Question

Draw a schematic arrangement of the Geiger – Marsden experiment for studying α-particle scattering by a thin foil of gold. Dsecribe briefly, by drawing trajectories of the scattered α-particles, how this study can be used to estimate the size of the nucleus.

Answer 1

At the suggestion of Rutherford, in 1911, H. Geiger, and E. Marsden performed an important experiment called Geiger-Marsden experiment (or Rutherford’s scattering experiment). It consists of 

1. Source of a-particles : The radioactive source polonium emits high energetic alpha (α–) particles. Therefore, polonium is used as a source of a-particles. This source is placed in an enclosure containing a hole and a few slits A_1, A₂, etc. are placed in front of the hole. This arrangement provides a fine beam of α-particles. 

2. Thin gold foil : It is a gold foil* of thickness nearly 10^-6m, α-particles are scattered by this foil. The foil taken is thin to avoid multiple scattering of a-particles, i. e., to ensure that α-particle be deflected by a single collision with a gold atom. 

3. Scintillation counter : By this the number of a-particles scattered in a given direction may be counted. The entire apparatus is placed in a vacuum chamber to prevent any energy loss of α-particles due to their collisions with air molecules. 

Method: When α-particle beam falls on gold foil, the α-particles are scattered due to collision with gold atoms. This scattering takes place in all possible directions. The number of α-particles scattered in any direction is counted by scintillation counter. 

Observations and Conclusions 

(i) Most of α-particles pass through the gold foil undeflected. This implies that “most part of the atom is hollow.” 

(ii) α-particles are scattered through all angles. Some α-particles (nearly 1 in 2000), suffer scattering through angles more than 90°, while a still smaller number (nearly 1 in 8000) retrace their path. This implies that when fast moving positively charged α-particles come near gold-atom, then a few of them experience such a strong repulsive force that they turn back. On this basis Rutherford concluded that whole of positive charge of atom is concentrated in a small central core, called the nucleus.

The distance of closest approach of α-particle gives the estimate of nuclear size. If Ze is charge of nucleus E_k  kinetic energy of a particle 2e charge on α-particle the size of nucleus r₀ is given by

Calculations show that the size of nucleus is of the order of10^-14 m, while size of atom is of the order of 10^-14m; therefore the size of nucleus is about 10^-14/10^-10 = 1/10,000,  times the size of atom. 

(iii) The negative charges (electrons) do not influence the scattering process. This implies that nearly whole mass of atom is concentrated in nucleus.