Question 205: Units , Dimensions and Error Analysis

Question

The force of interaction between two atoms is given by F = $\alpha $$\beta $exp $\left( { - {{{x^2}} \over {\alpha kt}}} \right)$;  where x is the distance, k is the Boltzmann constant and T is temperature and $\alpha $ and $\beta $ are two constants. The dimension of $\beta $ is :

Accepted Answer

$F = \alpha \beta {e^{\left( {{{ - {x^2}} \over {\alpha KT}}} \right)}}$
$\left[ {{{{x^2}} \over {\alpha KT}}} \right] = {M^o}{L^o}{T^o}$
${{{L^2}} \over {\left[ \alpha  \right]M{L^2}{T^{ - 2}}}}$ $=$ ${M^o}{L^o}{T^o}$
$ \Rightarrow $  $\left[ \alpha  \right] = {M^{ - 1}}{T^2}$
$\left[ F \right] = \left[ \alpha  \right]\left[ \beta  \right]$
MLT
$-$2
= M
$-$1
T
2
[$\beta $]
$ \Rightarrow $  [$\beta $] = M
2
LT
$-$4

Answer

M
2
L
2
T
$-$2

Answer

M
2
LT
$-$4

Answer

MLT
$-$4

Answer

M
0
L
2
LT
$-$4

Units , Dimensions and Error Analysis

The force of interaction between two atoms is given by F = \alpha \beta exp \left( { - {{{x^2}} \over {\alpha kt}}} \right); where x is the distance, k is the Boltzmann constant and T is temperature and \alpha and \beta are two constants. The dimension of \beta is :

Choose the correct answer: