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  3. how to find dimension of beta in f=alpha beta e x p multiplied with -xsquare by alpha k t where k is boltzman constant and t is temperature
# Engineering

The 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:

Answers (1)
L Lovekush Kumar Saini

Check the dimensional correctness -

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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