MHTCET 5 May 2025 Shift 2 Paper

Concept:Wien's displacement law states that the product of the maximum wavelength and the absolute temperature of a black body is constant, i.e., $\lambda_m T = \text{constant}$.Explanation:At temperature $T_1 = 2000 \, \text{K}$, the maximum wavelength is given as $\lambda_m$.At temperature $T_2 = 3000 \, \text{K}$, let the new maximum wavelength be $\lambda_m'$.Using Wien's law, we equate the two products:$$\lambda_m T_1 = \lambda_m' T_2$$Rearranging for $\lambda_m'$:$$\lambda_m' = \lambda_m \cdot \frac{T_1}{T_2}$$Substituting the given temperatures:$$\lambda_m' = \lambda_m \cdot \frac{2000}{3000}$$Simplifying the fraction:$$\lambda_m' = \frac{2}{3} \lambda_m$$Thus, the maximum wavelength decreases when the temperature increases, as expected from Wien's law.Answer:The maximum wavelength at $3000 \, \text{K}$ is $\displaystyle \frac{2}{3} \lambda_m$.Therefore, the correct option is D: $\frac{2}{3} \lambda_m$.