Question

The Wien's displacement law expresses relation between: -
A. Wavelength corresponding to maximum energy and temperature
B. Radiation energy and wavelength
C. Temperature and wavelength
D. Colour of light and temperature

Answer 1

Hint:The Wien's displacement law is related to thermodynamics. Think of that chapter and recall the associated terms. It has got the unit $mK$ or meter Kelvin. Now you can relate to the quantities given and find out by doing the perfect operation between the quantities and checking the units.

Complete step by step answer:
Wien's displacement law states that the wavelength corresponding to maximum energy is inversely proportional to the temperature of the body in Kelvin. It can also be said that the black-body radiation curve for different temperatures will peak at different wavelengths that are inversely proportional to the temperature.
$$\begin{gathered} \Rightarrow \lambda \propto {\displaystyle \frac{1}{T}} \\ \Rightarrow \lambda ={\displaystyle \frac{k}{T}} \\ \therefore \lambda T=k \end{gathered}$$
Here the value of $k$ is given by Wien's displacement constant and is denoted by $b$.
The value of Wien's displacement constant is $b=2.89\times {10}^{-3}mK$

This has been given by Wilhelm Wein in 1983. Practically it means that hot objects will emit blue light more than cold objects. Thus, Wien's displacement law is a relation between the wavelength corresponding to maximum energy and temperature in Kelvin of the radiation emitted with the temperature of the body.

Hence option (A) is correct.

Note: Wien's displacement law has nothing to do with displacement as the name suggests. A most common mistake done is that students think that the wavelength mentioned is the maximum wavelength, which is wrong. It is the wavelength corresponding to the maximum energy.