Question

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

• A. $[M^0{L}^2{T}^0]$
• B. $[M{L}^{2}T]$
• C. $[M{L}^0{T}^{-1}]$
• D. $[M^0{L}^2{T}^{-1}]$

Answer 1

Answer: (A)

In the given equation, $\frac{\alpha z}{k\theta }$ should be dimensionless.
$\therefore \alpha =\frac{k\theta }{z}$
$\Rightarrow [\alpha ]=\frac{\left[M{L}^2{T}^{-2}{K}^{-1}\right]\times [K]}{[L]}$
$=\left[ML{T}^{-2}\right]$
and $p=\frac{\alpha }{\beta }$
$\Rightarrow [\beta ]=\left[\frac{\alpha }{p}\right]$
$=\frac{\left[ML{T}^{-2}\right]}{\left[M{L}^{-1}{T}^{-2}\right]}=\left[M^0{L}^2{T}^0\right]$