In the relation, P = $\frac{\alpha}{\beta}e^\frac{\alpha z}{k\theta}$ P is pressure, z is distance , k is boltzmann constant and θ is the temperature. The dimension of β will be

$[M^0L^2T^0]$ $[ML^2T]$ $[ML^0T]$ $[ML^2T^{-1}]$

$[M^0L^2T^0]$

P = $\frac{\alpha}{\beta}e^\frac{\alpha z}{k\theta}​$   The dimension of power of e is zero. $\frac{\alpha z}{k\theta}$ = $[M^0L^0T^0]$   Thus unit of: α=zkθ​ Unit of boltzmann's constant K is [$K]=\; \$[ML^2T^\{-2\}K^\{-1\}]\$$   By putting these values we get, Dimension of  $\$\backslash alpha\; =\; [L][ML^2T^\{-2\}K^\{-1\}][K]\; =\; [\; MLT^\{-2\}K^0]\$$     Therefore unit of $P=\; \$\backslash frac\{\backslash alpha\}\{\backslash beta\}\$$ ​   Dimension of $\beta$ = $\frac{\alpha}{P}$​   $[\$\backslash beta\$]=\; \$\backslash frac\{[MLT^\{-2\}K^0]\}\{[MLT^\{-1\}K^0]\}\; =\; [M^0L^2T^0]\$$