A silver nucleus contains 108 nucleons (47 protons and 61 neutrons) packed tight

Question

A silver nucleus contains 108 nucleons (47 protons and 61 neutrons) packed tightly against each other. A single nucleon (proton or neutron) has a radius of about 1 10^15 m. Remember that the volume of a sphere is 4/3 r^3.

(a) Calculate the approximate radius of the silver nucleus.

(b) Calculate the approximate radius of the alpha particle, which consists of 4 nucleons, 2 protons and 2 neutrons.

(c) What kinetic energy must alpha particles have in order to make contact with a silver nucleus?

MeV Rutherford correctly predicted the angular distribution for 10-MeV (kinetic energy) alpha particles colliding with gold nuclei. He was lucky: if the alpha particle had been able to touch the gold nucleus, the strong interaction would have been involved and the angular distribution would have deviated from that predicted by Rutherford, which was based solely on electric interactions.

Explanation / Answer

given number of nucleons or Nucleon number A = 108 nucleons

r0 =radius of single nucleon = 1 x 10^-15m

we have the formula as

R = r0 A^1/3-----------(1)

SUBSTITUTING IN THE ABOVE FORMULA WE HAVE

R = (1 X 10^-15) (108)^1/3

R.= 4.75 X 10^-15m

this gives the approximate radius of the silver nucleus

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