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

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M0L2T0

ML2 T

[ML T -1 ]

M0 L2 T-1

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detailed solution

Correct option is A

αZkθ=M0L0T0 [α]=kθZFurther,[p]=αβ ∴[β]=αp=kθZpDimensions of kθ are that to energy. Hence,[β]=ML2T-2LML-1T-2=M0 L2 T0

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In the relation p=αβe-azkθ, p is pressure, Z is distance, k is Boltzmann constant and θ is the temperature. The dimensional formula of β will be

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