A particle of mass m, charge q > 0 and initial kinetic energy K is projected from infinity towards a heavy nucleus of charge Q assumed to have a fixed position.
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Sol. Let minimum distance is r 0 . by
∴ by cons. of ME. between ∞ and point P:
U ∞ + K ∞ = U p + K p
or 0 + K = 
+ 0
∴ r 0 = 
.........(i)
As shown in diagram, Let particle approach closest distance point S from ∞ at speed v.
∴ By C.O.M.E. between ∞ & S.
U ∞ + K ∞ = U s + K s
or 0 + K = 
+ 
mV 2 ............(ii)
Putting r o from (i) in (ii)
K = 
mv 2
∴ v = 
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