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}}] $
Show Answer
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}] $ .
