Analysis On Nuclear Density

Nuclear matter is an idealized system of interacting nucleons (protons and neutrons) that exists in several phases of exotic matter that, as of yet, is not fully established. It does not matter in an atomic nucleus, but a hypothetical substance consisting of a huge number of protons and neutrons held together by only nuclear forces and no coulomb force. But ideally, it is considered as a matter which contains the same number of neutrons and protons. And also considered to have extremely high densities like stars or stellar matter. So basically, this is used to find and compare properties of different stellar matters, and an important parameter considered is nuclear density.

So the next possible question is, what is Nuclear Density?

Various scattering experiments were done to find the density, and all suggest that nuclei are roughly spherical and appear to have essentially the same density. This was almost confirmed by the fermi model. From this, they elucidated Nuclear density as the density of the nucleus of an atom, averaging about 2.3×1017 kg/m3. The descriptive term nuclear density is also applied to situations where similarly high densities occur, like in stars.

Experimental workout:

The formula for the number density of a nucleus is 

Here A-Mass number

n=A4πR3

The number density for any nucleus, in terms of mass number, is thus constant, not dependent on A or r, theoretically:

n=A43(A13R0)3=34π(1.25fm)3=1.22 ×1044m-3

The mass density is the product of n by the nuclear mass. The calculated mass density, using a nucleon mass of 1.67×10−27 kg, and thus the density is found out to be ;

1.76×10-271.22×1044=2.04×1017kg.m-3

As we have found the approx. value of nuclear density now we can clearly tell the order of nuclear density, which is 1017kg.m-3

Nuclear density being a constant value is Independent of mass number?

All the experiments done on the nuclear matter show that the nuclear density seems to be independent of the details of neutron number or proton number, i.e., it doesn’t depend on the mass number.

Still, the mass number is irrelevant in the real case, and the force between the particles is essentially the same whether they are protons or neutrons. 

This correlates with other evidence that the strong force is the same between any pair of nucleons. Nuclei are made up of protons and neutrons bound together by the strong force, which is the main factor that decides the nuclear density. In general terms, both protons and neutrons are referred to as nucleons. The number of protons is the atomic number and determines the chemical element. Nuclei of a given element (same atomic number) may have different neutrons and are then said to be different isotopes of the element.

Applications Of Nuclear Density

• The descriptive term nuclear density is also applied to situations where similarly high densities occur, such as within neutron stars.
• Using deep inelastic scattering has helped with finding the size of an electron.
• Probing deeper within particles, one finds quarks that appear to be very dense and hard. There are possibilities for still-higher densities when it comes to quark matter. 

Conclusion

As we have seen, Rutherford and his finding have been a breakthrough since the 1900s. This article deals with a nuclear density of matter, which is applied mainly in astronomical research to find and compare the densities and masses of different stellar matters. We have also discussed its properties and found and derived how it is a constant independent of its mass number. These are the only basic framework of the vast theories and discoveries of nuclear physics and radioactivity. This knowledge will help us understand further the complexities that we’ll encounter.