A black body radiates maximum energy when its surface temperature T and the corresponding wavelength \(\lambda\)max are related by the equation \(\lambda\)m...
Question 1 Report
A black body radiates maximum energy when its surface temperature T and the corresponding wavelength \(\lambda\)max are related by the equation \(\lambda\)max T = constant. Given the values of the constant and surface temperature as 2.9 x 10\(^{-3}\) mK and 57°C respectively; Calculate the frequency of the energy radiated.
Answer Details
Wien's displacement law
Given \(\lambda_{\max}T = 2.9\times10^{-3}\ \text{m K}\), and \(T = 57^{\circ}\text{C} = 57 + 273 = 330\ \text{K}\).
\(\lambda_{\max} = \dfrac{2.9\times10^{-3}}{330} = 8.79\times10^{-6}\ \text{m}\).
Frequency: \(f = \dfrac{c}{\lambda_{\max}} = \dfrac{3.0\times10^{8}}{8.79\times10^{-6}}\).
\(f = 3.41\times10^{13}\ \text{Hz}\).
The frequency of the radiated energy is \(3.4\times10^{13}\ \text{Hz}\).
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