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)

${{\lambda }_{m}}\propto {{T}^{-1}}$

Answer 2

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 ${{\lambda }_{m}}\propto {{T}^{-1}}$