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) $U_2>U_1$
Show Answer
Answer:
Correct Answer: 14. (d)
Solution:
- (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.
