Aproton and art alpha particle are released from rest when they are 0.225 nm apart.

Explanation

Acceleration will be maximum  at the moment when they are at the closest distance ie at the distance of .225 nm because at time,  force will be maximum.

Force at that time = k Qq/r² where q and Q are charges and r is distance between the two

Here q , charge on proton = 1.6 x 10⁻¹⁹

Q is charge on alpha particle = 2 x 1.6 x 10⁻¹⁹= 3.2 x 10⁻¹⁹

r = .225 x 10⁻⁹

Force =

Force F =

= 910.22 x 10⁻⁵ N

Acceleration in proton = force / mass

=545.04 x 10²² ms⁻²

Acceleration in alpha particle will be 4 times less because its mass is 4 times more .

acceleration in alpha particle

= 136.25 x 10²²ms⁻²

Maximum speed will be when they reach at infinity . At that time all their energy ( potential ) will be converted into kinetic energy .

energy when they were at .225 nm

=

=204.77 x 10⁻²³ J

This energy will be distributed among them in the inverse ratio of their mass

energy of proton = 204.77/5 x 4 x 10⁻²³ = 163.81 x 10⁻²³ J

energy of alpha particle = 204/5 x 1 x 10⁻²³

=40.8 x 10⁻²³ J.

Velocity of proton =

=

= 1400 m/s

velocity of alpha particle

Velocity of alpha particle = 350 m/s

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