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Science Grade XII Physics

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Chapter 13: Nuclei

Grade 12 Science | Chapter 13

Nuclei

The nucleus holds immense energy. This chapter develops its composition, mass and binding energy, the stability curve, radioactivity, and nuclear fission and fusion.

Core Concepts

Key Principles

Worked Examples

Practice Sets

Contents

Introduction: The Nucleus

Composition of the Nucleus

Mass, Energy and Binding Energy

Nuclear Stability

Radioactivity

Fission and Fusion

Key Reasoning (Principles)

Worked Examples (10)

Practice Sets A to D

10.

Summary and Exam Quick-Check

1. Introduction: The Nucleus

At the heart of every atom is the nucleus, tiny but holding nearly all the atom’s mass and an enormous store of energy. Understanding the nucleus explains radioactivity, the energy of stars, and nuclear power. This chapter looks at what the nucleus is made of, why some nuclei are stable and others decay, and how splitting or joining nuclei releases energy.

Core idea

The nucleus is made of protons and neutrons. Mass is converted to energy by E equals m c squared, and the binding energy per nucleon decides stability, peaking near iron.

2. Composition of the Nucleus

The nucleus is built from two kinds of particle, together called nucleons: positively charged protons and uncharged neutrons. The number of protons fixes which element it is, while the number of neutrons can vary, giving isotopes, atoms of the same element with different masses. A strong force, acting only over very short distances, binds the nucleons tightly together against the repulsion of the protons.

Diagram 1 – The Nucleus

A nucleus made of protons and neutrons packed together

Fig 1. The nucleus is a tight cluster of protons and neutrons, the nucleons.

3. Mass, Energy and Binding Energy

Einstein showed that mass and energy are linked by E equals m times c squared, so a small mass holds a huge energy. Curiously, a nucleus weighs slightly less than its separate nucleons; this missing mass has been converted into the binding energy that holds the nucleus together. The more binding energy per nucleon, the more tightly bound and stable the nucleus is.

4. Nuclear Stability

Plotting the binding energy per nucleon against the mass number gives a key curve. It rises steeply for light nuclei, reaches a peak near iron, and then falls slowly for heavy nuclei. Nuclei near the peak are the most stable. This shape explains where nuclear energy comes from: moving toward iron, by joining light nuclei or splitting heavy ones, releases energy.

Diagram 2 – Binding Energy per Nucleon

The binding energy per nucleon curve peaking near iron

Fig 2. The binding energy per nucleon peaks near iron, so energy is released moving toward it.

5. Radioactivity

Unstable nuclei give out radiation as they change, a process called radioactivity. There are three kinds: alpha decay emits a helium nucleus, beta decay emits an electron, and gamma decay emits a high energy photon. Each unstable nucleus decays at its own rate, described by its half-life, the time for half of a sample to decay. After each half-life, half of what remains decays again.

Diagram 3 – Radioactive Decay

The three types of radioactive decay: alpha, beta and gamma

Fig 3. Alpha decay emits a helium nucleus, beta decay an electron, and gamma decay a photon.

6. Fission and Fusion

Two processes release the nucleus’s energy. In fission, a heavy nucleus such as uranium splits into smaller ones, releasing energy, which powers nuclear reactors. In fusion, light nuclei such as hydrogen join to form a heavier one, releasing even more energy, which powers the Sun and stars. Both move nuclei toward the stable peak near iron, which is why they release energy.

7. Key Reasoning (Principles)

Principle 1: The nucleus is protons and neutrons

Protons fix the element and neutrons may vary to give isotopes, all held by a strong short range force against proton repulsion.

Principle 2: Binding energy comes from missing mass

A nucleus weighs less than its separate nucleons, and that missing mass, by E equals m times c squared, is the binding energy that holds it together.

Principle 3: Moving toward iron releases energy

Because binding energy per nucleon peaks near iron, splitting heavy nuclei or joining light ones releases energy as they become more stable.

8. Worked Examples

Example 1

Q: What two particles make up the nucleus?

▶ Show Solution

Protons and neutrons.

Answer: Protons and neutrons.

Example 2

Q: What are protons and neutrons together called?

▶ Show Solution

Nucleons.

Answer: Nucleons.

Example 3

Q: What are isotopes?

▶ Show Solution

Atoms of the same element with different numbers of neutrons.

Answer: Same element, different neutrons.

Example 4

Q: Write the mass energy relation.

▶ Show Solution

E equals m times c squared.

Answer: E = m c squared.

Example 5

Q: What is binding energy?

▶ Show Solution

The energy holding the nucleus together, from the missing mass.

Answer: Energy holding the nucleus together.

Example 6

Q: Where does the binding energy per nucleon peak?

▶ Show Solution

Near iron.

Answer: Near iron.

Example 7

Q: Name the three kinds of radioactive decay.

▶ Show Solution

Alpha, beta and gamma.

Answer: Alpha, beta, gamma.

Example 8

Q: What is the half-life of a sample?

