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Radioactive Decay and the Origin of Gamma and X-Radiation

1.1 Introduction

In this chapter, I intend to show how a basic understanding of simple decay schemes, and of the role gamma radiation plays in these, can help in identifying radioactive nuclides and in correctly measuring quantities of such nuclides. In doing so, I need to introduce some elementary concepts of nuclear stability and radioactive decay. X-radiation can be detected by using the same or similar equipment, and I will also discuss the origin of X-rays in decay processes and the light that this knowledge sheds on characterization procedures.

I will show how the Karlsruhe Chart of the Nuclides can be of help in predicting or confirming the identity of radionuclides, being useful both for the modest amount of nuclear data it contains and for the ease with which generic information as to the type of nuclide expected can be seen.

First, I will briefly look at the nucleus and nuclear stability. I will consider a nucleus simply as an assembly of uncharged neutrons and positively charged protons; both of these are called nucleons.

Z is the atomic number and defines the element. In the neutral atom, Z will also be the number of extranuclear electrons in their atomic orbitals. An element has a fixed Z, but in general will be a mixture of atoms with different masses, depending on how many neutrons are present in each nucleus. The total number of nucleons is called the mass number.

A, N and Z are all integers by definition. In practice, a neutron has a very similar mass to a proton and so there is a real physical justification for this usage. In general, an assembly of nucleons should be referred to as a nuclide. Conventionally, a nuclide of atomic number Z and mass number A is specified as , where Sy is the chemical symbol of the element. Thus, is a nuclide with 27 protons and 31 neutrons. Because the chemical symbol uniquely identifies the element, unless there is a particular reason for including it, the atomic number as subscript is usually omitted – as in 58Co. This format leaves room for chemical information to follow; for example, 58Co2+. As it happens, this particular nuclide is radioactive and could, in order to impart that extra item of knowledge, be referred to as a radionuclide. Unfortunately, in the world outside of physics and radiochemistry, the word isotope has become synonymous with radionuclide – something dangerous and unpleasant. In fact, isotopes are simply atoms of the same element (i.e. same Z, different N) – radioactive or not. Thus, , and are isotopes of cobalt. Here, 27 is the atomic number, and 58, 59 and 60 are mass numbers equal to the total number of nucleons. 59Co is stable; it is, in fact, the only stable isotope of cobalt.

Returning to nomenclature, 58Co and 60Co are radioisotopes, as they are unstable and undergo radioactive decay. It would be incorrect to say, ‘the radioisotopes 60Co and 239Pu…’ because two different elements are being discussed; the correct expression would be ‘the radionuclides 60Co and 239Pu…’.

Figure 1.1 A Segrè chart. The symbols mark all known stable nuclides as a function of Z and N. At high Z, the long half-lived Th and U nuclides are shown. The outer envelope encloses known radioactive species. The star marks the position of the heaviest known nuclide, 294Og.

If all stable nuclides are plotted as a function of Z (y-axis) and N (x-axis), then Figure 1.1 will result. This is a Segrè chart. The star marks the position of the largest nuclide known to date, , oganesson with 118 protons. Named in 2016, it is one of the only two elements named after a person who was alive at the time of naming; the other being seaborgium and the only element whose eponym was alive at the time of writing (2023).

The Karlsruhe Chart of the Nuclides has this same basic structure but with the addition of all known radioactive nuclides. The heaviest stable element is bismuth (Z = 83, N = 126). The figure also shows the location of some high-Z unstable nuclides – the major thorium (Z = 90) and uranium (Z = 92) nuclides. Theory has predicted that there could be stable nuclides, as yet unknown, called superheavy nuclides on an island of stability at about Z = 114, N = 184, well above the current known range.

Radioactive decay is a spontaneous change within the nucleus of an atom that results in the emission of particles. The modes of radioactive decay are principally alpha and beta decays, with spontaneous fission as one of a small number of rarer processes. Radioactive decay is driven by mass change – the mass of the product or products is smaller than the mass of the original nuclide. Decay is always exoergic; the small mass change appears as energy in an amount determined by the following equation introduced by Einstein:

where the energy difference is in joules, the mass in kilograms and the speed of light in ms−1.

The unit of energy we use in gamma spectrometry is the electron-volt (eV), where 1 eV = 1.602 177 × 10–19 J.1 Hence, 1 eV = 1.782 663 × 10−36 kg or 1.073 533 × 10−9 u (‘u’ is the unit of atomic mass (amu), defined as 1/12th of the mass of 12C). Energies in the gamma radiation range are conveniently in keV.

Gamma-ray emission is not, strictly speaking, a decay process; it is a de-excitation of the nucleus. I will now explain each of these decay modes and show, in particular, how gamma emission frequently appears as a by-product of alpha or beta decay, being one way in which residual excitation energy is dissipated.

1.2 Beta Decay

Figure 1.2 shows a three-dimensional version of the low-mass end of the Segrè chart with energy/mass plotted on the third axis, shown vertically here. We can think of the stable nuclides as occupying the bottom of a nuclear-stability valley that runs from hydrogen to bismuth. The stability can be explained in terms of particular relationships between Z and N. Nuclides outside this valley bottom are unstable and can be imagined as sitting on the sides of the valley at heights that reflect their relative nuclear masses or energies.

Figure 1.2 The beta stability valley at low Z (

adapted from a figure published by New Scientist, and reproduced with permission).

Figure 1.3 Part of the Chart of the Nuclides. Heavy boxes indicate the stable nuclides.

The dominant form of radioactive decay is movement down the hillside directly to the valley bottom. This is beta decay. It corresponds to transitions along an isobar or line of constant A. What is happening is that neutrons are changing to protons (β− decay), or, on the opposite side of the valley, protons are changing to neutrons (β+ decay or electron capture). Figure 1.3 is part of the (Karlsruhe) Nuclide Chart.

If we consider the isobar A = 61, 61Ni is stable, and beta decay can take place along a diagonal (in this format) from either side. 61Ni has the smallest mass in this sequence, and the driving force is the mass difference; this appears as energy released. These energies are shown in Figure 1.4. There are theoretical grounds, based on the liquid drop model of the nucleus, for thinking that these points fall on a parabola.

1.2.1 β− or Negatron Decay

The decay of 60Co is an example of β− or negatron decay (negatron = negatively charged beta particle). All nuclides unstable to β− decay are on the neutron-rich side of stability. (On the Karlsruhe Chart, these are coloured blue.) The decay process addresses that instability. An example of β− decay is as follows:

Figure 1.4 The energy parabola for the isobar A = 61. 61Ni is stable, while other nuclides are beta-active (EC, electron capture).

A beta particle, β−, is an electron; in all respects, it is identical to any other electron. Following on from Section 1.1, the sum of the masses of the 60Ni plus the mass of the β−, and , the anti-neutrino, are less than the mass of 60Co. That mass difference drives the decay and appears as the energy of the decay products. What happens during the decay process is that a neutron is converted to a proton within the nucleus. In that way, the atomic number increases by one, and the nuclide drops down the side of the valley to a more stable condition. A fact not often realized is that the neutron itself is radioactive when it is not bound within a nucleus. A free neutron has a half-life of only 10.2 m and decays by beta emission:

That process is essentially the conversion process happening within the nucleus.

The decay energy is shared between the particles in inverse ratio to their masses in order to conserve momentum. The mass of 60Ni is very large compared with the mass of the beta particle and neutrino and, from a gamma spectrometry perspective, takes a very small, insignificant...