"Nuclei and Radioactivity"

About

The nucleus — a tiny, dense core containing nearly all the mass of an atom — is the seat of radioactivity and nuclear energy. This chapter explores nuclear composition, the forces binding nucleons together, and the spontaneous disintegration of unstable nuclei through radioactive decay.

Key Concepts

26.1 Nuclear Structure

• Atomic number (Z): Number of protons — defines the element
• Mass number (A): Total number of protons + neutrons (nucleons)
• Neutron number (N): $N=A-Z$
• Neutron is slightly heavier than proton
• Protons and neutrons together are called nucleons
• Two atoms belong to different elements if their atomic numbers are different

Atomic number CANNOT be different in two atoms of the same element — it defines the element. Mass number and neutron number can differ (isotopes).

26.2 Isotopes, Isobars, Isotones

Examples:

• Isotopes: ²³⁵U and ²³⁸U (Z = 92)
• Isobars: ⁷⁶Ge and ⁷⁶Se (A = 76)
• Isotones: ²⁷Al (N = 14) and ²⁸Si (N = 14)

26.3 Mass Defect and Binding Energy

Mass defect: $\Delta m=[Z{m}_p+(A-Z)m_n]-M_{\text{nucleus}}$

Binding energy: $BE=\Delta m\cdot c^2$

Binding energy per nucleon ($BE/A$) measures nuclear stability. Maximum at $A\approx 56$ (iron) — most stable.

26.4 Radioactivity

Spontaneous disintegration of unstable nuclei with emission of radiation.

Types of decay:

26.5 Radioactive Decay Law

$N=N_0{e}^{-\lambda t}$

Half-life: $T_{1/2}=\frac{\ln 2}{\lambda }=\frac{0.693}{\lambda }$

Mean life: $\tau =\frac{1}{\lambda }$

Activity: $R=\lambda N$. SI unit: becquerel (Bq) = 1 decay/s.

INTEXT QUESTIONS 26.1

Q1. Make groups of Isotopes, Isobars, and Isotones.

Ans:

• Isotopes (same Z): ¹²C & ¹⁴C; ¹H, ²H & ³H; ¹⁶O & ¹⁸O; ²³⁵U & ²³⁸U
• Isobars (same A): ⁷⁶Ge & ⁷⁶Se; ⁴⁰Ar & ⁴⁰Ca; ³H & ³He
• Isotones (same N): ²H & ³He (N=1); ¹⁴C & ¹⁶O (N=8); ²⁷Al & ²⁸Si (N=14)

Q2. Fill in the blanks:

(i) Neutron is heavier than proton. (ii) Total protons + neutrons = mass number. (iii) Protons and neutrons together = nucleons. (iv) Neutrons in ²⁷Al = 14 (27 − 13). (v) Protons in ²⁸Si = 14. (vi) Different elements → different atomic numbers.

Q3. Which number cannot be different in two atoms of the same element?

Ans: Atomic number (Z). It defines the element. Mass number and neutron number can differ (isotopes).

Terminal Exercise

1. Define atomic number, mass number, and neutron number. Write the symbolic representation of a nucleus.

2. Distinguish between isotopes, isobars, and isotones with examples.

3. What is mass defect? How is it related to binding energy? Draw the BE/A vs A curve.

4. Explain the three types of radioactive decay. Compare their penetrating powers and ionisation abilities.

5. State the radioactive decay law. Derive $N=N_0{e}^{-\lambda t}$.

6. Define half-life and mean life. Derive the relation between them.

7. The half-life of ²³⁸U is $4.5\times 10^9$ years. Find its decay constant.

8. A radioactive sample has $10^{20}$ nuclei and a half-life of 10 days. How many nuclei remain after 30 days?

9. Explain why: (a) α-particles are the most ionising, (b) γ-rays are the most penetrating.

10. Complete the nuclear reactions: (a) ²³⁸U → ²³⁴Th + ? (b) ¹⁴C → ¹⁴N + ?

Quick Revision