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

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Solution

Given that

$F = \frac{C e^{- k r}}{r^{2}}$

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

$C = \frac{F r^{2}}{e^{- k r}}$
$e^{- k r}$ is a dimensional quantity.

Dimension of $F = [M L T^{- 2}]$

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

So, the dimension of $C = [M L^{3} T^{- 2}]$
SI unit of $C = N m^{2}$

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Suppose an attractive nuclear force acts between two protons which may be written as F=Ce−kr/r2. (a) write down the dimensional formula and appropriate SI units

Given that F=Ce−krr2 Fr2=Ce−kr C=Fr2e−kre−kr is a dimensional quantity. Dimension of F=[MLT−2] Dimension of r2=[L2] So, the dimension of C=[ML3T−2] SI unit of C=Nm2

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

Given that

$F = \frac{C e^{- k r}}{r^{2}}$

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

$C = \frac{F r^{2}}{e^{- k r}}$
$e^{- k r}$ is a dimensional quantity.

Dimension of $F = [M L T^{- 2}]$

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

So, the dimension of $C = [M L^{3} T^{- 2}]$
SI unit of $C = N m^{2}$