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.
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Correct Answer: Option n
Explanation:
\(\lambda\) max = \(\frac{2.9 \times 10^{-3}}{330}\) = 8.8 x 10\(^{-6}\)m
v = f\(\lambda\) or f = \(\frac{v}{\lambda}\)
where v = velocity of light = 3.0 x10\(^{-8}\) m/s
\(\lambda\) = 8.8 x 10\(^{-6}\)
f = \(\frac{v}{\lambda}\)
= \(\frac{3.0 \times 10^8}{8.8 \times 10^{-6}}\)
= 3.4 x 10\(^{13}\) Hz
\(\lambda\) max = \(\frac{2.9 \times 10^{-3}}{330}\) = 8.8 x 10\(^{-6}\)m
v = f\(\lambda\) or f = \(\frac{v}{\lambda}\)
where v = velocity of light = 3.0 x10\(^{-8}\) m/s
\(\lambda\) = 8.8 x 10\(^{-6}\)
f = \(\frac{v}{\lambda}\)
= \(\frac{3.0 \times 10^8}{8.8 \times 10^{-6}}\)
= 3.4 x 10\(^{13}\) Hz