# With what velocity should an alpha particle travel towards the nucleus of a copper atom so as to arrive at a distance 10-13 m from the nucleus of a copper atom?

As $\alpha$-particle can appraoch towards the Cu nucleus up to the distance r$°$ which is equal to 10-13m here.
To arrive at a distance r$°$ from the nucleus, the kinetic energy of alpha particle should be equal to the potential energy of interaction of alpha particle with Cu nucleus.
or KE = PE
​1/2 m$\alpha$v​$\alpha$2 = K q​$\alpha$qCu/r$°$ ..................(1)
m$\alpha$ = ​mass of $\alpha$-particle = 4 x 1.67 x 10-27 kg.
K = 9 x 109 N$·$m2 / C2
q​​$\alpha$ = charge on alpha particle is +2 = 2 x (+1.6 x 10-19C)​
qCu = 29 x (+1.6 x 10-19C)​​
r0 = 10–13 m​
Putting all the values in given equation (1) we get v​$\alpha$2

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