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

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.

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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.