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In the relation: P=(alpha)/(beta)e^(-(al...

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

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
A
Argument of exponential term must be dimensionless
i.e., `[(alphaZ)/(K theta)]=M^(0)L^(0)T^(0)]`
Now, `[K theta]=["Energy"]=[ML^(2)T^(-2)]=[alphaZ], [alpha]=[(ML^(2)T^(-2))/(L)]`
Hence, `[beta]=([alpha])/([P])=([MLT^(-2)])/([ML^(-1)T^(-2)])=[M^(0)L^(2)T^(0)]`
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