In the relation P = $\frac{α}{β}e^{-\frac{aZ}{kθ}}$, P is pressure Z is distance k is Boltzman constant and θ is the temperature. The dimension formula of β will be :

M⁰L²T⁰

$-\frac{aZ}{kθ}$ is dimension less quantity

∴ dimension of α = $\frac{kθ}{z}$

= $\frac{ML^2T^{-2}K^{-1}}{L}×K$

α = MLT^-2

Dimension of $\frac{\alpha}{\beta}$ is equal to dimension of pressure P

$P=\left(\frac{\alpha}{\beta}\right)$

$M L^{-1} T^{-2}=\frac{M L T^{-2}}{\beta}$

$\beta=\frac{M L T^{-2}}{M L^{-1} T^{-2}}$

$\beta=M^0 L^2 T^0$