The ratio of the magnitudes of electrostatic force between an electron and a proton separated by a distance $ r $ to that between a proton and an alpha particle separated by the same distance $ r $ is:

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Using Coulomb’s law, the force between two charges $ q_1 $ and $ q_2 $ is given by: $$ F = k \frac{q_1 q_2}{r^2} $$ For an electron ($ e $) and a proton ($ e $), and a proton ($ e $) and an alpha particle ($ 2e $): $$ F_{e-p} = k \frac{e \cdot e}{r^2}, \quad F_{p-\alpha} = k \frac{e \cdot 2e}{r^2} = 2k \frac{e^2}{r^2} $$ $$ {Ratio} = \frac{F_{e-p}}{F_{p-\alpha}} = \frac{k \frac{e^2}{r^2}}{2k \frac{e^2}{r^2}} = \frac{1}{2} $$

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The ratio of the magnitudes of electrostatic force between an electron and a proton separated by a distance \( r \) to that between a proton and an alpha particle separated by the same distance \( r \) is:

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