The electric potential energy of the alpha particle at the distance of closest approach from the nucleus was found to be equal to
Potential energy x charge on a particle
Where Z is the atomic number of the Gold foil,
K = 9x109 Nm2/C2
+e = the charge on a proton
At r = r0 K.E. of particle = P.E. of a particle
Kinetic energy of a particle
On substituting the value of
(K.E)a = 5.5 Mev
= 5.5 x 1.6 x 10 13
Z = 79, e = 16 x 10-19C
Value of ro = 4.13 x 10-14 m
= 41.3 x 10 -13 m
= 41.3 Fermi (1 fermi = 10-13 m)
This was approximate radius of the gold nucleus.
