
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
471.9k+ views
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.
$
\Rightarrow \lambda \propto \dfrac{1}{T} \\
\Rightarrow \lambda = \dfrac{k}{T} \\
\therefore\lambda T = k $
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.
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.
$
\Rightarrow \lambda \propto \dfrac{1}{T} \\
\Rightarrow \lambda = \dfrac{k}{T} \\
\therefore\lambda T = k $
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.
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