Thermal Properties of Matter - Result Question 14

14. A black body is at a temperature of $5760 K$. The energy of radiation emitted by the body at wavelength $250 nm$ is $U_1$, at wavelength 500 $nm$ is $U_2$ and that at $1000 nm$ is $U_3$. Wien’s constant, $b=2.88 \times 10^{6} nmK$. Which of the following is correct?

[2016]

(a) $U_1=0$

(b) $U_3=0$

(c) $U_1>U_2$

(d) $U_2>U_1$

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Answer:

Correct Answer: 14. (d)

Solution:

  1. (d) According to Wein’s displacement law, maximum amount of emitted radiation corresponding to $\lambda_m=\frac{b}{T}$

$ \lambda_m=\frac{2.88 \times 10^{6} nmK}{5760 K}=500 nm $

From the graph $U_1<U_2>U_3$

At a given temperature, intensity of heat radiation increases with wavelength, reaches a maximum at a particular wavelength and with further increase in wavelength it decreases.



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