The work done by a gas molecule in an isolated system is given by, $W = \alpha {\beta ^2}{e^{ - {{{x^2}} \over {\alpha kT}}}}$, where x is the displacement, k is the Boltzmann constant and T is the temperature. $\alpha$ and $\beta$ are constants. Then the dimensions of $\beta$ will be :

Question

The work done by a gas molecule in an isolated system is

given by, $W = \alpha {\beta ^2}{e^{ - {{{x^2}} \over {\alpha kT}}}}$, where x is the displacement, k is the Boltzmann constant and T is the temperature. $\alpha$ and $\beta$ are constants. Then the dimensions of $\beta$ will be :

$[{M^0}L{T^0}]$

$[M{L^2}{T^{ - 2}}]$

$[ML{T^{ - 2}}]$

$[{M^2}L{T^2}]$

Solution

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