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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.
Solution
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
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