Question

According to Wein’s law:
\[{\lambda _m}T{\text{ }} = {\text{ }}Constant\]
\[\dfrac{{{\lambda _m}}}{T}{\text{ }} = {\text{ }}Constant\]
\[{\lambda _m}\sqrt T {\text{ }} = {\text{ }}Constant\]
\[\dfrac{{{\lambda _m}}}{{\sqrt T }}{\text{ }} = {\text{ }}Constant\]

Answer 1

Hint:Wein’s Law (also known as Wein’s Displacement Law) gives us the relationship between the temperature of a Black Body and the Wavelength of light emitted by the Black Body while cooling.
According to Wein’s Law,
\[{\lambda _m}T{\text{ }} = {\text{ }}0.2898\]
Where,
\[{\lambda _m}\] is the wavelength of light in cm
T is the temperature of the body in kelvin


Complete step by step solution:
Named after a German physicist Wilhelm Wein (the person who gave this law), Wein’s Law (also known as Wein’s Displacement Law) gives us the relationship between the temperature of a Black Body (Black Body is defined as a substance which absorbs all the frequencies of light hitting its surface and then re-emits them) and the Wavelength of light emitted by the Black Body while cooling.

Fact: - Vanta Black is a colour that absorbs ninety-nine per cent of light directed at it. A body painted in vanta black colour is the closest real-life example of a black body.
According to Wein’s Law,
\[{\lambda _m}T{\text{ }} = {\text{ }}0.2898\]
Where,
\[{\lambda _m}\] is the wavelength of light in cm
T is the temperature of the body in kelvin
The above equation clearly implies that \[{\lambda _m}T{\text{ }} = {\text{ }}Constant\]

Hence Option (A) is correct.

It is to be noted that Wein’s Displacement Law is only applicable to ideal black bodies. In real life, the product \[{\lambda _m}T\] would differ from the value given by Wilhelm Wein.


Note:In order to solve such theoretical kind of questions, one must have a clear conceptual understanding of Wein’s Law.