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 α-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 mαv​α2 = K q​αqCu/r° ..................(1)
 mα = ​mass of α-particle = 4 x 1.67 x 10-27 kg.
K = 9 x 109 N·m2 / C2
q​​α = 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​α2

vα2=2×9×109 (2×1.6×10-19)(29×1.6×10-19)4×1.67×10-27×10-13=400.09×1011=4000.9×1010vα=4000.9×1010= 63.25×105 ms-1


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