Analysing Decay Series Diagrams (VCE SSCE Physics): Revision Notes

Analysing Decay Series Diagrams

Introduction

Earth generates significant internal heat that keeps our planet warm and geologically active. Scientists have measured heat flow from over 20,000 boreholes worldwide and estimate that approximately 44 TW (44 trillion watts) of heat continuously flows from Earth's interior into space. Remarkably, about half of this heat (22 TW) comes from radioactive decay chains occurring within Earth's crust and mantle.

Three naturally occurring decay chains contribute to this heat: the thorium series, the uranium/radium series (from U-238), and the actinium series (from U-235). Each chain releases energy as it progresses through multiple decay stages, eventually ending with a stable lead isotope.

Key definitions

Understanding decay series requires familiarity with several important terms:

Radioactive decay series: The sequence of stages a radioisotope passes through to become more stable. The chain continues until a stable isotope forms.

Parent nucleus: The original decaying nucleus that undergoes radioactive decay.

Daughter nucleus: A nucleus formed by the radioactive decay of another nucleus (the parent). The daughter may itself be radioactive and undergo further decay.

Decay chain: The complete sequence of stages a radioisotope passes through until it reaches a stable nucleus.

Understanding radioactive decay series

The heaviest naturally occurring radioactive elements don't simply decay once and become stable. Instead, they undergo multiple successive decays, forming what we call a radioactive family or decay series. Each decay in the series produces a new isotope, which may itself be unstable and decay further.

Three major decay series include most naturally radioactive elements in the periodic table:

• The uranium series (starting from U-238)
• The actinium series (starting from U-235)
• The thorium series (starting from Th-232)

The uranium-238 decay chain

The uranium-238 decay series provides an excellent example of how decay chains work. This series begins with uranium-238, which has a half-life of $4.5 \times 10^9$ years (4.5 billion years).

How alpha decay affects nuclei in decay chains

When a nucleus undergoes alpha decay, it emits an alpha particle ($_{2}^{4}\text{He}$). This has a predictable effect on the daughter nucleus. Understanding these changes is essential for tracking elements through decay chains.

The daughter nucleus has:

• Two fewer protons than the parent (atomic number decreases by 2)
• Four fewer nucleons than the parent (mass number decreases by 4)

How beta decay affects nuclei in decay chains

When a nucleus undergoes beta decay, it emits a beta particle ($_{-1}^{0}\beta$), which is a high-energy electron. The process involves a fundamental change within the nucleus itself.

During beta decay:

• One neutron converts to a proton
• The atomic number increases by 1
• The mass number remains unchanged

This means beta decay produces daughter nuclei that move up the periodic table to the next element.

Gamma decay and decay chains

Alpha and beta decay are often accompanied by gamma ray emission. However, gamma rays play a different role in nuclear reactions compared to alpha and beta particles.

For example, when U-238 undergoes alpha decay, two gamma rays of different energies are emitted in addition to the alpha particle:

$_{92}^{238}\text{U} \rightarrow _{90}^{234}\text{Th} + _2^4\text{He} + 2\gamma_0^0$

Interpreting decay chain diagrams

Decay chain diagrams are essential tools for visualising radioactive decay series. Understanding how to read these diagrams is a key skill for VCE Physics students. These diagrams contain multiple layers of information that, once decoded, reveal the complete story of a decay series.

Diagram axes

The vertical axis shows the mass number ($A$), while the horizontal axis shows the atomic number ($Z$).

For example, uranium-238 appears where $A = 238$ and $Z = 92$, because uranium-238 is written as $_{92}^{238}\text{U}$.

Alpha decay arrows

Alpha decays are shown as red diagonal arrows running from upper right to lower left at 45°. These arrows end in a box where:

• The mass number has decreased by 4
• The atomic number has decreased by 2

This makes sense because the alpha particle ejected is $_{2}^{4}\text{He}$.

For example, when radium-226 ($_{88}^{226}\text{Ra}$) undergoes alpha decay, the arrow points to element $_{86}^{222}\text{X}$. Checking the periodic table shows element 86 is radon, correctly shown as $_{86}^{222}\text{Rn}$ on the diagram.

Beta decay arrows

Beta decays are shown as blue horizontal arrows pointing to the right. These arrows end in a box where:

• The mass number is unchanged
• The atomic number has increased by 1

This makes sense because the beta particle ejected is $_{-1}^{0}\beta$.

For example, when lead-214 ($_{82}^{214}\text{Pb}$) undergoes beta decay, the arrow points to element $_{83}^{214}\text{X}$. Checking the periodic table shows element 83 is bismuth, correctly shown as $_{83}^{214}\text{Bi}$ on the diagram.

Half-life information

Decay chain diagrams also provide the half-life ($t_{1/2}$) for each decay step. This information reveals the relative stability of each nucleus in the chain.

Half-lives are given in various units depending on their magnitude:

• Years (for very long half-lives)
• Days
• Hours (h)
• Minutes (min)
• Seconds (s)
• Milliseconds (ms)
• Microseconds (μs)