Modern Physics

Chapter in a nutshell: Unstable nuclei undergo radioactivity, emitting alpha (α), beta (β) or gamma (γ) radiation, each with characteristic charge, mass, penetration and ionising power. Emission changes the nucleus by fixed displacement rules. Fission and fusion release huge nuclear energy. Radiation has vital uses but serious hazards, demanding strict safety.

1. Structure of the Atom (recap)

• Atomic number (Z) = number of protons; Mass number (A) = protons + neutrons.
• Isotopes: same Z, different A (e.g. $^{12}_{6}\text{C}$ and $^{14}_{6}\text{C}$).
• A nuclide is written $^{A}_{Z}\text{X}$.

2. Radioactivity

• It is a nuclear phenomenon — independent of temperature, pressure or chemical combination.
• Nuclei are unstable when the neutron-to-proton ratio is unfavourable (often heavy nuclei, Z > 82).

3. The Three Radiations Compared

4. Nuclear Change — Displacement (Soddy–Fajans) Rules

5. Nuclear Energy: Fission & Fusion

• Nuclear fission: a heavy nucleus (e.g. $^{235}\text{U}$) splits into two lighter nuclei + neutrons, releasing enormous energy; the released neutrons can sustain a chain reaction (nuclear reactors, atom bomb).
• Nuclear fusion: light nuclei (e.g. hydrogen) combine to form a heavier nucleus, releasing even more energy per unit mass — the source of the Sun's energy and the hydrogen bomb. Requires extremely high temperature/pressure.
• Both convert a small mass defect into energy ($E=mc^2$).

6. Uses of Radioactivity

• Medicine: cancer therapy (cobalt-60 gamma rays), diagnosis with tracers (iodine-131), sterilising instruments.
• Carbon dating (carbon-14) to find the age of fossils and archaeological samples.
• Industry: detecting flaws/cracks in metals, measuring thickness, tracing leaks in pipelines.
• Agriculture: improving crop varieties; nuclear power for electricity.

7. Hazards & Safety

• Hazards: radiation damages living cells and DNA → burns, mutations, cancer, radiation sickness; genetic effects on future generations.
• Safety measures: lead/concrete shielding, handle sources with remote tongs, maximise distance, minimise exposure time, store in lead containers, wear film badges/dosimeters, proper disposal of nuclear waste.
• Background radiation: weak, ever-present radiation from cosmic rays, rocks, soil and building materials.

8. Worked / Structured Examples (ICSE pattern)

Q2. A nucleus $^{14}_{6}\text{C}$ emits a β particle. Find the product. Solution: A unchanged (14), Z → 6+1 = 7 → $^{14}_{7}\text{N}$ (nitrogen).

Q3. A nuclide emits 1 α then 2 β particles. Net change in A and Z? Solution: A: −4 (α) + 0 + 0 = −4; Z: −2 (α) + 1 + 1 = 0 → same element, mass number reduced by 4 (an isotope).

Q4. Which radiation would you use to (a) treat a deep tumour, (b) is stopped by a sheet of paper? Solution: (a) gamma (most penetrating); (b) alpha.

Q5. Arrange α, β, γ in increasing order of (i) penetrating power, (ii) ionising power. Solution: (i) α < β < γ; (ii) γ < β < α.

9. Key Terms — Quick Glossary

10. Common Mistakes to Avoid

• Saying radioactivity involves electrons/chemical bonds — it is a nuclear process.
• Reversing penetration vs ionisation: γ is most penetrating but least ionising; α is the opposite.
• Wrong displacement rule for β (Z increases by 1, A unchanged).
• Confusing fission (splitting) with fusion (joining).
• Thinking temperature/pressure affect the rate of radioactive decay — they do not.

