88 	imes 10^6	ext{ nm K}$, which of the following is correct?

Accepted Answer

According to Wien's displacement law, the wavelength $\lambda_m$ corresponding to maximum energy emission is given by $\lambda_m = \frac{b}{T}$.
Given $b = 2.88 	imes 10^6	ext{ nm K}$ and $T = 5760	ext{ K}$:
$\lambda_m = \frac{2.88 	imes 10^6}{5760} = 500	ext{ nm}$
Therefore, the energy of radiation emitted is maximum at a wavelength of $500	ext{ nm}$.
This means $U_2$ (energy at $500	ext{ nm}$) is the maximum energy among all wavelengths.
Hence, $U_2 > U_1$ and $U_2 > U_3$. The correct option is $U_2 > U_1$.

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