An alpha particle ( a helium nucleus, consisting of two protons and two neutrons

Question

An alpha particle ( a helium nucleus, consisting of two protons and two neutrons) has a radius of approximately 1.6*10^-15m. A certain heavy nucleus contains 76 protons in addition to all its neutrons and has a radius of approximately 5.8 * 10^-15 m. An alpha particle is shot directly from a large distance at such a resting heavy nucleus.

Assuming that the heavy nucleus remains at rest during the ensuing process, what initial kinetic energy, in joules, must the alpha particle have in order to just reach the surface of the heavy nucleus.

Explanation / Answer

r = distance between the center of two nucleus when closest = ralpha + rnucleus = 1.6 x 10-15 + 5.8 x 10-15 = 7.4 x 10-15

Qalpha = charge on alpha particle = 2 x 1.6 x 10-19 C
Qnucleus  = charge on nucleus = 76 x 1.6 x 10-19 C

using conservation of energy

kinetic energy = electric potential energy

KE = k Qalpha Qnucleus /r

KE = (9 x 109) (2 x 1.6 x 10-19 ) (76 x 1.6 x 10-19)/(7.4 x 10-15 ) = 4.73 x 10-12 J

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