ICSE 10 Physics Radioactivity Basic Notes

1.0 Introduction to Radioactivity

Radioactivity is a nuclear phenomenon. Unlike chemical reactions which only involve the valence electrons of an atom, radioactivity originates from an unstable nucleus. It is a spontaneous and random process where a nucleus emits radiations to reach a more stable state.

Key Concepts

• Spontaneous Process: It cannot be started, stopped, or accelerated by physical changes (temperature, pressure) or chemical changes.
• Atomic Structure Recap:
  • Atomic Number ($Z$): Number of protons.
  • Mass Number ($A$): Total number of protons + neutrons (nucleons).
• Stable vs Unstable: Nuclei with $Z > 82$ (after Lead) are generally unstable because the repulsive force between protons overcomes the strong nuclear force.

1.1 Alpha, Beta, and Gamma Radiations

An unstable nucleus can emit three distinct types of radiations. Their properties are frequently tested in the "Distinguish Between" section of the ICSE paper.

[attachment_0](attachment)

Property	Alpha ($\alpha$)	Beta ($\beta$)	Gamma ($\gamma$)
Nature	Helium nucleus ($_{2}^{4}He$)	Fast electron ($_{-1}^{0}e$)	Photons (EM Waves)
Ionizing Power	Highest ($10^4$ times $\gamma$)	Medium ($10^2$ times $\gamma$)	Lowest
Penetrating Power	Lowest (Stopped by paper)	Medium (Stopped by Al)	Highest (Stopped by Pb)

1.2 Nuclear Changes (Transmutation)

When a nucleus emits radiation, it changes into a different element. This is represented by Nuclear Equations. (Note: In all equations, the total $A$ and total $Z$ must be conserved).

Radioactive Decay Rules

Alpha Emission: $_{Z}^{A}X \xrightarrow{\alpha} _{Z-2}^{A-4}Y + _{2}^{4}He$

Beta Emission: $_{Z}^{A}X \xrightarrow{\beta} _{Z+1}^{A}Y + _{-1}^{0}e$

Tip: A $\beta$-particle is emitted when a neutron inside the nucleus converts into a proton and an electron.

⚠️ The Gamma Emission Secret

Gamma rays do not change the identity of the element ($A$ and $Z$ remain same). They only carry away excess energy from a nucleus that is in an "excited" state after $\alpha$ or $\beta$ decay.

📝 Solved Example:

A nucleus $_{92}^{238}U$ emits an alpha particle and then two beta particles. What is the final daughter nucleus?

---

Solution:
1. After $\alpha$: $_{92}^{238}U \rightarrow _{90}^{234}Th$.
2. After 1st $\beta$: $_{90}^{234}Th \rightarrow _{91}^{234}Pa$.
3. After 2nd $\beta$: $_{91}^{234}Pa \rightarrow _{92}^{234}U$.
Final Answer: The final nucleus is an isotope of the original Uranium ($_{92}^{234}U$).

💡 Did You Know?

Radioactivity was discovered by accident! Henri Becquerel left some uranium salts on a photographic plate in a dark drawer. Even without light, the plate was "developed" by invisible rays, proving that some materials emit energy on their own.

2.0 Applications and Hazards of Radioactivity

Radioactive isotopes are used extensively in various fields, but they also pose significant biological risks. Understanding how to harness this energy while protecting ourselves is a major focus of the ICSE curriculum.

2.1 Medical, Scientific, and Industrial Uses

• Medical (Therapy): Gamma rays from Cobalt-60 are used to kill cancer cells (Radiotherapy).
• Medical (Diagnostics): Radio-iodine ($I^{131}$) is used to track thyroid function; Sodium-24 is used to detect blood clots.
• Scientific (Archaeology): Carbon-14 dating is used to find the age of ancient organic remains.
• Industrial: Used as thickness gauges in paper mills and to detect invisible cracks in metal castings using Gamma radiography.

2.2 Biological Effects of Radiations

Radiations can be extremely harmful because they ionize the molecules within our cells, leading to two types of damage:

• Somatic Damage: Affects the individual exposed (e.g., burns, hair loss, leukemia, or cataracts).
• Genetic Damage: Affects future generations by causing mutations in the DNA of reproductive cells.

2.3 Safety Precautions & Waste Disposal

For the ICSE Board Exam, you must memorize the specific safety measures used in laboratories and nuclear power plants.

Safety Protocol Checklist

1. Storage: Sources must be kept in thick-walled lead containers with narrow openings.

2. Handling: Always use long-handled tongs; never touch sources with bare hands.

3. Monitoring: Wear film badges to check the total amount of radiation absorbed over time.

⚠️ Nuclear Waste: The Disposal Crisis

Nuclear waste remains radioactive for thousands of years. It should be sealed in thick lead casks and buried in deep underground salt mines or far from human habitation to prevent contamination of the food chain and water table.

📝 Board Reasoning Question:

Why is it safe to keep a radioactive source in a lead container?

---

Solution:
1. Lead has a very high density and high atomic number.
2. It has the highest stopping power for all three types of radiations ($\alpha, \beta, \gamma$).
3. Most of the energy of the radiations is absorbed by the thick lead walls, preventing it from reaching the surroundings.
Final Answer: Because lead effectively absorbs the ionizing radiations due to its high density.

💡 Did You Know?

