Structure of Nucleus

The nucleus of an atom consists of two types of particles, positively charged particles called protons and neutrally charged particles called neutrons. Protons + Neutrons in an atom represent the nucleus of an atom. The nucleus of an atom is represented by _ZX^A, where X is the nucleus of an atom, Z is the atomic number and A is the mass number.

Terms Related to the Nucleus of an Atom

• Nucleons: Protons and neutrons which are present in the nuclei of atoms are collectively known as nucleons.
• Atomic Number: The number of protons in the nucleus is called the atomic number of the element. It is denoted by Z.
• Mass Number: The total number of protons and neutrons (collectively known as nucleons) present in a nucleus is called the mass number of the element. It is denoted by A.
• Nuclear Mass:  The total mass of the protons and neutrons present in a nucleus is called nuclear mass.

Note: Few important points to remember regarding the nucleus are:

• Number of protons in an atom = Number of electrons in an atom = Z
• Number of nucleons in an atom = A
• Number of neutrons in an atom N = A – Z
• A proton has a positive charge Q_p= 1.6×10^-19 C and mass m_p = 1.6726×10^-27kg  
• A neutron has no charge and its mass m_n = 1.6749×10^-27kg  
• No electrons are present inside the nucleus.

Types of Nuclei

Various types of Nuclei are discussed below:

• Isotopes: These are nuclei of the same element having the same Z but different A.  Ex– ₈O¹⁶, ₈O¹⁷, ₈O¹⁸
• Isotones: These are nuclei of different elements having the same N but different A. Ex– ₆C¹³₇ and ₇N¹⁴₇
• Isobars: These are nuclei of different elements having the same A but different N and Z. Ex– ₆C¹⁴ and ₇N¹⁴
• Mirror Nuclei: These are nuclei with the same A but in which neutron and proton numbers are interchanged. Ex– ₄Be⁷₃(Z= 4, N=3) and ₃Li⁷₄(Z=3, N=4)
• Isomer Nuclei: These are nuclei with the same A and same Z but differ in their nuclear energy states. They have different lifetimes and internal structures. These nuclei have different radioactive properties. Ex– Co⁶⁰ and Co^60*

Size of the Nucleus

Rutherford assumed the distance of the closest approach as a measure of the size of an atomic nucleus. Assuming, the nuclei are spherical, the relation between the radius of the nucleus and the mass number is given by:

R = R₀A^1/3 

where, 
R₀ is constant
For electrons R₀ = 1.25×10^-15m = 1.25 fermi(fm)

The Radius R of a nucleus is proportional to the cube root of its mass number. 

Density of Nucleus

The nuclear density is independent of mass number A. The nuclear density is nearly constant and is equal to

ρ = (3m)/(4πR₀ ³) = 2.04×10¹⁷ kg/m³

where m is the mass of a nucleus

Atomic Mass Unit (u or amu)

One atomic mass unit is defined as (1/12)th of the actual mass of a carbon-12 atom. It is denoted by amu or u.

1 amu = (1/12)× Mass of carbon-12 atom

           = (1/12) × 1.992678×10^-26 kg

1 amu = 1.660565×10^-27 kg

Electron Volt

It is defined as the energy acquired by an electron when it is accelerated through a potential difference of 1 volt and is denoted by eV.

1 eV = 1.602×10^-19J

Relation between amu and MeV: 

1 amu = 931 MeV

Nuclear Forces

The strong forces of attraction which firmly hold the nucleons in the small nucleus and account for the stability of the nucleus are called nuclear forces.

Characteristics of Nuclear Force

Some important characteristics of Nuclear Forces are:

• Nuclear force is a short-range force.
• Nuclear forces are the strongest force in nature.
• Nuclear forces are charge-independent.
• Nuclear forces are spin-dependent.
• Nuclear forces show saturation property.
• Nuclear forces are non-central forces.
• Nuclear forces are exchange forces.

Mass Defect

The mass of the nucleus is always less than the sum of the masses of nucleons composing the nucleus. The difference between the rest mass of the nucleus and the sum of the rest masses of nucleons constituting the nucleus is known as mass defect.

