Physics And Measurement Question 35

Question: In the relation $ P=\frac{\alpha }{\beta }{{e}^{-\frac{\alpha Z}{k\theta }}} $ P is pressure, Z is the distance, k is Boltzmann constant and q is the temperature. The dimensional formula of b will be

[IIT (Screening) 2004]

Options:

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}}] $

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Answer:

Correct Answer: A

Solution:

In given equation, $ \frac{\alpha z}{k\theta } $ should be dimensionless

$ \therefore $ $ \alpha =\frac{k\theta }{z}\Rightarrow [\alpha ]=\frac{[ML^{2}{{T}^{-2}}{{K}^{-1}}\times K]}{[L]}=[ML{{T}^{-2}}] $

and $ P=\frac{\alpha }{ \beta }\Rightarrow [\beta ]=[ \frac{\alpha }{p} ]=\frac{[ML{{T}^{-2}}]}{[M{{L}^{-1}}{{T}^{-2}}]}=[M^{0}L^{2}T^{0}] $ .



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