Question

Suppose an attractive nuclear force acts between two protons which may be written as F=Ce^−kr/r². Write down the dimensional formulae and appropriate SI units of C and k.   

Answer 1

Given, nuclear force of attraction, 

\[F = C\frac{e^{- Kr}}{r^2}\]

Here e^−Kr is just a pure number, i.e. a dimensionless quantity. So,

\[\left[ C \right] = \left[ F \right] \times \left[ r^2 \right]\] 

\[\left[ C \right] = \left[ {MLT}^{- 2} \right] \times \left[ L^2 \right]\]

\[\left[ C \right] = \left[ {ML}^3 T^{- 2} \right]\]

C = kg ⋅ m³ ⋅ s ⁻²

\[\text{ And } \left[ K \right] = \frac{1}{\left[ r \right]} = \left[ L^{- 1} \right]\] 

SI units: m⁻¹