Physics

Suppose an attractive nuclear force acts between two protons which may be written as $$F=Ce^{-kr}/r^{2}$$. (a) write down the dimensional formula and appropriate $$SI$$ units


SOLUTION

Given that

$$ F=\dfrac{C{{e}^{-kr}}}{{{r}^{2}}} $$

$$ F{{r}^{2}}=C{{e}^{-kr}} $$

$$ C=\dfrac{F{{r}^{2}}}{{{e}^{-kr}}} $$

$${{e}^{-kr}}$$ is a dimensional quantity.

Dimension of $$F=\left[ ML{{T}^{-2}} \right]$$

Dimension of $${{r}^{2}}=\left[ {{L}^{2}} \right]$$

So, the dimension of $$C=\left[ M{{L}^{3}}{{T}^{-2}} \right]$$

SI unit of $$C=N{{m}^{2}}$$ 
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