The relation $\mathrm{p}=\frac{\mathrm{\alpha }}{\mathrm{\beta }}{\mathrm{e}}^{\frac{-\mathrm{\alpha Z}}{\mathrm{k\theta }}}$ , where p is pressure, Z is distance, k is Boltzmann constant and $\mathrm{\theta }$ is temperature. The dimensional formula of $\mathrm{\beta }$ will be

In the given equation, $\frac{\alpha Z}{k\theta }$ should be dimensionless.

$\therefore \left[\alpha \right]=\left[\frac{k\theta }{Z}\right]\Rightarrow \left[\alpha \right]=\frac{\left[{\mathrm{ML}}^2{ \mathrm{T}}^{-2}{ \mathrm{K}}^{-1} mo{l}^{-1}\right]\left[\mathrm{K}\right]}{\left[\mathrm{L}\right]}=\left[{\mathrm{MLT}}^{-2} mo{l}^{-1}\right]$

and $p=\frac{\alpha }{\beta }\Rightarrow \left[\beta \right]=\left[\frac{\alpha }{p}\right]=\frac{\left[{\mathrm{MLT}}^{-2} mo{l}^{-1}\right]}{\left[{\mathrm{ML}}^{-1}{ \mathrm{T}}^{-2}\right]}=\left[{\mathrm{M}}^0{ \mathrm{L}}^2{ \mathrm{T}}^0 {\mathrm{mol}}^{-1}\right]$