AIPMT PRELIMS 2001 Physics Black Body Radiation MCQ Question

According to Wien's Displacement Law, the wavelength corresponding to maximum energy ($\lambda_{max}$) of a black body is inversely proportional to its temperature ($T$). This is mathematically expressed as: $\lambda_{max} T = b$ where $b$ is Wien's displacement constant. For the first case at 2000 K, we have: $\lambda_{m} \cdot 2000 = b$. For the second case at 3000 K, we can express it as: $\lambda_{max}' \cdot 3000 = b$. By equating the two expressions for $b$, we get: $\lambda_{m} \cdot 2000 = \lambda_{max}' \cdot 3000$. Rearranging gives us: $\lambda_{max}' = \frac{2000}{3000} \lambda_{m} = \frac{2}{3} \lambda_{m}$. Therefore, the correct answer is B.

The other options are incorrect because they do not satisfy the relationship established by Wien's Displacement Law. For example, option A ($\frac{3}{2} \lambda_{m}$) suggests an increase in wavelength with temperature, which contradicts the law. Similarly, options C and D do not align with the inverse relationship between wavelength and temperature.