Question 190: 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

M2L2T$$-$$2

Answer

M2LT$$-$$4

Answer

MLT$$-$$4

Answer

M0L2LT$$-$$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 :

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