Nuclear stability on an N–Z graph

An N–Z graph shows nuclei according to their proton and neutron numbers. Each point represents a nucleus: its proton number $$Z$$ is plotted on the horizontal axis and its neutron number $$N$$ on the vertical axis.

Stable nuclei occupy a band of stability rather than occurring at arbitrary neutron-to-proton ratios. For light stable nuclei, $$N$$ is generally close to $$Z$$, so their points lie near the line $$N = Z$$. For heavier stable nuclei, $$N$$ is generally greater than $$Z$$, so the stable band lies increasingly above that line.

Neutron-rich and proton-rich nuclei on an N–Z graph

Nuclei outside the stable band are unstable and can decay towards greater stability. A nucleus above the stable band has too many neutrons relative to the stable nuclei in that region: it is neutron-rich. A nucleus below the stable band has too few neutrons relative to those stable nuclei: it is proton-rich.

These descriptions depend on the local position of the stable band, not simply on whether $$N$$ is greater or less than $$Z$$. For example, a heavy nucleus can have more neutrons than protons and still be proton-rich if it lies below the stable band in its region of the graph.

Alpha decay

In alpha decay, an unstable nucleus emits an alpha particle. An alpha particle is a helium-4 nucleus: it contains two protons and two neutrons.

The nucleus left behind is called the daughter nucleus. Because the original nucleus loses two protons and two neutrons, the daughter has:

• proton number $$Z-2$$;
• neutron number $$N-2$$;
• mass number $$A-4$$.

Here, $$Z$$ is the original number of protons, $$N$$ is the original number of neutrons, and $$A$$ is the original total number of protons and neutrons. The daughter is a different element because its proton number has changed.

Alpha decay equation

The general equation for alpha decay is:

In the equation, $$X$$ is the original nucleus and $$Y$$ is the daughter nucleus. The upper number gives the mass number, while the lower number gives the proton number.

The mass numbers balance: the daughter has four fewer particles in its nucleus, and those four particles are carried away in the alpha particle. The charges also balance: the daughter has two fewer protons, while the alpha particle carries the positive charge of two protons.

Beta-minus decay

In beta-minus decay, a neutron in an unstable nucleus changes into a proton. An electron and an electron antineutrino are emitted. The emitted electron is called the beta-minus particle.

The daughter nucleus has one more proton and one fewer neutron than the original nucleus. Because the number of protons determines the element, the daughter nucleus is a different element. The total number of protons and neutrons remains unchanged.

Beta-minus decay equation

The decay can be represented generally as:

Here, $$X$$ is the original nucleus and $$Y$$ is the daughter nucleus. The symbols $$ {}^{0}_{-1}e $$ and $$\bar{\nu}_e$$ represent the emitted electron and electron antineutrino, respectively.

The proton number $$Z$$ increases by one, while the neutron number $$N$$ decreases by one. The mass number $$A$$, the total number of protons and neutrons, is unchanged.

Beta-plus decay

In beta-plus decay, a proton in an unstable nucleus changes into a neutron. The nucleus emits a positron and an electron neutrino. The positron, a positively charged antiparticle of the electron, is the beta-plus particle.

The daughter nucleus has one fewer proton and one more neutron than the original nucleus. Its proton number $$Z$$ therefore decreases by one, while its neutron number $$N$$ increases by one. The total number of protons and neutrons, called the mass number $$A$$, remains unchanged.

Here, $$X$$ is the original nucleus and $$Y$$ is the daughter nucleus. The symbol $${}^{0}_{+1}e$$ represents the positron, and $$\nu_e$$ represents the electron neutrino. Because the daughter nucleus has a different proton number, it is an atom of a different element.

Electron capture

In electron capture, an unstable nucleus captures an electron from an inner shell of its atom. A proton in the nucleus combines with the electron and changes into a neutron. An electron neutrino is emitted.

The daughter nucleus therefore has one fewer proton and one more neutron than the original nucleus. Its proton number $$Z$$ decreases by one, so the daughter is a different element. Its neutron number $$N$$ increases by one. Because no nucleon is gained or lost, the total number of protons and neutrons—the mass number $$A$$—is unchanged.

The general equation for electron capture is:

Here, $$X$$ is the original nucleus, $$Y$$ is the daughter nucleus, and $$\nu_e$$ represents the emitted electron neutrino.

Nuclear excited states and gamma emission

A nucleus can have different energy states. Its lowest-energy state is called the ground state. A nucleus with more energy than this is in an excited state.

An excited nucleus can move to a lower energy state by emitting a gamma-ray photon. The photon carries away the difference in energy between the two nuclear states.

Here, $$E_\gamma$$ is the photon energy, $$\Delta E$$ is the difference between the nuclear energy levels, $$h$$ is the Planck constant and $$f$$ is the photon’s frequency. A larger energy difference produces a higher-frequency gamma photon.

Nuclear energy-level diagrams

A nuclear energy-level diagram represents the nucleus’s possible energy states as horizontal lines. Higher lines represent higher energies. A downward arrow between two lines shows a transition to a lower state and the emission of a photon. The photon’s energy equals the energy difference between the levels at the ends of the arrow.

Gamma emission changes neither the number of protons nor the number of neutrons in the nucleus. The nucleus loses energy, but remains the same nuclide.

Technetium-99m

Technetium-99m is a metastable excited nuclear state: it remains in its excited state for a measurable time before moving to a lower energy state. It emits gamma radiation as it transitions to technetium-99.

Technetium-99m is used as a gamma source in medical diagnosis. The emitted radiation can be detected to obtain information about how the technetium is distributed in the body.