Chapter 13 - Nuclei

Almost the entire mass of an atom is concentrated in its tiny nucleus. The nucleus contains positively charged protons packed extremely close together, yet it can remain stable.

Nuclei Class 12 studies nuclear composition, size, nuclear force, mass defect, binding energy, fission and fusion.

Composition of the nucleus

The nucleus contains:

• Protons

• Neutrons

Together, they are called nucleons.

The atomic number gives the number of protons. The mass number gives the total number of protons and neutrons.

Atoms with the same atomic number but different neutron numbers are isotopes.

Nuclear size

Nuclear radius increases approximately with the cube root of mass number.

Because nuclear volume is proportional to mass number, nuclear density is approximately constant across many nuclei under the model.

The nucleus is extremely small compared with the atom.

Nuclear force

Protons repel each other electrically, but nuclei can remain bound because of the strong nuclear force.

At the school level, students learn that nuclear force is:

• Very strong

• Short-ranged

• Approximately charge-independent between nucleons

• Attractive over the relevant nuclear separation range

• Saturating, so a nucleon interacts strongly mainly with nearby nucleons

Mass-energy equivalence

Einstein’s mass-energy relation shows that mass can be treated as a form of energy.

A small change in mass can correspond to a very large change in energy because it is multiplied by the square of the speed of light.

Mass defect

The measured mass of a nucleus is less than the sum of the separate masses of its protons and neutrons.

The difference is called mass defect.

This “missing” mass corresponds to the energy released when the nucleus forms.

Binding energy

Binding energy is the energy required to separate a nucleus completely into its individual nucleons.

A larger total binding energy does not automatically mean greater stability when comparing nuclei of different sizes.

Binding energy per nucleon is a more useful measure of average nuclear binding.

Binding-energy curve

The binding-energy-per-nucleon curve explains the relative stability of nuclei.

It rises for light nuclei, reaches a broad maximum for medium-mass nuclei and then decreases gradually for heavy nuclei.

This explains why energy can be released through:

• Fusion of light nuclei

• Fission of heavy nuclei

Both processes move products towards more strongly bound configurations.

Nuclear fission

In nuclear fission, a heavy nucleus splits into lighter nuclei and releases energy.

Additional neutrons may also be produced, allowing further reactions under suitable conditions.

Students study the energy release using mass difference and binding-energy ideas.

Nuclear fusion

In nuclear fusion, light nuclei combine to form a heavier nucleus.

Fusion can release large amounts of energy because the product has greater binding energy per nucleon.

Very high temperatures are required to overcome electrical repulsion between positively charged nuclei.

Fusion powers stars, including the Sun.

Common student difficulties

Students often:

• Confuse atomic number and mass number

• Mix atomic mass with nuclear mass

• Forget electron masses when using atomic-mass data

• Treat mass defect as an experimental error

• Confuse binding energy with binding energy per nucleon

• Assume larger total binding energy always means greater stability

• Mix fission and fusion

• Make unit errors between atomic mass unit, joule and electron-volt

How Teachoo helps

Teachoo provides:

• Nuclear-composition explanations

• Radius and density questions

• Mass-defect calculations

• Binding-energy numericals

• Binding-energy curve interpretation

• Fission and fusion questions

• NCERT solutions

• MCQs and competency-based questions

Frequently Asked Questions

What is the difference between atomic number and mass number?

Atomic number is the number of protons. Mass number is the total number of protons and neutrons.

Why is nuclear mass less than the sum of nucleon masses?

Some mass is converted into binding energy when the nucleus forms.

What is binding energy per nucleon?

It is the total binding energy divided by the number of nucleons and is used to compare average nuclear binding.

Why does fission release energy?

The fission products are more strongly bound per nucleon than the original heavy nucleus.

Why does fusion release energy?

Light nuclei combine to form a nucleus with greater binding energy per nucleon.

Are fusion and fission opposite processes?

They involve combining and splitting nuclei respectively, but both release energy only when the products are more tightly bound.