Question

Describe nuclear forces explaining the structure of nucleus.

Answer 1

Nuclear Force:

We have read that the size of nucleus is 10^-15 m and in the nucleus the positive protons and neutral neutrons are present. There should be so much electrical repulsion between the protons of such a short distance that the nucleus cannot be stable, but the nucleus is still stable. It means that there is another force other than the gravitational and electric force, which keeps the nucleons in such a small place. This force is called nuclear force.

It could not be found yet, on changing the distance, the nuclear force changes according to which rule, but it is very certain that the rate of change of the nuclear forces on changing the distance is much higher than the gravitational force and the electrical force otherwise the nucleus is not stable. Gravitational force, Coulomb’s force and the nuclear force have the following ratio :
F_g : F_e : F_n = 1 : 10³⁶ : 10³⁸
The following facts have been found in about the nuclear force :
(i) Nuclear forces are independent on electric charges. For a given system, the force between learn about charge distribution in the nucleus. Similarly, we get to know about the nuclear force (and not the nuclear charge) from the neutron-nucleus scattering experiment, from
which we know about the mass distribution in the nucleus.

(ii) The range of nuclear forces is very small, of the order of nuclear size (of few femtometres), but from such type of scattering experiments, we inside this range, the nuclear force is much stronger than the electric force (50 ~ 60 times). Outside this range, nuclear forces are not two protons and two neutrons and that between 1 neutron and 1 proton is almost equal in magnitude. Electrons are not affected by the nuclear force. That is why in the scattering experiments by high energy electrons, electrons are scattered by the nuclear charge only and effective.

(iii) Nuclear forces are not central forces in nature. For the pairing of two nucleons, they do not depend upon the distance between them but also on the direction of their spin.

(iv) The density of nuclear matter is almost constant and the nuclear binding energy in the middle mass range is almost constant. This shows that each nucleon in a nucleus does not interact with the other nucleons present but interact with only some of them. (Think about a nucleon in a nucleus of mass number A. If it interacts with all other nucleons, then we will get interactions to be A (A – 1) / 2, then the total binding energy is proportional to A (A -1) and for A > >1, it is proportional to A². This would mean the binding energy per nucleon is proportional to A i. e., it is not constant). This property of nuclear force is called “saturation nf nuclear force.” This is different from electric force. Each proton interacts with all other protons (and number of \(\frac{Z(Z-1)}{2} \sim Z^{2}\))

(v) Nuclear forces are dependent or spin or angular momentum of nucleons. Force between nucleons having parallel spins is greater than the force between nucleons having antiparallel spins.

(vi) Nuclear forces are due to exchange of π mesons between the nucleon,

(vii) When the distance between nucleons becomes less than 0.8 fermi, the nuclear forces become strongly repulsive. The graph ploted between force and distance are given below:

The potential energy is minimum at distance r₀ = 0.8 fm. At this distance, force between nucleons is zero. For distance larger than 0.8 fm. negative potential energy goes on decreasing. The nuclear forces are attractive. For distance less than 0.8 fm. The negative potential energy decreases to zero and then becomes positive. The graph between potential energy and distance is given below:
(viii)Nuclear forces are generally attractive but repulsion is observed when the distance between the nucleons is found to be less than the order of 1 fm

Nuclear Structure:

After the discovery of neutron in 1932 by James Chadwick, the scientist Heisenberg told that the nucleus is compared with protons and neutrons.

1. The number of protons present in the nucleus is called atomic number (Z).

2. The sum of the number of protons ad neutrons present in the nucleus in called mass number (A).

3. The proton has a positive charge equal to the electronic charge, while the neutron is the neutral particle.

4. The mass of the neutrons and protons present in the nucleus is almost identical. The mass of neutron is more than 0.5% of the mass of proton. Mass of Neutron m_n = 1.67626231 × 10^-27 kg
Mass of Proton m_p – 1.6749286 × 10^-27 kg

5. Electron is the original particle of nature, but neutrons and protons are not pure particles because they are made from other particles, they are known as Quarks.

6. Nuclear number and mass number can be detected by the symbol of nuclear species or nuclides. According to the sign convention for nuclear species  or ^AX_Z or _ZX^A are used.
Where,
X: Chemical symbol of an element.
Z : Atomic number of a element which is equal to the number of proton present in nucleus.
A: Mass number of nuclear species which is also to the total number of nucleons.
N.: Number of neutrons in nucleus is given by the relation A – Z.

7. Neutron and proton present in the nucleus experienced the same nuclear force so the combined form of these are called nucleons.