The workdone by a gas molecule in an isolated system is given by, $W =\alpha \beta^{2} e ^{-\frac{ x ^{2}}{\alpha kT }},$ where $x$ is the displacement, $k$ is the Boltzmann constant and $T$ is the temperature, $\alpha$ and $\beta$ are constants. Then the dimension of $\beta$ will be
The workdone by a gas molecule in an isolated system is given by, $W =\alpha \beta^{2} e ^{-\frac{ x ^{2}}{\alpha kT }},$ where $x$ is the displacement, $k$ is the Boltzmann constant and $T$ is the temperature, $\alpha$ and $\beta$ are constants. Then the dimension of $\beta$ will be
- [JEE MAIN 2021]
- A
$\left[ M L ^{2} T ^{-2}\right]$
- B
$\left[ M L T ^{-2}\right]$
- C
$\left[ M ^{2} L T ^{2}\right]$
- D
$\left[ M ^{0} L T ^{0}\right]$
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- [AIEEE 2002]