The force of interaction between two atoms is given by F=α β (- x^...

Force of interaction between two atoms, $\mathrm{F}=\alpha \beta \mathrm{e}^{\left(\frac{-\mathrm{x}^{2}}{\alpha \mathrm{\text{ kT }}}\right)}$$Since exponential terms are dimensionless$\therefore\left[\frac{\mathrm{x}^{2}}{\alpha \mathrm{k} \mathrm{T}}\right]=\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{0} \Rightarrow \frac{\mathrm{L}^{2}}{[\alpha] \mathrm{ML}^{2} \mathrm{~T}^{-2}}=\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{0} \Rightarrow[\alpha]=\mathrm{M}^{-1} \mathrm{~T}^{2} [\mathrm{F}]=[\alpha][\beta] \mathrm{MLT}^{-2}=\mathrm{M}^{-1} \mathrm{~T}^{2}[\beta] \Rightarrow[\beta]=M^{2} L T^{-4}