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


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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