△m = [Zm_p +(A-Z)m_n] – M(_ZX^A)

where,
m_p = mass of protons
Z = Atomic number
A = Mass number

Binding Energy

The energy required to break a nucleus into its constituent nucleons and place them at an infinite distance is called binding energy.

BE = (△m) c² = c² [Zm_p +(A-Z)m_n– M(_ZX^A)]

where,
m_p = mass of protons
Z = Atomic number
A = Mass number
c = speed of light

Rest Mass of Protons + Rest Mass of Neutrons = Rest Mass of Nucleus + BE

Binding Energy per Nucleon

The binding energy per nucleon of a nucleus is the average energy required to extract a nucleon from the nucleus.

Binding energy per nucleon 

Solved Examples of Structure of Nucleus

Example 1: Compare the radii of two nuclei with mass numbers 1 and 27 respectively.

Solution:

Radius of nucleus R = R₀A^1/3

 

 R₁/R₂ = (1/27)^1/3

            = 1/3

Example 2: What is the nuclear radius of ¹²⁵Fe if that of ²⁷Al is 3.6 fermi?

Solution:

Nuclear radius, R = R₀A^1/3 ⇒ R∝A^1/3

For Al, A = 27, R_Al = 3.6 fermi, 

For Fe A = 125

R_Fe/R_Al = (125/27)1/3

RFe = (5/3)R_Al 

       = (5/3) ×3.6 fermi

R_Fe = 6 fermi

Example 3: A neutron breaks into a proton and electron. Calculate the energy produced in this reaction in MeV. Mass of an electron = 9.1 ×10^-31 kg, Mass of proton = 1.6725×10^-27 kg, Mass of neutron 1.6747×10^-27 kg. Speed of light = 3×10⁸ ms^-1.

Solution: 

Mass defect (△)m = Mass of neutron – (mass of proton + mass of electron)

△m = [(1.6747×10^-27) – (1.6725×10^-27 + 9.1 ×10^-31)]

△m = 0.0013×10^-27 kg

Energy released Q = △mc²

Q = (0.0013×10^-27) × (3×10⁸)²

    = 1.17×10^-13 J

Q = (1.173×10^-13) / (1.6×10^-19)

    = 0.73×10⁶ eV

Q = 0.73 MeV

Example 4: Find the binding energy of ¹²₆C. Also, find the binding energy per nucleon. Given mass of ¹₁H = 1.0078 u, 10n =1.0087 u, ¹²₆C = 12.00004u.

Solution: 

One atom of ¹²₆C consists of 6 protons, 6 electrons, and 6 neutrons. The mass of the uncombined protons and electrons is the same as that of six ¹₁H atoms.

Mass of six ¹₁H atoms = 6×1.0078 = 6.0468 u

Mass of six neutrons = 6 × 1.0087 = 6.0522 u

Total mass of particles = 6.0468 +6.0522 
                                    = 12.0990 u

Mass of ¹²₆C atom = 12.00004

Mass defect = 12.0990 – 12.00004 
                   = 0.0990 

Binding energy = 931 × (0.099) 
                        = 92 MeV

Binding energy per nucleon = 92/12
                                            = 7.66 MeV

FAQs on Structure of Nucleus

Question 1: What are nucleons?

Answer: 

Protons and neutrons which are present in the nuclei of atoms are collectively known as nucleons.

Question 2: What is a mass number?

Answer: 

The total number of protons and neutrons (collectively known as nucleons) present in a nucleus is called the mass number of the element. It is denoted by A.

Question 3: What do you mean by atomic mass unit (amu)?

Answer: 

One atomic mass unit is defined as (1/12)th of the actual mass of a carbon-12 atom. It is denoted by amu or u. 1 amu = 1.660565×10^-27 kg

Question 4: State the relation between amu and MeV.

Answer:

1 amu = 931 MeV

Question 5: How to find the number of neutrons in an atom?

Answer:

Number of neutrons in an atom (N) = Mass number (A) – Number of protons in an atom (Z)

Question 6: State the relation between the radius of a nucleus and mass number.

Answer:

R = R₀A^1/3 

where, 
R₀ is constant
For electrons R₀ = 1.25×10^-15m = 1.25 fermi(fm)

Related Resource

• Molecule and Compound
• Isotopes and Isobars
• Density of Gas