The Electric Potential Energy

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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 r_o = 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.