In this lecture, we study the phenomenon of radioactivity, understand the properties of alpha, beta, and gamma radiations, and analyze the mathematics of radioactive decay, including the concept of half-life.

☢️ What is Radioactivity?

Radioactivity is defined as:

The spontaneous disintegration of an unstable atomic nucleus accompanied by the emission of radiation.

It is a natural process and does not depend on external conditions like temperature or pressure.

🔹 Types of Radioactive Radiations

There are three main types:

1️⃣ Alpha (α) Decay

• Consists of helium nucleus (2 protons + 2 neutrons)

• Symbol: 24He^4_2He24​He

• Heavy and positively charged

🔸 Properties:

• Low penetrating power

• High ionizing power

• Deflected slightly in electric and magnetic fields

Example:

92238U→90234Th+24He^{238}_{92}U \rightarrow ^{234}_{90}Th + ^4_2He92238​U→90234​Th+24​He

Mass number decreases by 4
Atomic number decreases by 2

2️⃣ Beta (β) Decay

• High-speed electrons (β⁻) or positrons (β⁺)

🔸 β⁻ Decay:

n→p+e−+νˉn \rightarrow p + e^- + \bar{\nu}n→p+e−+νˉ

Example:

614C→714N+e−^{14}_6C \rightarrow ^{14}_7N + e^-614​C→714​N+e−

Atomic number increases by 1

🔸 Properties:

• Medium penetrating power

• Moderate ionizing power

• Strongly deflected in electric and magnetic fields

3️⃣ Gamma (γ) Decay

• High-energy electromagnetic radiation

• No mass

• No charge

Example:

ZAX∗→ZAX+γ^{A}_{Z}X^* \rightarrow ^{A}_{Z}X + \gammaZA​X∗→ZA​X+γ

🔸 Properties:

• Very high penetrating power

• Low ionizing power

• Not deflected in fields

📊 Radioactive Decay Law

Radioactive decay follows exponential law:

dNdt=−λN\frac{dN}{dt} = -\lambda NdtdN​=−λN

Solution:

N=N0e−λtN = N_0 e^{-\lambda t}N=N0​e−λt

where:

• N0N_0N0​ = initial number of nuclei

• $N$ = remaining nuclei

• $\lambda$ = decay constant

⏳ Half-Life (T₁/₂)

Half-life is:

The time required for half of the radioactive nuclei to decay.

Relation with decay constant:

T1/2=0.693λT_{1/2} = \frac{0.693}{\lambda}T1/2​=λ0.693​

📌 Important Concepts

• Activity:

$$A=\lambda N$$

• Unit of activity → Becquerel (Bq)

• Radioactive decay is random but predictable statistically

🌟 Applications of Radioactivity

• Carbon dating

• Cancer treatment (radiotherapy)

• Medical imaging

• Nuclear power

🎯 By the End of This Lecture

You will:

• Define radioactivity

• Differentiate alpha, beta, and gamma radiations

• Write decay equations

• Apply exponential decay law

• Calculate half-life and activity

This lecture prepares you for studying nuclear reactions, fission, and fusion in upcoming lessons.