AIIMS 2000 Physics Temperature and Wavelength Relationship MCQ Question

To find the ratio of the surface temperatures of the Sun and star x based on their maximum wavelengths, we can use Wien's displacement law, which states that the maximum wavelength $\lambda_{max}$ is inversely proportional to the temperature $T$. The law is given by the formula: $\lambda_{max} T = b$, where $b$ is Wien's displacement constant (approximately $2898 \, \mu m \cdot K$). Thus, we can express the ratio of temperatures as follows: $\frac{T_{Sun}}{T_{star}} = \frac{\lambda_{max, star}}{\lambda_{max, Sun}}$. Given that the maximum wavelength for the star is 350 nm (or 0.35 $\mu m$), and assuming the maximum wavelength for the Sun is around 500 nm (or 0.5 $\mu m$), we can calculate the ratio: $\frac{T_{Sun}}{T_{star}} = \frac{0.5}{0.35} \approx 1.43$. However, the question asks for the ratio of the surface temperature of the Sun to star x, which is the inverse: $\frac{T_{star}}{T_{Sun}} = \frac{0.35}{0.5} = 0.7$. This is approximately equal to the provided option B (0.68), indicating that the correct answer is B. The other options do not match the calculated ratio, hence they are incorrect.