(g) If a black body at temperature 6174 K emits 4700 \text{\AA} with maximum energy; Calculate the temperature at which it will emit a wavelength of \( 1.4 \times 10^{-5} \text{m} \) with maximum energy.

Another Explanation (5): Using Wien's displacement law, \( \lambda_{max} T = b \), where \( b \) is Wien's displacement constant (\(2.898 \times 10^{-3} \, m \cdot K\)). Given: \( \lambda_{max1} = 4700 \, \text{\AA} = 4700 \times 10^{-10} \, m \) and \( T_1 = 6174 \, K \). We need to find \( T_2 \) when \( \lambda_{max2} = 1.4 \times 10^{-5} \, m \). Since \( \lambda_{max1} T_1 = \lambda_{max2} T_2 \), we have: \( T_2 = \frac{\lambda_{max1} T_1}{\lambda_{max2}} = \frac{(4700 \times 10^{-10} \, m)(6174 \, K)}{1.4 \times 10^{-5} \, m} \approx 207 \, K \)