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 dimension of \(\beta \) is

\(\begin{array}{l}
Power\,of\,e\,should\,be\,\dim ensionless.\\
So,\left[ \lambda  \right] = \left( {\alpha Tk} \right)\\
 \Rightarrow \,\,\,\,\,\,\,\,{L^2} = \left[ \alpha  \right]\left( {M{L^2}{T^{ - 2}}} \right)\\
 \Rightarrow \,\,\,\,\,\,\,\,\,\left( \alpha  \right) = \left( {{M^{ - 1}}{T^2}} \right)\\
 \Rightarrow \,\,\,\,\,\,\,\,\,\,\,E = \frac{1}{2}KT\\
 \Rightarrow \,\,\,\,\,\,\,\,\,\,\,\left( {M{L^2}{T^{ - 2}}} \right)\,\,;\,\,\left( E \right) = \left[ {KT} \right]\\
 \Rightarrow \,\,\,\,\,\,\,\,\,\,\,\left( {\alpha \beta } \right) = \left( F \right)\\
 \Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\left( {{M^{ - 1}}{T^2}} \right)\left( \beta  \right) = \left( {ML{T^{ - 2}}} \right)
\end{array}\)