# 2019The force of interaction between two atoms is given by $F = \alpha \beta exp\left [ -\frac{x^{2}}{\alpha kT} \right ]$; where x is the distance , k is the Boltzmann constant and T is temperature and $\alpha$ and $\beta$ are two constants. The dimensions of $\beta$ is:

Check the dimensional correctness -

$\dpi{100} L.H.S.=R.H.S.$

- wherein

It is based on the principle of homoginity. According to this principle both sides of an equation must be the same .

$F= d\: \beta\: e\left [ \frac{-x^{2}}{dkT} \right ]$

$\left [ \frac{x^{2}}{dkT} \right ]= M^{o} L^{o} T^{o}$

$\frac{L^{2}}{[d]ML^{2}T^{-2}}= M^{o}L^{o}T^{o}$

$\Rightarrow [d]=M^{-1}T^{2}$

$[F]=[d][\beta ]$

$MLT^{-2}=M^{-1}T^{2}[\beta ]$

$[\beta ]=M^{2}LT^{-4}$

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