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In the relation $P = \frac{α}{β} e^{- α z / k θ}$ P is pressure, k is Boltzmann constant, z is distance and ' $θ$ ' temperature. The dimensional formula of $β$ will be

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$M^{0} L^{2} T^{0}$

$M^{0} L^{2} T^{1}$

$M^{1} L^{- 2} T^{1}$

$M L^{0} T^{1}$

answer is A.

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Detailed Solution

$P = \frac{α}{β}$

$α z = k θ$

$\begin{array}{l} P = \frac{α}{β} = \frac{M L T^{- 2}}{M L^{- 1} T^{- 2}} = L^{2} \\ α = \frac{k θ}{z} = \frac{M L T^{- 2} k^{- 1} k}{L} = M L T^{- 2} \\ β = M^{0} L^{2} T^{0} \end{array}$

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