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 $\beta$ will be

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

Answer 1

Answer: (A)

$\left[\frac{\alpha Z}{k \theta}\right]=\left[ M ^{0} L ^{0} T ^{0}\right]$
$[\alpha]=\left[\frac{k \theta}{Z}\right]$
Further
$[p]=\left[\frac{\alpha}{\beta}\right]$
$\therefore[\beta]=\left[\frac{\alpha}{p}\right]=\left[\frac{k \theta}{Z p}\right]$
Dimensions of $k \theta$ are that to energy. Hence,
$[\beta]=\left[\frac{ ML ^{2} T ^{-2}}{ LML ^{-1} T ^{-2}}\right]=\left[ M ^{0} L ^{2} T ^{0}\right]$