Question

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

Answer 1

Explanation:

As α-particle can approach towards the Cu nucleus upto the distance ro = 10-13 m

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.

i.e., KE = PE

1/2 mαvα2 = K qαqCu/ro ---------> (1)

mα = mass of α-particle = 4 x 1.67 x 10-27 kg

K = 9 x 109 Nm2/C2

qα = charge on alpha particle is = 2 x (1.6 x 10-19 C)

qCu = 29 x (1.6 x 10-19 C)

ro = 10-13 m

Putting all the values in given equation (1), we get vα2.

vα2 = 4000.9 x 1010

vα = 63.25 x 105 m/s