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

The Correct Option is A

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