Nuclear Physics: Radioactivity, Fission, Fusion, and Applications

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## **1. Introduction to the Atom and Nucleus**
### **1.1 Structure of the Atom**
An atom consists of:
- **Protons (p⁺)** – Positively charged particles in the nucleus.
- **Neutrons (n⁰)** – Neutral particles in the nucleus.
- **Electrons (e⁻)** – Negatively charged particles orbiting the nucleus.

```figure
{"type":"layers","layers":["Electrons","Nucleus"],"right":["Orbiting nucleus","Protons + Neutrons"],"highlight":["Nucleus"],"caption":"Simplified atomic structure showing electrons orbiting the nucleus (protons and neutrons)"}

The nucleus is extremely small but contains almost all the mass of the atom.

Key Idea: The nucleus is held together by the strong nuclear force, which is much stronger than the electrostatic repulsion between protons.

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2. Radioactivity

Radioactivity is the process by which unstable nuclei emit radiation to become more stable.

2.1 Types of Radioactive Emissions

There are three main types of radioactive decay:

2.2 Half-Life

• Half-life (T₁/₂) is the time taken for half of the radioactive nuclei in a sample to decay.
• It is a constant for a given isotope.
• Formula: [ N = N_0 \left( \frac{1}{2} \right)^{\frac{t}{T_{1/2}}} ] where:
  • ( N ) = remaining nuclei after time ( t )
  • ( N_0 ) = initial number of nuclei
  • ( t ) = elapsed time
  • ( T_{1/2} ) = half-life

Example: If a radioactive sample has a half-life of 5 years, how much remains after 15 years? Solution: After 15 years (3 half-lives), only ( \frac{1}{8} ) of the original sample remains.

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3. Nuclear Reactions

3.1 Nuclear Fission

• Definition: A heavy nucleus (e.g., Uranium-235) splits into smaller nuclei when struck by a neutron, releasing energy.
• Example: [ ^{235}_92U + ^1_0n \rightarrow ^{141}_56Ba + ^{92}_36Kr + 3^1_0n + \text{Energy} ]
• Applications:
  • Nuclear power plants (e.g., Koshi Power Station, Nepal)
  • Atomic bombs

3.2 Nuclear Fusion

• Definition: Two light nuclei (e.g., Hydrogen isotopes) combine to form a heavier nucleus, releasing huge energy.
• Example (Sun’s reaction): [ ^2_1H + ^3_1H \rightarrow ^4_2He + ^1_0n + \text{Energy} ]
• Advantages:
  • No radioactive waste (clean energy).
  • Huge energy output (1 kg of fuel = 10 million kg of coal).
• Challenges:
  • Requires extremely high temperatures (~100 million °C).
  • Not yet commercially viable (experimental reactors like ITER).

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4. Applications of Nuclear Physics

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5. Safety and Hazards of Radioactivity

5.1 Hazards

• Alpha (α): Harmful if ingested (e.g., Radon gas).
• Beta (β⁻): Can penetrate skin, causing burns.
• Gamma (γ): Highly penetrating, dangerous even outside the body.

5.2 Safety Measures

• Use lead shields for gamma rays.
• Wear protective suits (e.g., in hospitals).
• Store radioactive materials in lead-lined containers.
• Follow time, distance, shielding rules.

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6. Solved Examples (NEB Style)

Example 1: Alpha Decay

Question: A Polonium-210 nucleus undergoes alpha decay. What is the daughter nucleus? Solution: $${}_{84}^{210}Po{\to }_2^{4}He{+}_Z^{A}X$$

• Mass number (A): $210-4=206$
• Atomic number (Z): $84-2=82$
• Daughter nucleus: Lead-206 (${}_{82}^{206}Pb$)

Example 2: Half-Life Calculation

Question: A radioactive sample has a half-life of 8 days. If the initial activity is 1000 Bq, what is the activity after 24 days? Solution:

• Number of half-lives = $\frac{24}{8}=3$
• Remaining activity = $1000\times {\left(\frac{1}{2}\right)}^3=125$ Bq

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7. NEB Board-Style Questions

Short Answer Questions

1. Define half-life and explain its importance in nuclear medicine.
2. What is the difference between nuclear fission and nuclear fusion?
3. Why is gamma radiation more dangerous than alpha radiation?

Long Answer Questions

4. Explain the process of nuclear fission with an example. How is it used to generate electricity?
5. Describe the safety precautions taken while handling radioactive materials in hospitals.
6. Compare fission and fusion in a table, mentioning their advantages and disadvantages.

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Exam Tip

✅ For NEB exams:

• Memorize the three types of radioactivity (α, β, γ) and their properties.
• Practice half-life calculations—it’s a common question!
• Understand the difference between fission and fusion (fission = splitting, fusion = combining).
• Draw diagrams for nuclear reactions (e.g., fission/fusion) to earn extra marks.
• Relate to real life: Mention applications like medical uses, power plants, or carbon dating in answers.

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Good luck with your NEB Physics exam! 🚀