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 θ θ is the temperature. The dimensional formula of β β will be
Text Solution
Verified by ExpertsA
In given equation, \(\frac{\alpha Z}{k \theta}\) should be dimensionless
\(\alpha = \frac{k \theta}{z} \Rightarrow \left[\alpha\right] = \frac{\left[ML^{2}T^{-2}K^{-1} \times K\right]}{\left[L\right]} = \left[MLT^{-2}\right]\)
and \(P = \frac{\alpha}{\beta} \Rightarrow [\beta] = \left[\frac{\alpha}{p}\right] = \frac{\left[ M L T^{-2} \right]}{\left[ M L^{-1} T^{-2} \right]} = \left[ M^{0} L^{2} T^{0} \right]\) .
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems