question_answer

Two stars radiate maximum energy at wavelengths \[\mathbf{3}\mathbf{.6\times 1}{{\mathbf{0}}^{\mathbf{-7}}}\mathbf{m}\]and \[\mathbf{4}\mathbf{.8\times 1}{{\mathbf{0}}^{\mathbf{-7}}}\mathbf{m}\] respectively. What is the ratio of their temperatures?

Answer:

                Here      \[{{\lambda }_{m}}=3.6\times {{10}^{-7}}m,\]                                 \[\lambda {{'}_{m}}=4.8\times {{10}^{-7}}m\]                 By Wien?s law, \[{{\lambda }_{m}}T=\lambda {{'}_{m}}T'\]                 \[\therefore \]   \[\frac{T}{T'}=\frac{\lambda {{'}_{m}}}{{{\lambda }_{m}}}=\frac{4.8\times {{10}^{-7}}}{3.6\times {{10}^{-7}}}=\mathbf{4:3}.\]