Question

In the relation, $p=\frac{\alpha }{\beta }{e}^{-\frac{\alpha Z}{k\theta }}$

$P$ is pressure, $Z$ is distance, $k$ is Boltzmann's constant and $\theta$ is the temperature. The dimensional formula of $\alpha$ will be:

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

Answer 1

Answer: (A)

$\left[ML{T}^{-2}\right]$

In the given equation $\frac{\alpha Z}{k\theta }$ is dimensionless.

$\alpha =\frac{k\theta }{Z}$

$\Rightarrow \left[\alpha \right]=\frac{[{ML}^2{T}^{-2}{k}^{-1}\times k]}{\left[L\right]}=\left[{MLT}^{-2}\right]$

Hence, the correct option is $A$