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# Nuclei

The discovery of the nucleus is usually credited to Rutherford as a result of his scattering experiments. The experiments of Rutherford and others showed that all nuclei are composed to two particles, protons and neutrons. These two types of particles, called nucleons, are both much more massive than an electron. Every nucleus can be specified by the numbers of protons and neutrons it contains. The number of protons in a nucleus is called the atomic number, Z. Because each element has a particular and unique number of protons in its nucleus, each has a characteristic value of Z. For example, the atomic number of He is Z = 2, while the atomic number of O is Z = 8. Since atoms are electrically neutral, Z is also equal to the number of electrons in an atom. The number of neutrons in a nucleus is usually denoted by the symbol N. The value of N for a particular element can vary. For example, He nuclei can have N = 1, N = 2 or N = 4 and other values are also possible. The number of neutrons in atomic nuclei generally increases as the atomic number increases.

## Atomic Masses

When differentiating between kinds of atoms, it becomes important to be able to tell them apart by their masses. Atomic mass is the mass of an atom as measured in atomic mass units. Although many standards for calculating the mass of atoms were used in the past, currently scientists use the atomic mass unit, which is the unit of mass equal to 1/12 the mass of a carbon-12 atom. The carbon-12 atom is an atom that has six protons, six neutrons and 12 electrons, making in total a mass of 1.9926 × 10-23 g. This means that 1/12 of that mass or one atomic mass unit, is equal to 1.6605 × 10-24 g. The atomic mass unit is often abbreviated as amu and more recently as just the letter u. The atomic mass of each element is given on the periodic table and is actually a weighted average of all the naturally occurring isotopes of an element. For example, there are isotopes of carbon-13 and carbon-14, but because they occur in much smaller amounts than carbon-12, they don't change the atomic mass of carbon very much. However, the mass of carbon is listed as 12.0111 u and not exactly 12 u.

## Isotopes

Atoms that have the same number of protons but differ in their number of neutrons are called isotopes. For example, there are three isotopes of the element hydrogen for which Z = 1 is Hydrogen or Protium, Deuterium, Tritium. The general symbol for an isotope is  $_{Z}^{A}\textrm{X}$
Where, A = Mass number = number of protons + number of neutrons, Z = Atomic number = number of protons, X = Element symbol

• The atomic number Z defines an element; it also tells you how many electrons a neutral atom of that element possesses. Thus, the number of neutrons equals A-Z.
• Isotopes of an element have the same charge on the nuclei of their atoms and the same number of electrons; only the masses of their nuclei differ.

A nuclide is a nucleus of a specific isotopes. Almost every element has one or more stable isotopes and every element has a number of unstable, radioactive isotopes, that is, isotopes that spontaneously decay to become other elements.

## Isobars and Isotones

Isobars
Atoms with the same mass but belonging to different chemical elements are called isobars. Obviously, isobars possess different number of protons and electrons in their atoms. Total number of protons and neutrons in each of their nuclei is also same. The example of first pair of isobars is argon and calcium. Argon (atomic number 18) has 18p, 18e and 22n in its atom. Calcium (atomic number 20) has 20p, 20e and 20n in its atom.

Isotones

These are the nuclides having the same numbers of neutrons (N) but a different Z and A. Example of isotones are $_{6}^{13}\textrm{C}$ and $_{7}^{14}\textrm{N}$. Isotones having a given value of N, obviously do not all correspond to the same chemical element.

The analysis of the properties of isotopes, isotones and isobars helps us to disclose several features of atomic nuclei. Such analysis helps us to predict that what will happen to the stability of a nucleus when an extra n or p is added to the nucleus.

## Composition and Size of Nucleus

The nucleus was first discovered by Lord Rutherford in 1911 while performing the experiments on scattering of alpha particles by heavy atoms. The nucleus is situated at the center of atoms. It contains whole positive charge and almost whole mass of atom. The size of nucleus is of the order of 10-14 m and it is 10000 times smaller than the size of atom. The study of radioactivity revealed that the nucleus is constituted of particles.
Electron-Proton Hypothesis: Before the discovery of neutron, it was assumed that the atomic nucleus consists of protons and electrons. As mass of electron is negligible as compared to mass of proton; therefore it was assumed that the atomic weight (or the mass number) of atom is equal to the number of protons and number of electrons in the nucleus. That is,
Atomic weight = Number of protons in the nucleus
Atomic Number = Number of protons-Number of electrons in nucleus

## Mass Defect and Binding Energy

Mass Defect
The mass of a nucleus is always less than the total mass of its constituent nucleons. The difference in mass is called the mass defect of the nucleus, i.e.
Mass defect = Mass of nucleons - Mass of nucleus

Binding Energy
The reduction in mass arises because the act of combining the nucleons to form the nucleus causes some of their mass to be released as energy (in the form of gamma rays). Any attempt to separate the nucleons would involve them being given this same amount of energy-it is therefore called the binding energy of the nucleus. It follows from equation (1) that

Binding energy = Mass defect × c2
It follows from equation (2) that
Binding energy = 932 × Mass defect

Tables normally give atomic masses rather than nuclear masses and it is useful to redefine the mass defect as
Mass defect = Mass of nucleons and electrons - Mass of atom

The binding energy of a nucleus is the energy required to break it up into its component neutrons and protons. The binding energy of an atom, on the other hand, is the energy required to break it up into its component neutrons, protons and electrons. The difference between the two is negligible, because the energy required to remove the electrons is very much less than that required to remove the neutrons and protons. For example, the binding energy of a helium nucleus is also 28.3 MeV.
A useful measure of the stability of a nucleus is its binding energy per nucleon (i.e, binding energy divided by mass number), since this represents the (average) energy which needs to be supplied to remove a nucleon. The given figure shows the way this quantity varies with mass number for the naturally occurring nuclides with mass numbers in the range 2-238.

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