18.1.1 Rutherford Alpha-Particle Scattering Experiment

In 1911, Rutherford instructed his assistant Hans Geiger, who instructed the graduate student Marsden, to perform the experiment that has come to be known as the Rutherford scattering experiment. Why didn’t Rutherford and Geiger conduct the experiment themselves? Probably because they expected it to be a tedious and exhausting experiment with no interesting results. To Marsden’s credit, he conducted the experiment meticulously and resiliently. And the results blew everyone’s mind.

The basic setup of this experiment involves firing a stream of alpha particles at a very thin gold foil. A microscope with a glass screen coated with zinc sulphide is used to detect alpha particles at different deflection angles q. (Marsden had to spend hours squinting into the microscope, for each value of q, counting the flashes each time an a-particle impacts the screen at that angle)

At the time of experiment, the prevailing model for the atom was the Plum Pudding Model, proposed by J J Thomson after he discovered that the electron is a component of every atom. It was believed that other than the electrons, the rest of the atom (i.e. the mass and the positive charge) was distributed uniformly throughout the volume of the atom.

Based on calculations done using the total volume, mass and charge of the atom, the alpha particles (which were known to be massive and moving at very high speeds) were expected to experience negligible deflection by the few gold atoms they encounter as they cruise through the thin gold leaf[1].

However, actual experimental observations showed that even though most (> 99%) of alpha particles passed through with little or no angular deflection, a few alpha particles (about 1 in 8000) suffered deflections of more than 90°. A very small number were even deflected backwards!

Without a doubt, those alpha particles had encountered a far greater electrostatic force than predicted by the Plum Pudding model. These results were so unexpected that Rutherford later wrote: “It was quite the most incredible event that ever happened to me in my life. It was almost as incredible as if you had fired a 15-inch shell at a piece of tissue paper and it came back and hit you.”

Rutherford realized that a much more concentrated positive charge is required to produce such a strong electric repulsion on the alpha particles. To understand this, recall that the strongest electric field strength of a (uniformly) charged sphere is at the surface of the sphere: the smaller the sphere, the stronger the field. For example, a 1 uC of charge distributed evenly in a spherical volume of radius 1 m has an electric field strength of $\displaystyle \frac{1}{{4\pi {{\varepsilon }_{0}}}}\frac{{1\times {{{10}}^{{-6}}}}}{{{{1}^{2}}}}\text{ N }{{\text{C}}^{{-1}}}$ on its surface. If the same amount of charge is squeezed into a sphere of radius 1 mm, the field strength on the surface would be $\displaystyle \frac{1}{{4\pi {{\varepsilon }_{0}}}}\frac{{1\times {{{10}}^{{-6}}}}}{{{{{0.001}}^{2}}}}\text{ N }{{\text{C}}^{{-1}}}$ , one million times stronger!

Rutherford worked out the required size of the nucleus to match the distribution of deflection angles observed in the experiment. The conclusion was astounding: instead of being distributed over a sphere of radius 10^-10 m (the estimated size of an atom), the positive charge (and the remaining mass of the atom) had to be concentrated in a tiny sphere of radius 10^-15 m! This very dense particle (both in mass and charge) came to be known as the nucleus.

This is a shocking revelation. Firstly, the nucleus occupies only a tiny fraction $\displaystyle {{(\frac{{{{{10}}^{{-15}}}}}{{{{{10}}^{{-10}}}}})}^{3}}={{10}^{{-15}}}$ of the volume of the atom. But everything is made of atoms! So look around you, every object is 99.9999999999999% empty space by volume! Secondly, the density of the nucleus ( $\displaystyle 2.3\times {{10}^{{17}}}\text{ kg }{{\text{m}}^{{-3}}}$ ) is out-of-this-worldly high. If water were to have the same density, a raindrop ~1 mm in diameter is going to weigh about 120,428 tons (heavier than an aircraft carrier). Truth is indeed stranger than fiction.