11. Likely Exam Questions (with crisp answers)

1. Define radioactivity. → Spontaneous disintegration of an unstable nucleus emitting α, β or γ radiation.
2. Name the three radiations and their charges. → Alpha (+2), beta (−1), gamma (0).
3. Which radiation is most penetrating / most ionising? → Most penetrating: gamma; most ionising: alpha.
4. State the change in A and Z on α emission. → A decreases by 4, Z decreases by 2.
5. State the change on β emission. → A unchanged, Z increases by 1.
6. What happens to the nucleus on γ emission? → No change in A or Z; only energy is released.
7. Distinguish nuclear fission and fusion. → Fission = heavy nucleus splits; fusion = light nuclei combine; both release energy.
8. What is the source of the Sun's energy? → Nuclear fusion of hydrogen.
9. Give two uses of radioactivity. → Cancer therapy; carbon dating (also flaw detection, tracers).
10. State two hazards of radiation. → Cell/DNA damage (cancer, mutations); radiation sickness.
11. List three radiation-safety precautions. → Lead shielding, distance, limited exposure time (also remote handling, dosimeters).
12. What is background radiation? → The weak radiation always present from cosmic rays, rocks and surroundings.
13. Why is radioactivity unaffected by temperature or chemical state? → It originates in the nucleus, not in the electrons/bonds.
14. Define isotopes with an example. → Same Z, different A; e.g. $^{12}_{6}\text{C}$ and $^{14}_{6}\text{C}$.

12. Half-Life

• After n half-lives, the fraction remaining $= \left(\tfrac{1}{2}\right)^n$.
• Example: with T½ = 5 days, after 15 days (3 half-lives) only $\left(\tfrac12\right)^3 = \tfrac18$ of the original remains.
• Half-lives range hugely (fraction of a second to billions of years, e.g. $^{238}$U ≈ 4.5 billion years).

13. Detecting Radiation

• Gold-leaf electroscope: radiation ionises the air, discharging the leaf.
• Geiger–Müller (GM) counter: clicks/counts each ionising particle.
• Cloud chamber / photographic film: show or record particle tracks.

14. Nuclear Reactor (idea)

• Fuel: $^{235}$U or plutonium.
• Moderator (graphite/heavy water): slows neutrons to sustain fission.
• Control rods (cadmium/boron): absorb neutrons to control the chain reaction.
• Coolant: carries heat to make steam → drives turbines → electricity.

15. More Worked Examples

Q7. $^{238}_{92}\text{U}$ decays by emitting 1 α and then 1 β. Write the final nuclide. Solution: α: $^{234}_{90}\text{Th}$; then β: $^{234}_{91}\text{Pa}$.

Q8. 80 g of a radioactive isotope (T½ = 6 days) is stored. How much remains after 18 days? Solution: 18/6 = 3 half-lives → $80\times\tfrac18=\mathbf{10\ g}$.

Q9. An element $^{A}_{Z}X$ emits 2 α and 1 β. Find the new A and Z. Solution: A: −8; Z: −4 (from α) +1 (β) = −3 → $^{A-8}_{Z-3}Y$.

16. More Exam Questions (with crisp answers)

1. Define half-life. → Time in which half the nuclei of a radioactive sample decay.
2. Does temperature change the half-life? → No — radioactive decay is a nuclear process, unaffected by external conditions.
3. Name a device to detect radiation. → Geiger–Müller counter (or gold-leaf electroscope).
4. What is the role of control rods in a reactor? → They absorb neutrons to control the rate of the chain reaction.
5. Why is lead used for shielding? → It is dense and absorbs penetrating gamma radiation effectively.
6. Why is fusion not yet used for power generation on Earth? → It needs extremely high temperature/pressure that are hard to sustain and contain.
7. Name the scientist who discovered radioactivity. → Henri Becquerel.
8. Give one use of carbon-14. → Carbon dating to estimate the age of fossils/old organic samples.

17. Effect of Electric & Magnetic Fields on the Radiations

• Alpha (+): deflected slightly (heavy, positive) — towards the negative plate.
• Beta (−): deflected strongly in the opposite direction (light, negative) — towards the positive plate.
• Gamma (0): undeflected (no charge).

18. Nuclear Waste & Disposal

19. Final Quick-Revision Q&A

1. Why is gamma radiation the most dangerous externally? → It penetrates deep into the body (needs thick lead/concrete to stop).
2. Why is alpha radiation dangerous if a source is swallowed/inhaled? → Inside the body its very high ionising power damages nearby tissue intensely.
3. How is the direction of deflection of β different from α in a magnetic field? → Opposite (β is negative, α positive) and β deflects much more (much lighter).
4. Name two moderators used in nuclear reactors. → Graphite and heavy water.
5. State Einstein's mass–energy relation. → $E = mc^2$.