Physics

o .
NUCLEI
Atomic mass unit (u)
An atomic mass unit is defined as 1/12th the mass of a carbon (12C) atom. According to this-




Isotopes and Average Atomic mass
Isotopes
Atoms with same atomic number (exhibit the same chemical properties) but different mass number are known as
isotopes of each other. For e.g., Chlorine (34.98Cl and 36.98Cl), Hydrogen.

Average Atomic mass
Different isotopes of the same element have different relative abundances. Therefore, the atomic mass of such an
element is given by its average atomic mass which is calculated as follows-
For e.g., consider an element A with two isotopes A1 and A2 with relative abundance of A1 being b%. The average
atomic mass of A is given by-

Percentage of A 2 = 100-b




Note: Hydrogen has three isotopes- Protium, Deuterium and Tritium. Tritium nuclei is radioactive and is unstable
therefore, it is not found naturally.


Composition of the nucleus
The nucleus consists of two entities namely, protons and neutrons (collectively known as nucleons). The positive
charge inside the nucleus comes from the protons.
Neutrons are neutral particles. Free neutrons, unlike protons are unstable. It decays into a proton, an electron, and a
antineutrino.
The composition of the nucleus can be described using the following symbols and terms-
Z-atomic number = number of protons
N-neutron number = number if neutrons
A-mass number = Z + N = total number of protons and neutrons.

Note: 1. Notation for nuclear species or nuclides-
Where X is the chemical symbol of the species.

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

3. All nuclides with same mass number are called isobars

4. Nuclides with same neutron number N but different atomic number Z are called isotones

, Mass-Energy Equivalence
According to Einstein’s Special Theory of Relativity, mass is another form of energy and one can convert mass-energy
into other forms of energy and vice-versa.
Mass-energy equivalence relation-


Size of the Nucleus (PYQ 2015, 2013)
The radius of a nucleus of mass number A-


Where R˳ = 1.2 × 10-15 m
This means that the volume of the nucleus is proportional to A and thus the density of the nucleus is independent of
A. Different nuclei are like drops of liquid of constant density

Nuclear Binding Energy (PYQ 2010)
We know that the nucleus is made up of neutrons and protons. Therefore, it is logical to conclude that the mass of
the nucleus is equal to the total mass of the its individual protons and neutrons. However, the nuclear mass M is
always found to be less than this.
The difference in mass of a nucleus and its constituents, ΔM, is called mass defect and is given by-



Meaning of Mass Defect
Since the mass of the nucleus is less than the sum of masses of its constituents, the equivalent energy of the nucleus
is less than the sum of equivalent energies of its constituents. Therefore, if one wants to break a nucleus into
protons and neutrons, the extra energy ΔMc2 has to be supplied. This energy required Eb is related to mass defect-



If a certain number of neutrons and protons are brought together to form a nucleus of a certain charge and mass, an
energy Eb will be released in the process. The energy Eb is called the binding energy of the nucleus. If we separate a
nucleus into its nucleons, we would have to supply a total energy equal to Eb, to those particles.


Binding Energy per Nucleon (PYQ 2016)
The average energy per nucleon needed to separate a nucleus into its individual nucleons.
The following is a plot for the binding energy per nucleon (Ebn)-




We can make the following observations-
1. the binding energy per nucleon, Ebn, is practically constant, i.e., practically independent of the atomic number for
nuclei of middle mass number (30 < A < 170).
2. Ebn is lower for both light nuclei (A<30) and heavy nuclei (A>170).