A level revision

Discovery of the nucleus

In 1909 two physicists named Hans Geiger and Ernest Marsden, under the direction of Ernest Rutherford, discovered the first modern model of the atom with a small massive positive centre (now known as the nucleus) orbited by distant electrons.

Marsden and Geiger fired alpha decay at a thin sheet of gold. Alpha particles are just the nucleus of a helium atom, 2 protons and 2 neutrons giving the particles a positive charge. The pair found that whilst the majority of the particles went through the gold sheet as they had expected however a small number were directed back towards the alpha source, seemingly 'bouncing' off of the gold sheet.

Alpha particles typically have lots of energy so for them to be turned 180 degrees back on themselves required something massive. However as only a small proportion (around 1 in 8,000) alpha particles were scattered this way whatever was causing the force was also very small. It must also be positively charged in order to repel the positively charged alpha particle. It was from this that Rutherford concluded the atom consisted of a massive but small positively charged centre surrounded by distant electrons. This meant that most of the atom was space which was why most alpha particles went through the gold sheet.

Forces between the alpha particle and nucleus

Using coulombs law the force between the alpha particle nucleus can be calculated.

Coulombs law which describes the force between two charged particle is:

See: Electric fields of charged spheres for more information on this equation.

The charge on the alpha particle is +2e, where e is the charge on an electron. This is because the alpha particle is just the nucleus of a helium atom and as such contains two protons. The charge on the nucleus is +Ze where Z is the atomic number (number of protons) of the element. Substituting these into the coulombs law equation for and gives:

Where is the distance between the centers of the two particles.

Estimating the size of the nucleus

If the energy of the particle has is known it is possible to work out how close it comes to the nucleus and therefore estimate the size of the nucleus. This is done using the equation for electrical potential energy around a charged sphere:

As with force it is possible to substitute values for and :

The closest an alpha particle is going to come to a nucleus is in a head on collision. At the point that the electron potential energy of the nucleus is equal to that of the energy of the alpha particle it will come to stop before being repelled back towards the alpha source. If the amount of energy the alpha particle has is denoted by the distance, , it stops from the centre of the nucleus is given by the equation:

From the gold sheet experiment the size of the nucleus of gold can be estimated to be in the range of metres.