Discovery of Neutron,Radius and Density of Nucleus

We know that matter is made up of atoms. We also know that in atom, at the Center, mass is concentrated with the combination of protons and neutrons. That central part of the atom is called nucleus and the elements of the nucleus are called nucleons. We also know that electrons revolve around the nucleus in specified orbits.

The number of the protons inside the nucleus is called atomic number. The total number of the nucleons inside the nucleus is equal to the sum of number of the protons and the number of the neutrons. This total number of the nucleons is called mass number. The number of the nucleons present inside the nucleus is the difference between the mass number and the atomic number. The conversion of one element into the other element by artificial means is called artificial transmutation of element.

Discovering neutrons has taken much longer time than the discovery of electrons and protons. It is simply because they are not having a charge and hence identifying their presence has taken a little bit longer time. A scientist by the name James Chadwick has discovered the neutrons.

When a helium particle is allowed to strike a beryllium atom, carbon atom is farmed which is in unstable state. It further splits into a stable carbon atom and a neutron. The problem with the identification of the neutron is it is not having charge. Therefore it is allowed to pass through paraffin material which is a rich resource of protons.

Whenever a neutron strikes the paraffin, one proton is released. Identifying the proton is very easy with electronic counter. The number of the neutrons released in this process is nothing but equal to the number of the protons. The experimental arrangement is as shown in the block diagram.

Properties of neutrons

It has no charge.
It is not influenced by electric and magnetic fields as it is not having a charge.
It has a high penetration power so that it can penetrate deep into the materials.
It has low ionization ability.
It is stable inside the nucleus but not stable outside the nucleus. It has average life of thousand seconds outside the nucleus. It means once if it is outside the nucleus it can stay like the neutron only for thousands seconds and within that time it converts into anti-neutrino, electron and proton.
The speed of the neutron can be slowed down by passing it through heavy water.
The mass of the neutron is approximately equal to mass of the proton.

Classification of nuclei

The nuclei having the same atomic number but different mass number are called isotopes. They have same number of protons but different number of neutrons.

The nuclei having the same mass number but different atomic number are called isobars. Here total number of the nucleons is same but the number of the protons and neutrons are different in each case.

The nuclei having the same number of the neutrons are called isotones. They have different mass numbers and different atomic numbers but the difference between mass number and atomic number is same.

In the following attracted paper the examples of this different kinds of nuclei are given.

To measure the mass of fundamental particles like electrons and protons the regular systems like standard international system are not directly useful. As these masses are very small, in accordance to them, small unit of mass is defined and that unit is called atomic mass unit. One atomic mass unit is defined as one by 12^th of the mass of the carbon atom.

Nuclear size

Nucleus consists of both protons and neutrons. Neutrons are neutral particles whereas the protons are having positive charge. The total charge of the nucleus is equal to the product of number of the protons and the charge of each proton. In terms of magnitude charge of proton and electron are equal. But the proton has a positive charge whereas the electron has a negative charge.

There is a lot of empty space inside the atom. The size of the nucleus is very small when compared with the size of the atom. The size of the nucleus is directly proportional to number of nucleons. It is simply because the nucleus is nothing but the group of the nucleons.

Therefore we can conclude that the volume of the nucleus is directly proportional to mass number. We can also assume that the nucleus is approximately spherical in shape. Basing on this we can derive the relation between the radius of the nucleus and the mass number as shown below. We can also express this radius in terms of the mass number as shown below.

Application

A stationary nucleus splits into two lighter nuclei. Find the ratio of velocity of the two elements of the nuclei?

As there is no external force acting on the system, the linear momentum of the system is always conserved. Initially the nucleus is being in the state of rest and hence its initial momentum equal to 0. After the explosion both the particles will have same the momentum in the opposite direction. Hence we can express the equation for velocity and kinetic energies as shown below.

We have already explained that the mass of the fundamental particles can be measured with the unit called atomic mass unit. Similarly to measure their corresponding energies we need to use a unit called electron volts. We know according to Einstein’s mass energy relation that each mass will have correspondingly some energy.

In the above diagram the conversion is made and it is proved that one atomic mass unit is having energy equal to 931.5 million electron volt.

Nuclear density

We know that density is defined as mass per unit volume. Density of the nucleus is also defined as the ratio of total mass of the nucleus to its volume. By substituting the expression for the radius in the above equation and by simplifying we can calculate that the density of the nucleus. It is a very high value as shown below. It is also proved that the density of the nucleus is independent of mass number. It means whatever may be the name of the nuclei; the density is going to be the same. The derivation is shown below.