Radon gas is a natural radioactive gas that seeps out of the ground from the decay of uranium in rocks. In some parts of the world, it is a leading cause of lung cancer in non-smokers, making ventilation a crucial safety measure in basements!

3.0 Nuclear Energy: Fission and Fusion

Nuclear energy is the energy released during a nuclear reaction, either by splitting a heavy nucleus or by joining light nuclei. This energy arises from the conversion of mass into energy, a concept defined by Albert Einstein.

3.1 Mass-Energy Equivalence

Einstein's equation states that mass and energy are interconvertible. When a nuclear reaction occurs, the total mass of the products is slightly less than the total mass of the reactants. This mass defect ($\Delta m$) is converted into energy ($E$).

$$E = \Delta m c^2$$

• $c$: Speed of light ($3 \times 10^8 \, m/s$).
• Atomic Mass Unit (amu): $1 \, amu = 931 \, MeV$ of energy.

3.2 Nuclear Fission

Nuclear Fission is the process in which a heavy nucleus (like $U^{235}$) splits into two lighter nuclei of nearly equal mass when bombarded with slow neutrons, releasing a tremendous amount of energy and more neutrons.

$$_{92}^{235}U + _{0}^{1}n \rightarrow _{56}^{141}Ba + _{36}^{92}Kr + 3_{0}^{1}n + \text{Energy}$$

• Chain Reaction: The neutrons released can further split other Uranium nuclei, leading to a self-sustaining reaction.
• Application: Controlled chain reactions are used in Nuclear Reactors to generate electricity.

3.3 Nuclear Fusion

Nuclear Fusion is the process in which two light nuclei combine to form a heavy nucleus at extremely high temperature and pressure, releasing a vast amount of energy.

• Condition: Requires temperatures of $\approx 10^7 \, K$ to overcome the electrostatic repulsion between positive nuclei. This is why it is called a Thermonuclear reaction.
• Source of Energy: It is the source of energy in the Sun and Stars.

Feature	Nuclear Fission	Nuclear Fusion
Process	Splitting a heavy nucleus.	Joining light nuclei.
Fuel	Uranium, Plutonium.	Deuterium, Tritium.
Waste	Highly radioactive.	Mostly non-radioactive (Helium).

⚠️ Why is Fusion difficult on Earth?

We haven't yet mastered commercial fusion because maintaining $10,000,000^\circ C$ in a controlled environment is incredibly difficult. No material container can withstand such heat, so the plasma must be held in place using magnetic fields.

📝 Solved Example:

If $1 \, g$ of mass is fully converted into energy, how many Joules are released?

---

Solution:
1. Convert mass to kg: $m = 0.001 \, kg$.
2. Apply $E = mc^2$: $E = 0.001 \times (3 \times 10^8)^2$.
3. Calculation: $E = 10^{-3} \times 9 \times 10^{16} = \mathbf{9 \times 10^{13} \, J}$.
Final Answer: $90$ trillion Joules of energy!

💡 Did You Know?

The energy from nuclear fusion in the Sun takes about 100,000 years to reach the Sun's surface, but once it escapes as light, it reaches Earth in just 8 minutes and 20 seconds!

4.0 Numericals and Unit Conversions

The final hurdle in the Radioactivity chapter involves calculating the energy released during nuclear changes. For the ICSE Board, you must be comfortable switching between mass units ($amu$ or $u$) and energy units ($MeV$ or $J$).

The Physicist's Cheat Sheet

• 1 amu (or u): $1.66 \times 10^{-27} \, kg$
• 1 eV: $1.6 \times 10^{-19} \, J$
• 1 MeV: $1.6 \times 10^{-13} \, J$
• Mass to Energy Conversion: $1 \, amu \approx 931 \, MeV$

4.1 Calculating Mass Defect ($\Delta m$)

In any nuclear reaction, the mass of the parent nucleus is always greater than the combined mass of the products. This difference is the mass defect.

Mass Defect ($\Delta m$) = [Mass of Reactants] - [Mass of Products]

4.2 Background Radiation

Often asked in Section A, you should be able to identify sources of radiation that exist even without a radioactive source present in the lab.

• Internal: Potassium-40 ($K^{40}$) inside our bones.
• Terrestrial: Radon gas seeping from rocks.
• Cosmic: High-energy particles from the sun and stars.

⚠️ Exam Tip: Significant Figures

In mass defect calculations, the differences are often very small (e.g., $0.0035 \, amu$). Do not round off your intermediate steps. Keep as many decimal places as provided in the question to ensure your final energy value is accurate.

📝 Solved Example (Mass Defect):

In a nuclear reaction, the mass defect is found to be $0.02 \, amu$. Calculate the energy released in (i) MeV and (ii) Joules.

---

Solution:
1. Energy in MeV:
We know $1 \, amu = 931 \, MeV$.
$E = 0.02 \times 931 = \mathbf{18.62 \, MeV}$.

2. Energy in Joules:
$1 \, MeV = 1.6 \times 10^{-13} \, J$.
$E = 18.62 \times 1.6 \times 10^{-13} = \mathbf{2.9792 \times 10^{-12} \, J}$.
Final Answer: $18.62 \, MeV$ or $2.98 \times 10^{-12} \, J$.

💡 Did You Know?

The energy released in a single fission event of $U^{235}$ is about $200 \, MeV$. While this sounds small, $1 \, kg$ of Uranium can produce as much energy as 2,500 tons of coal! That's the power of the nucleus.