# 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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