Question

If $ {{\lambda }_{m}} $ denotes the wavelength at which the radiative emission from a black body at a temperature $T \,K$ is maximum, then

• A. $ {{\lambda }_{m}}\propto {{T}^{4}} $
• B. $ {{\lambda }_{m}} $ is independent of T
• C. $ {{\lambda }_{m}}\propto T $
• D. $ {{\lambda }_{m}}\propto {{T}^{-1}} $

Answer 1

Answer: (D)

According to Wiens displacement law, the wavelength $ ({{\lambda }_{m}}) $ of maximum intensity of emission of black body radiation is inversely proportional to absolute temperature (T) of the black body. Therefore, Wiens law is
$ {{\lambda }_{m}}T=$ constant
Or $ {{\lambda }_{m}}=\frac{\text{constant}}{T} $
Or $ {{\lambda }_{m}}\propto \frac{1}{T} $
Or $ {{\lambda }_{m}}\propto {{T}^{-1}} $