Atoms and Nuclei Problems - Numerical 01

01.

What is the distance of closest approach to the nucleus of an alpha particle which undergoes scattering by 180^o in the Gelger- Marsden experiment?

Suggested solution:

For this case, when the alpha-particle is closest to the nucleus, it comes to rest and its initial kinetic energy is completely converted into potential energy. We assume that this takes place when the alpha particle is outside the nucleus. The condition is expressed by the relation

where u_i is the initial speed, Z is the atomic number of the nucleus, m is the mass of the alpha-particle and r₀ is the distance of closest approach of the alpha-particle to the nucleus.

= 5.5 x 10⁶ x 1.6 x 10^-19 J

= 4.14 x 10^-14 m

The radius of the gold nucleus is, therefore less that = 4.1 x 10^-14 m.