Physics

Problem

The force of interaction between two atoms is given by

F = \alpha\beta \exp\left(-\frac{x^2}{\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 dimensions of

\beta

is: a.

M^0L^2T^{-4}

M^2LT^{-4}

MLT^{-2}

M^2L^2T^{-2}

Intuitive explanation

This problem tests whether you can extract dimensions from a physically meaningful equation. The key insight is that the exponential argument must be dimensionless—so $\frac{x^2}{\alpha kT}$ has no units—which immediately tells you what $\alpha$ must be. Once you know $\alpha$ 's dimensions, you can work backward from the fact that $F$ (a force) equals $\alpha\beta$ times a dimensionless exponential to find $\beta$ 's dimensions.

Intuitive explanation

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