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Home » A black body is at a temperature of . The energy of radiation emitted by the body at wavelength is , at wavelength is and that at is . Wien’s constant, . Which of the following is correct? A B C D
A black body is at a temperature of 5760 \mathrm{~K}. The energy of radiation emitted by the body at wavelength 250 \mathrm{~nm} is \mathrm{U}_{1}, at wavelength 500 \mathrm{~nm} is \mathbf{U}_{2} and that at 1000 \mathrm{~nm} is \mathrm{U}_{3}. Wien’s constant, b=2.88 \times 10^{6} \mathrm{nmK}. Which of the following is correct?
A \quad \mathrm{U}_{1}=0
B \quad \mathrm{U}_{3}=0
C \quad \mathrm{U}_{1}>\mathrm{U}_{2}
D \quad \mathrm{U}_{2}>\mathrm{U}_{1}
Physics
A black body is at a temperature of 5760 \mathrm{~K}. The energy of radiation emitted by the body at wavelength 250 \mathrm{~nm} is \mathrm{U}_{1}, at wavelength 500 \mathrm{~nm} is \mathbf{U}_{2} and that at 1000 \mathrm{~nm} is \mathrm{U}_{3}. Wien’s constant, b=2.88 \times 10^{6} \mathrm{nmK}. Which of the following is correct?
A \quad \mathrm{U}_{1}=0
B \quad \mathrm{U}_{3}=0
C \quad \mathrm{U}_{1}>\mathrm{U}_{2}
D \quad \mathrm{U}_{2}>\mathrm{U}_{1}

Correct Option D

Solution:

According to Wien’s displacement law

    \[\begin{aligned} &\lambda_{\min }=\frac{\mathrm{b}}{\mathrm{T}} \\ &=\frac{2.88 \times 10^{6}}{5760} \\ &=500 \mathrm{~nm} \end{aligned}\]

We can thus observe \mathrm{U}_{2} is maximum.

i

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