 # Proton-Neutron theory of nuclear structure

#### Introduction

In this particular article Proton-Neutron theory of nuclear structure, we are going to discuss the history of neutron structure in the easiest way possible.

# Proton-Neutron theory of nuclear structure

Chadwick discovered neutron in 1932. The charge of the neutron is zero i.e. it is neutral and its mass about 1 amu i.e. its mass is nearly equal to the mass of the proton. The spin(intrinsic angular momentum) of the neutron is also found equal to h/2 i.e. like proton; the spin quantum number of the neutron is 1/2. From experiments, the magnetic moment of proton and neutron is found to be μp = 2.793 μN and μn = -1.913 μN respectively i.e. the order of the magnetic moment of both particles is the same.

After the discovery of the neutron in 1932, Heisenberg proposed that nuclide is made up of protons and neutrons. This assumption is called the proton-neutron theory of the structure of the nucleus. According to this theory, a nuclide of mass number A and atomic number Z is made up of Z protons and (A-Z) neutrons. For examples, nitrogen nuclide (A = 14, Z = 7) has 7 protons and 14-7=7 neutrons, uranium nuclide (A = 238,Z = 92) has 92 protons and 238-92 = 146 neutrons, similarly lead nuclide (A = 208, Z = 82) has 82 protons and 208-82= 126 neutrons.

Proton-neutron theory of nuclear structure is acceptable for the explanation of angular momentum of the nucleus structure is acceptable for the explanation of angular momentum of the nucleus, the magnetic moment of the nucleus, uncertainty principle etc. Due to this reason, this theory of nuclear structure is now accepted universally by all in the scientific world.

### 1. Agreement with the experimental values of the nuclear magnetic moment

Spin quantum number of both proton and neutron is 1/2. The sum of the number of protons and neutrons in the nucleus is equal to the mass number A. Thus if mass number A of the nuclide is even number, the total angular momentum of protons and neutrons in the nuclide of the even number, then the total angular momentum of protons and neutrons in the nuclide of even number A will be either zero or integer multiple of (h/2π) and if mass number A of nuclide is an odd number, the total angular momentum of protons and neutrons in nuclide of odd number A will be odd half-integer multiple of (h/2π).

For example, nitrogen has mass number 14. Thus the total number of protons and neutrons in nitrogen nuclide will be 14 or even number and the total angular momentum of nitrogen nucleus should be the integer multiple of (h/2π). From experiments, the total angular momentum of nitrogen nuclide is found equal to (h/2π). These theoretical and experimental results are in agreement.

#### 2. Agreement with the magnetic moment of the nucleus

The magnetic moment of the proton and neutron is of the order of the μN = 5×10 J/T. Since if we assume nucleus is made up of proton and neutron, then the magnetic moment of the nucleus should be of the order of μN.

From experiments, this fact has been verified.

##### 3. Some other facts in favour of proton-neutron theory-

(a) The size of the mass of a neutron is nearly the same as that of the proton. Therefore the possibility of the neutron is very much in the nucleus with the proton.

(b) Compton wavelength of neutron

λ = h/mc

λ = 6.6 ×10⁻³⁴/ 1.67× 10⁻²⁷× 3× 10⁻⁸ =1.3× 10 ⁻¹⁵m = 1.3 fermi

Hence Compton wavelength of the neutron is comparable to the minimum radius (≈1.3 fermi) of the nucleus, therefore it may exist in the nucleus.

(c) β⁻ decay can be explained by the decay of neutron as,

n⁰ = p⁺ + e⁻ + v

(d) β⁺ Decay can be explained by the decay of proton as,

P⁺ → n⁰+ e⁺+ v

(e) α particle may be assumed to be made up of two protons and two neutrons. This group of two protons of two neutrons may be emitted from the nucleus as a group particle i.e, α particle.

###### Conclusion

In this following article Proton-Neutron Theory of Nuclear Structure, we have studied the theory of Proton-Neutron model in detail. We have also studied Nuclear structure in the easiest way possible.

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