▶ Show Solution

The time for half of it to decay.

Answer: Time for half to decay.

Example 9

Q: After two half-lives, what fraction remains?

▶ Show Solution

Half of a half, which is one quarter.

Answer: One quarter.

Example 10

Q: What is the difference between fission and fusion?

▶ Show Solution

Fission splits a heavy nucleus; fusion joins light nuclei.

Answer: Splitting versus joining.

9. Practice Sets A to D

Set A – Multiple Choice (Basic)

1. The nucleus contains: (a) protons and electrons (b) protons and neutrons (c) only neutrons (d) only photons

2. Isotopes differ in their number of: (a) protons (b) neutrons (c) electrons (d) photons

3. Mass and energy are linked by: (a) E = m c (b) E = m c squared (c) E = m / c (d) E = c squared

4. Binding energy per nucleon peaks near: (a) hydrogen (b) iron (c) uranium (d) helium

5. Splitting a heavy nucleus is called: (a) fusion (b) fission (c) decay (d) ionisation

▶ Reveal Answers

1. (b) protons and neutrons.

2. (b) neutrons.

3. (b) E = m c squared.

4. (b) iron.

5. (b) fission.

Set B – Short Answer (Understanding)

1. What is the nucleus made of, and what holds it together?

2. What are isotopes?

3. Explain binding energy and the missing mass.

4. Describe the binding energy curve.

5. Name the three decays and what each emits.

▶ Reveal Answers

1. Protons and neutrons (nucleons), held by a strong short range force against proton repulsion.

2. Atoms of the same element with different numbers of neutrons.

3. A nucleus weighs less than its separate nucleons; the missing mass, by E equals m times c squared, is the binding energy.

4. It rises for light nuclei, peaks near iron, then falls slowly for heavy nuclei.

5. Alpha emits a helium nucleus, beta an electron, and gamma a high energy photon.

Set C – Application and Reasoning

1. A sample has a half-life of 2 hours. What fraction is left after 4 hours?

2. Why does the Sun release energy by fusion?

3. Why does a reactor release energy by fission?

4. Why is a nucleus near iron very stable?

5. Why does a nucleus weigh less than its parts?

▶ Reveal Answers

1. Two half-lives pass, so one half of a half, which is one quarter, is left.

2. Because joining light hydrogen nuclei moves them toward the stable peak, releasing energy.

3. Because splitting heavy uranium moves the pieces toward the peak, releasing energy.

4. Because it has the highest binding energy per nucleon, so it is held together most tightly.

5. Because some mass has been converted into the binding energy that holds it together.

Set D – Higher Order (Challenge)

1. Explain why both fission and fusion can release energy.

2. A sample has a half-life of 3 days. What fraction remains after 9 days?

3. Explain why heavy nuclei tend to be less stable than those near iron.

4. Explain how E equals m times c squared accounts for the energy of the Sun.

5. Explain why a tiny loss of mass can release a huge amount of energy.

▶ Reveal Answers

1. Because both move nuclei toward the binding energy peak near iron, splitting heavy nuclei or joining light ones, increasing stability and releasing energy.

2. Three half-lives pass, so one half cubed, which is one eighth, remains.

3. Because their binding energy per nucleon is lower than near iron, so they are held less tightly and can split to become more stable.

4. Because fusion in the Sun converts a little mass into a large energy through E equals m times c squared.

5. Because c squared is an enormous number, so even a small mass multiplied by it gives a very large energy.

Chapter Summary

Nucleus

Protons and neutrons (nucleons), strongly bound.

Isotopes

Same element, different neutron number.

Mass Energy

E equals m times c squared; missing mass is binding energy.

Stability

Binding energy per nucleon peaks near iron.

Radioactivity

Alpha, beta, gamma; described by half-life.

Fission and Fusion

Split heavy or join light nuclei to release energy.

Quantity

Unit

Symbol

Nucleons

protons + neutrons

–

Mass energy

E = m c^2

–

Most stable

near iron

–

8-Point Exam Quick-Check

The nucleus is made of protons and neutrons (nucleons).

Isotopes have the same protons but different neutrons.

Mass and energy are linked by E equals m times c squared.

A nucleus weighs less than its parts; the difference is binding energy.

Binding energy per nucleon peaks near iron.

Radioactive decay is alpha, beta or gamma, set by the half-life.

After each half-life, half of what remains decays.

Fission splits heavy nuclei; fusion joins light ones; both release energy.

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Class 12 Physics Chapter 13: Nuclei, Complete Notes and Practice

This revision guide follows the current NCERT Class 12 Physics syllabus and develops the nucleus, covering its composition of protons and neutrons, isotopes, the mass energy relation and binding energy, the binding energy per nucleon curve peaking near iron, radioactivity by alpha, beta and gamma decay and half-life, and nuclear fission and fusion, with three diagrams, ten worked examples and graded practice. Visit SchoolRevise.com to revise, practise and excel.