Radioactivity: alpha, beta, gamma and half-life: WASSCE Physics

Some atoms are unstable. Without any outside cause, their nuclei break up and fire out particles or rays. This radioactivity is used to treat cancer, date ancient bones and generate electricity — and it must be handled with respect.

Learning objectives

By the end of this lesson you should be able to:

define radioactivity and name the three types of radiation
compare the nature, charge, penetration and ionising power of alpha, beta and gamma radiation
write equations for alpha and beta decay
define half-life and solve half-life problems

Radioactivity

Definition

Radioactivity (radioactive decay) is the spontaneous disintegration of the unstable nuclei of certain atoms, with the emission of alpha particles, beta particles and/or gamma rays.

Decay is spontaneous (it happens by itself) and random (we cannot predict when a particular nucleus will decay). It is not affected by temperature, pressure or chemical combination.

The three radiations

Alpha particles are stopped by paper, beta particles by a few millimetres of aluminium, while gamma rays pass through both and are only reduced by thick lead

Figure 1. Penetrating power of alpha, beta and gamma radiation. WASSCE Tutor diagram.

Property	Alpha (α)	Beta (β)	Gamma (γ)
Nature	helium nucleus $^{4}_{2}\text{He}$ (2 protons + 2 neutrons)	fast electron $^{0}_{-1}e$	electromagnetic wave (photon)
Charge	+2	−1	0
Relative mass	4	$\dfrac{1}{1840}$	0
Speed	about 5% of the speed of light	up to about 99% of $c$	speed of light
Penetration	least: stopped by paper or a few cm of air	stopped by a few mm of aluminium	most: reduced by thick lead or concrete
Ionising power	strongest	moderate	weakest
Deflection in fields	slightly, towards negative	strongly, towards positive	not deflected

The greater the ionising power, the faster the radiation loses its energy, so the less penetrating it is.

Nuclear equations

In any nuclear equation, the nucleon numbers (top) and the proton numbers (bottom) must balance.

Alpha decay: the nucleus loses 2 protons and 2 neutrons. $A$ falls by 4, $Z$ falls by 2.

^{238}_{92}\text{U} \rightarrow\ ^{234}_{90}\text{Th} +\ ^{4}_{2}\text{He}

\begin{gathered}^{238}_{92}\text{U} \\[6pt] \rightarrow \ ^{234}_{90}\text{Th} +\ ^{4}_{2}\text{He}\end{gathered}

Beta decay: a neutron changes into a proton and an electron, which is emitted. $A$ is unchanged, $Z$ rises by 1.

^{14}_{6}\text{C} \rightarrow\ ^{14}_{7}\text{N} +\ ^{0}_{-1}e

\begin{gathered}^{14}_{6}\text{C} \\[6pt] \rightarrow \ ^{14}_{7}\text{N} +\ ^{0}_{-1}e\end{gathered}

Gamma emission: no change in $A$ or $Z$ ; the nucleus simply loses energy.

Worked example

$^{226}_{88}\text{Ra}$ emits an alpha particle, and the product then emits a beta particle. Find the final nuclide's proton and nucleon numbers.

After α: $A = 226 - 4 = 222$ , $Z = 88 - 2 = 86$ .

After β: $A = 222$ , $Z = 86 + 1 = 87$ .

Final: $^{222}_{87}\text{X}$ .

Half-life

Decay curve: the activity of a sample falls from 800 to 400 counts per minute in one half-life, to 200 after two half-lives and to 100 after three

Figure 2. Radioactive decay curve. WASSCE Tutor diagram.

Definition

The half-life $T_{1/2}$ of a radioactive substance is the time taken for half of the radioactive nuclei in a sample to decay (equivalently, for its activity to fall to half).

After $n$ half-lives, the fraction remaining is $\left(\dfrac{1}{2}\right)^n$ :

N = N_0\left(\dfrac{1}{2}\right)^{t/T_{1/2}}

\begin{aligned}N &= N_0\left(\dfrac{1}{2}\right)^{t/T_{1/2}}\end{aligned}

Half-lives range from fractions of a second to billions of years (uranium-238: 4.5 × 10⁹ years; carbon-14: 5730 years; iodine-131: 8 days).

Worked example

A radioactive sample has a half-life of 6 hours. What fraction remains after 24 hours? If it starts with 160 g, what mass remains?

Number of half-lives $= \dfrac{24}{6} = 4$ . Fraction remaining $= \left(\tfrac{1}{2}\right)^4 = \dfrac{1}{16}$ .

Mass remaining $= \dfrac{160}{16} = 10$ g. (160 → 80 → 40 → 20 → 10.)

Worked example

The activity of a sample falls from 800 to 100 counts per minute in 15 days. Find its half-life.

$800 \rightarrow 400 \rightarrow 200 \rightarrow 100$ : three half-lives in 15 days, so $T_{1/2} = 5$ days.

Common mistake

After two half-lives, a quarter remains, not none. Half-life halves what is left each time; it never reaches exactly zero.

Key points

Radioactive decay is spontaneous and random, unaffected by physical or chemical conditions.
α: helium nucleus, +2, least penetrating, most ionising. β: electron, −1. γ: EM wave, most penetrating, least ionising.
α decay: $A - 4$ , $Z - 2$ . β decay: $A$ same, $Z + 1$ .
Half-life: time for half the nuclei to decay; after $n$ half-lives, $(1/2)^n$ remains.

WASSCE examination focus

WAEC tests this

Compare alpha, beta and gamma radiation (nature, charge, penetration, ionisation, deflection), complete nuclear equations, and solve half-life problems (fractions remaining, masses, activities, or reading half-life from a decay curve). These appear in nearly every paper.

Quick check

Which radiation is the most penetrating?
$^{234}_{90}\text{Th}$ emits a beta particle. What is the product?
A source has a half-life of 2 days. What fraction remains after 6 days?

Answers: 1. Gamma. 2. $^{234}_{91}\text{Pa}$ (protactinium): $A$ unchanged, $Z$ up by 1. 3. $\tfrac{1}{8}$ .

Radioactivity: alpha, beta, gamma and half-life

Learning objectives

Radioactivity

The three radiations

Nuclear equations

Half-life

Key points

WASSCE examination focus

Quick check

Keep going with radioactivity and nuclear physics

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