6.1 Radioactive Decay
Radioactive decay is a natural, spontaneous, and random process by which an unstable nucleus releases radiation to achieve greater stability. Explore alpha, beta and gamma emissions, decay series, half-life and radioactive dating.
Learning Objectives
- State the meaning of radioactive decay and its random and spontaneous nature.
- Write and balance radioactive decay equations for alpha, beta and gamma decay.
- Define half-life and interpret radioactive decay series and decay curves.
- Solve numerical problems involving half-life, number of undecayed nuclei and radioactive activity.
Summary of Radioactive Decay Modes and Half-life Decay Curve
Compare how alpha, beta and gamma emissions change a nucleus, then read the exponential decay curve using half-life steps.
Decay Mode Balance Cards
Alpha Decay
Parent nucleus emits a helium nucleus.
A − 4, Z − 2\(^{A}_{Z}\mathrm{X} \rightarrow\ ^{A-4}_{Z-2}\mathrm{Y} +\ ^{4}_{2}\mathrm{He}\)
Beta Decay
A neutron changes into a proton and an electron.
A unchanged, Z + 1\(^{A}_{Z}\mathrm{X} \rightarrow\ ^{A}_{Z+1}\mathrm{Y} +\ ^{0}_{-1}\mathrm{e}\)
Gamma Decay
An excited nucleus releases excess energy.
A unchanged, Z unchanged\(^{A}_{Z}\mathrm{X} \rightarrow\ ^{A}_{Z}\mathrm{X} + \gamma\)
Half-life Decay Curve
Short Explanation
What is Radioactive Decay?
Radioactive decay is a process in which an unstable nucleus becomes more stable by emitting radioactive radiation. It is spontaneous and random.
Three Types of Radiation
An alpha particle is \(^{4}_{2}\mathrm{He}\). A beta particle is \(^{0}_{-1}\mathrm{e}\). A gamma ray is a high-frequency electromagnetic wave.
Alpha decay general equation
\(^{A}_{Z}\mathrm{X} \rightarrow\ ^{A-4}_{Z-2}\mathrm{Y} +\ ^{4}_{2}\mathrm{He}\)Proton number decreases by 2, nucleon number decreases by 4.
Beta decay general equation
\(^{A}_{Z}\mathrm{X} \rightarrow\ ^{A}_{Z+1}\mathrm{Y} +\ ^{0}_{-1}\mathrm{e}\)Proton number increases by 1, nucleon number remains unchanged.
Gamma decay general equation
\(^{A}_{Z}\mathrm{X} \rightarrow\ ^{A}_{Z}\mathrm{X} + \gamma\)No change in proton number or nucleon number; excess energy is released.
| Decay type | Emitted particle / ray | Change in proton number, Z | Change in nucleon number, A |
|---|---|---|---|
| Alpha | \(^{4}_{2}\mathrm{He}\) | −2 | −4 |
| Beta | \(^{0}_{-1}\mathrm{e}\) | +1 | 0 |
| Gamma | \(\gamma\) | 0 | 0 |
Radioactive Decay Series
A continuous series of successive decays starts from an unstable parent nucleus and passes through intermediate daughter nuclei until a stable nucleus is reached. The uranium-238 series begins at \(^{238}_{92}\mathrm{U}\) and ends at stable \(^{206}_{82}\mathrm{Pb}\).
Half-life and Activity
Half-life \(T_{\frac{1}{2}}\) is the time taken for half of the radioactive nuclei in a sample to decay. Activity \(A\) is the number of decays per second.
Remaining nuclei and activity after n half-lives
\(N = \left(\frac{1}{2}\right)^n N_0\) \(A = \left(\frac{1}{2}\right)^n A_0\)where \(n = \frac{t}{T_{\frac{1}{2}}}\).
Try to Answer First
Answer in your mind, then press “Check Answer”.
What happens to the nucleon number and proton number of a nucleus after emitting a beta particle?
Check Answer
A radioactive sample has an initial activity of \(800\ \mathrm{s^{-1}}\). If its half-life is 4 hours, what will its activity be after 12 hours?
Check Answer
Why cannot radioactive decay be accelerated by raising the temperature or pressure of the sample?
Check Answer
Common Mistakes
- Confusing the number of undecayed nuclei remaining with the number of decayed nuclei formed. After \(n\) half-lives, remaining fraction is \(\left(\frac{1}{2}\right)^n\), while decayed fraction is \(1 - \left(\frac{1}{2}\right)^n\).
- Subtracting 1 from the nucleon number during beta decay instead of keeping \(A\) unchanged and adding 1 to the proton number \(Z\).
- Failing to balance both the top nucleon number and bottom proton number on both sides of a nuclear equation.
- Assuming gamma emission creates a brand-new chemical element, whereas it only de-excites an existing nucleus to a lower energy state.
Concept Misunderstandings
Radioactive materials decay completely to zero at the end of two half-lives because \(50\% + 50\% = 100\%\).
In each successive half-life, half of the remaining nuclei decay. After 1 half-life, \(50\%\) remains; after 2 half-lives, \(25\%\) remains; after 3 half-lives, \(12.5\%\) remains.
“Spontaneous” means the decay occurs instantaneously or very rapidly.
“Spontaneous” means the decay occurs naturally without requiring external initiation and is unaffected by external environmental factors such as temperature or pressure.
Beta particles come from the electron shells surrounding the nucleus.
A beta particle is an electron that originates from inside the nucleus when an unstable neutron decomposes into a proton and an electron.
Summary
- Radioactive decay is a random and spontaneous disintegration of an unstable nucleus accompanied by the emission of ionizing radiation.
- Alpha decay: \(^{A}_{Z}\mathrm{X} \rightarrow\ ^{A-4}_{Z-2}\mathrm{Y} +\ ^{4}_{2}\mathrm{He}\). Proton number drops by 2, nucleon number drops by 4.
- Beta decay: \(^{A}_{Z}\mathrm{X} \rightarrow\ ^{A}_{Z+1}\mathrm{Y} +\ ^{0}_{-1}\mathrm{e}\). Proton number increases by 1, nucleon number remains constant.
- Gamma decay: \(^{A}_{Z}\mathrm{X} \rightarrow\ ^{A}_{Z}\mathrm{X} + \gamma\). Nucleon and proton numbers do not change.
- Half-life \(T_{\frac{1}{2}}\) is the time taken for half of the radioactive nuclei in a sample to decay.
- Remaining nuclei \(N = \left(\frac{1}{2}\right)^n N_0\) and remaining activity \(A = \left(\frac{1}{2}\right)^n A_0\), where \(n = \frac{t}{T_{\frac{1}{2}}}\).
Short Activity
Objective: Check your understanding of radioactive decay, half-life and decay equations.
A. Objective Quiz
1 Which statement correctly describes the change in a nucleus when it undergoes beta decay?
2 A sample of radioisotope has an initial activity of \(1\,200\ \mathrm{s^{-1}}\) and a half-life of 15 minutes. What is its activity after 45 minutes?
B. Fill in the Blanks
3 Radioactive decay is described as because it occurs naturally without being influenced by external physical factors like temperature and pressure.
4 An alpha particle is identical to the nucleus of a helium atom, consisting of two protons and two .
C. Matching / Drag and Drop
Drag each term to the correct meaning. If using a phone, tap the answer first, then tap the matching box.
