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Q.

In the relation $P = \frac{α}{β} e^{- \frac{α Z}{k θ}}$ P is pressure, Z is the distance, k is Boltzmann constant and $θ$ is the temperature. The dimensional formula of $β$ will be $[M^{0} L^{n} T^{0}]$ . The value of n is

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Detailed Solution

In given equation, $\frac{α z}{k θ}$ should be dimensionless

$\begin{array}{l} ∴ [α] = [\frac{k θ}{z}] \\ \Rightarrow [α] = \frac{[M L^{2} T^{- 2} K^{- 1} \times K]}{[L]} = [M L T^{- 2}] \\ and P = \frac{α}{β} \\ \Rightarrow [β] = [\frac{α}{P}] = \frac{[M L T^{- 2}]}{[M L^{- 1} T^{- 2}]} = [M^{0} L^{2} T^{0}] \end{array}$

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In the relation P=αβe−αZkθ P is pressure, Z is the distance, k is Boltzmann constant and θ is the temperature. The dimensional formula of β will be M0LnT0. The value of n is