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In the relation, P=alpha/beta e^((alphaZ...

In the relation, `P=alpha/beta e^((alphaZ)/(ktheta))P` is pressure, Z is distance, k is Boltzmann constant and `theta` is the temperature. The dimensional formula of `beta` will be-

A

`["M"^(0)"L"^(2)"T"^(0)]`

B

`["ML"^(2)"T"]`

C

`["ML"^(0)"T"^(-1)]`

D

`["M"^(0)"L"^(2)"T"^(-1)]`

Text Solution

Verified by Experts

The correct Answer is:
A
In the given equation, `(alphaZ)/(ktheta)` should be dimensionless.
`therefore" "alpha=(ktheta)/(Z)rArr[alpha]=(["ML"^(2)"T"^(-2)"K"^(-1)]["K"])/(["L"])=["MLT"^(-2)]`
and `" "p=(alpha)/(beta)`
`rArr" "[beta]=[(alpha)/(p)]=(["MLT"^(-2)])/(["ML"^(-1)"T"^(-2)])=["M"^(0)"L"^(2)"T"^(0)]`
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