Thermal Physics: Practice Problem & Solution
A black body is at a temperature of $5760\text{ K}$. The energy of radiation emitted by the body at wavelength $250\text{ nm}$ is $U_1$, at wavelength $500\text{ nm}$ is $U_2$ and that at $1000\text{ nm}$ is $U_3$. Wien's constant, $b = 2.88 \times 10^6\text{ nmK}$. Which of the following is correct? (2016 - I)
Solution Explained:
To solve this problem, we apply the core principles of Thermal Physics. Understanding the underlying formula is key to arriving at the correct answer below:
From Wien's displacement law, $\lambda_{max} = \frac{b}{T} = \frac{2.88 \times 10^6}{5760} = 500\text{ nm}$. This means maximum energy is radiated at $500\text{ nm}$. Therefore, the energy $U_2$ is maximum, so $U_2 > U_1$ and $U_2 > U_3$.
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