# A-level Physics/Forces, Fields and Energy/The nuclear atom

Up until the 19th century, atoms were once thought to be the smallest building blocks of matter, and that matter could not be broken down any further. We now know that atoms are made up of smaller, sub-atomic, particles. This has also helped us to understand the nuclear processes such as fission and fusion.

## Structure of the atom

Plum pudding atom

Near the end of the 19th century, it was widely accepted that the atom was neutral as a whole, and had areas of concentrated negative lumps within a larger positive structure. This model of the atom was called the plum pudding model, where the pudding was positive, and the plums were the negative electrons. This is also called the chocolate chip cookie model.

### Discovery of the nucleus

In 1906, Ernest Rutherford was investigating the passage of α particles through gold foil. What he found was that most of the α particles passed straight through the foil, and there was some that were deflected by an angle of greater than 90°. It was known that α particles were smaller than atoms and had a positive charge, and from this Rutherford concluded that the atom is mostly empty space and has a positively charged nucleus at the center, which was repelling the α particles. This experiment disproved the plum pudding model, and the new nuclear model was now the widely accepted model. He also calculated that the nucleus had a diameter of around ${\displaystyle 10^{-14}m}$.

Later, the negative "lumps" that originally led to the plum pudding model were found to actually be electrons orbiting the nucleus with a relatively large radius of about ${\displaystyle 10^{-10}m}$, also confirming that an atom is mostly empty space.

### Discovery of the proton

The next step was to find out what the nucleus was made up of. The proton was discovered, again by Rutherford, in 1919. To find the protons, he placed a source of α radiation inside a cylinder of nitrogen gas. The cylinder had an opening at one end, which was covered by a sheet of aluminium foil. A screen was placed outside the opening, and flashes of light were observed on the screen. The flashes of light were caused by particles hitting the screen, but since it was known that aluminium foil prevents α particles from passing through, another, smaller, particle must have been hitting the screen. Rutherford asked two of his research students, Geiger and Marsden, to take measurements of the deflection angles of the particles, and he found by calculations that the proton was smaller than most nuclei, and had a positive charge which was the same magnitude of an electron. The distribution of the deflected alpha particles is different for different forces (for example, magnetic, hard sphere etc.). Rutherford was able to be sure that the nucleus was positively charged.

### Discovery of the neutron

In 1932, James Chadwick discovered a particle that was slightly greater in mass than the proton and had no electric charge, which he called the neutron. He used α radiation from polonium, and directed it towards some beryllium. The beryllium emitted neutrons when it was bombarded with the α radiation, but since they have no charge, they were hard to detect. Chadwick placed some paraffin wax in the path of the neutrons, and the paraffin wax emitted high energy protons (paraffin wax contains a large amount of hydrogen). This showed that there were particles hitting the atoms of the paraffin wax without being slowed down by the positively charged nucleus of the atoms, and that they collide elastically with atoms.

### Evidence of crystal structure

A beam of X-rays can be directed at a piece of crystalline material, and the resulting dots on the screen behind it are a regularly spaced pattern. The regularly spaced dots are evidence that the atoms in the material have a crystal structure. If the atoms weren't in a crystal structure, the resulting pattern would be smeared rings.

X-rays are used because the wavelength of X-rays are roughly the same as the spacing between atoms, and therefore the diffraction is greatest. An electron beam can also be used to provide the same evidence.

### Evidence of the size of nuclei

A beam of high-energy electrons can be used to find the radius of nuclei. High-energy electrons are electrons that have been accelerated to high velocities, so that their de Broglie wavelength could be changed to match the spacings of nuclei. The electrons are diffracted around different nuclei and calculations are done to find the radius of a nucleus from the angle of diffraction.

### Relative sizes

The size of various particles were found from the above experiments as:

• radius of protonradius of neutron${\displaystyle 10^{-15}}$m
• radius of nucleus${\displaystyle 10^{-15}}$m to ${\displaystyle 10^{-14}}$m
• radius of atom${\displaystyle 10^{-10}}$m
• radius of molecule${\displaystyle 10^{-10}}$m to ${\displaystyle 10^{-6}}$m

## Nuclear processes

### Nuclear equations

A helium atom

If we look at a helium nucleus, we can see that it has two neutrons and two protons. It can be represented like this:

${\displaystyle \ _{2}^{4}He}$

The 4 at the top represents the number of nucleons in the nucleus, and is therefore called the nucleon number, and sometimes the mass number. It is sometimes denoted by the letter A.

The 2 at the bottom represents the number of protons, and is therefore called the proton number, or atomic number, and is sometimes denoted by the letter Z. To be more precise, however, the proton number represents the charge of the nucleus, so that an electron is represented by:

${\displaystyle \ _{-1}^{0}e}$

In all nuclear processes, there is always a balance. The number of neutrons and protons are always the same before and after a process, and so the nucleon and proton numbers must stay the same. Consider the reaction:

${\displaystyle \ _{1}^{2}H+\ _{1}^{2}H=\ _{2}^{4}He}$

Here 2 hydrogen nuclei fuse to form a helium nucleus. You can add the nucleon numbers together, to give ${\displaystyle 2+2=4}$, and you can add the proton numbers together, to give ${\displaystyle 1+1=2}$. As you can see, both sides of the equals sign are balanced.

### Nuclear fission

The splitting up of nucleus into two approximately equal fragments.

### Nuclear fusion

It is when smaller nuclei combines to form larger stable nuclei.

## Isotopes

Isotopes have same number of protons but different number of neutrons.