First slide

Radiation

Question

A black body is at a temperature of 2880 K. The energy of radiation emitted by this body with wavelength 499 nm and 500 nm is U₁, between 999 nm and 1000 nm is U₂ and between 1499 nm and 1500 nm is U₃. The Wien's constant b = 2.88 x 10⁶ nm K. Then

Easy

A

$U_{1} = 0$
B

$U_{3} = 0$
C

$U_{1} > U_{2}$
D

$U_{2} > U_{1}$

Solution

According to Wien's displacement law,
$λ_{m} T = b or λ_{m} = b / T$
$∴ λ_{m} = \frac{2 .88 \times 10^{6} nm}{2880 K} = 1000 nm .$
This shows that U₂ is maximum.
Further, black body spectrum is continuous. Hence, finite radiant energy is emitted at all wavelengths, i e ,
$U_{1} \neq 0 and U_{3} \neq 0$
Thus, $U_{2} > U_{1}$ .

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