Proton and \(\alpha\)

A proton and an \(\alpha \) particle are projected with velocity \(\large{v_{o}=\sqrt{\frac{k e^2 }{mL}}}\) towards each other, when they are far away from each other. The distance between their initial velocities is \(L\). Their closest approach distance can be represented as

\[\large{\frac{a+\sqrt{b}}{c}L}\]

where \(a,b,c\) are integers and \(b\) is square free.

Find \(a+b+c\)


Mass of proton=m and charge \(+e\).

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