Question

If ${\lambda }_m$ denotes the wavelength at which the radiative emission from a black body at a temperature $TK$ 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 ${\lambda }_m\propto T^{-1}$