Question

The unit of Wien's constant b is

• A. Wm^-2K^-4
• B. m^-1K^-1
• C. Wm²
• D. mk

Answer 1

The correct option is D

mk

Explanation for the correct answer:-

Option (D)

Formula used:

1. Wien’s constant is given by, $b={\lambda }_{m}T$ where ${\lambda }_m$ is the peak wavelength of the black body radiation and $T$ is the surface temperature of the black body.
2. Wien's Displacement Law provides the wavelength where the spectral radiance has a maximum value.
3. This law states that the black body radiation curve for different temperatures peaks at a wavelength inversely proportional to the temperature.

Express the Wien’s constant to determine its unit,

1. Wien’s law states that it is the product of surface temperature $T$ and the peak wavelength ${\lambda }_m$ of the blackbody radiation. It is denoted by a constant value$b$.
2. $b$ is the Wien’s constant. i.e., $b={\lambda }_{m}T$
3. The S.I. unit of wavelength is meters and that of the surface temperature is Kelvin.
4. So substituting the surface temperature $T$ and the units of the peak wavelength is $r$ meter
5. ${\lambda }_m$ in above equation we get, $b=\text{mK}$ .
6. Thus the unit of Wien’s constant is $\text{mK}$

Hence, option D is correct.