First slide

Radiation

Question

A black body is at a temperature of 5760 K. The energy of radiation emitted by the body at wavelength 250 nm is U₁, at wavelength 500 nm is U₂ and that at 1000 nm is U₃. Wien's constant, b = 2.88 X 10⁶ nmK. Which of the following is correct?

Moderate

A

U₃ = 0
B

U₁> U₂
C

U₂ > U₁
D

U₁ = 0

Solution

Given, temperature, T₁ = 5760 K
Since, it is given that energy of radiation emitted by the body at wavelength 250 nm is U₁, at wavelength 500 nm is U₂ and that at 1000 nm is U₃.
$∵$ According to Wien's law, we get
$λ_{m} T = b$
where, b = Wien's constant = 2.88 x 10⁶ nmK
$\Rightarrow λ_{m} = \frac{b}{T} \Rightarrow λ_{m} = \frac{288 \times 10^{6} nmK}{5760 K} \Rightarrow λ_{m} = 500 nm$
$∵ λ_{m} =$ wavelength corresponding to maximum energy, so U₂>U₁.

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