Nuclear excited states Revision Notes for AQA A-Level Physics

Nuclear excited states

Introduction to nuclear excited states

When studying radioactive decay, the simple model of a nucleus composed of protons and neutrons effectively explains alpha and beta decay processes. However, there is an additional complication: gamma emission. Gamma photons are electromagnetic radiation emitted from the nucleus after certain decay events.

To explain gamma emission, the nuclear model must be refined to include discrete energy levels within the nucleus. These are called nuclear excited states. A nuclear excited state is a higher energy configuration of the nucleus, similar to how electrons in atoms can occupy excited energy levels.

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When a nucleus undergoes alpha or beta decay, the resulting daughter nucleus may be formed with excess energy. This occurs because the decay process can leave the daughter nucleus in an elevated energy state rather than its lowest possible energy configuration.

The nucleus subsequently releases this excess energy by emitting one or more gamma photons as it transitions down to lower energy states.

Formation of excited states through radioactive decay

During alpha or beta decay, a parent nucleus transforms into a daughter nucleus. The daughter nucleus must be formed with the correct number of protons and neutrons, but it can exist at different energy levels. When the daughter nucleus forms in an excited state, it possesses more energy than necessary for its most stable configuration.

The nucleus cannot remain in this excited state indefinitely. To reach a more stable configuration, it undergoes a transition to a lower energy level by emitting a gamma photon. A gamma photon is a high-energy electromagnetic wave with the same nature as light but with much higher frequency and energy.

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Key characteristic of gamma emission:

Gamma photons emitted from any particular nuclide have specific, fixed energies. This occurs because the energy levels within a nucleus are discrete and unique to each isotope. The energy of each gamma photon corresponds exactly to the energy difference between two nuclear energy levels.

Representing excited states with energy level diagrams

Nuclear excited states are represented using energy level diagrams, which work similarly to atomic energy level diagrams. These diagrams show:

Horizontal lines representing different energy levels
The ground state at the bottom, which is the lowest possible energy state for the nucleus
Higher energy lines representing excited states
Arrows showing transitions between states, with gamma emission indicated

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Conventions for energy level diagrams:

By convention, the ground state energy is set to 0.0 MeV. All excited state energies are measured relative to this ground state. The energy of a gamma photon emitted during a transition equals the energy difference between the initial and final states.

An asterisk (*) is often used in nuclear equations to denote a nucleus in an excited state, distinguishing it from the same nucleus in its ground state.

Example: decay of cobalt-60

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Worked Example: Cobalt-60 Decay and Gamma Emission

Cobalt-60 is a synthetic isotope produced by bombarding stable cobalt-59 with neutrons in a nuclear reactor:

$^{60}_{27}\text{Co} + ^{1}_{0}\text{n} = ^{60}_{27}\text{Co}$

Cobalt-60 undergoes beta-minus decay to form nickel-60. The decay process can be represented by the equation:

$^{60}_{27}\text{Co} = ^{60}_{28}\text{Ni}^{*} + ^{0}_{-1}\beta + ^{0}_{0}\bar{\nu}_{e}$

The asterisk on the nickel-60 nucleus indicates it is formed in an excited state. The excited nickel-60 nucleus then returns to its ground state by emitting gamma photons:

$^{60}_{28}\text{Ni}^{*} = ^{60}_{28}\text{Ni} + \gamma$

Analysis of gamma emissions:

Analysis reveals two distinct gamma photon energies: 1.17 MeV and 1.33 MeV. This tells us that nickel-60 has at least two nuclear excited states above the ground state.

Energy level structure:

The ground state of nickel-60 is at 0.0 MeV
The first excited state is at 1.33 MeV
The second excited state is at 2.50 MeV

Decay pathways:

Most cobalt-60 decays (99.88%) produce nickel-60 in the second excited state at 2.50 MeV. This excited nucleus then transitions through the following pathway:

First, it emits a 1.17 MeV gamma photon, dropping to the 1.33 MeV excited state
Then, it emits a 1.33 MeV gamma photon, reaching the ground state at 0.0 MeV

A small percentage (0.12%) of decays produce nickel-60 directly in the first excited state at 1.33 MeV, which then emits a single 1.33 MeV gamma photon to reach the ground state.

Example: decay of radium-226

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Worked Example: Radium-226 Alpha Decay

Radium-226 provides another illustration of nuclear excited states. This naturally occurring isotope is an alpha emitter that decays to form radon-222.

Observation:

The decay exhibits an interesting feature: the alpha particles are emitted with two distinct energies, 4.78 MeV and 4.60 MeV.

Explanation:

This occurs because:

In approximately 94% of decays, the alpha particle carries away 4.78 MeV and the radon-222 nucleus forms directly in its ground state
In about 6% of decays, the alpha particle carries away 4.60 MeV and the radon-222 nucleus forms in an excited state at 0.18 MeV above the ground state

When radon-222 forms in the excited state, it subsequently emits a gamma photon of energy 180 keV (0.18 MeV) to reach its ground state.

Result: A sample of radium-226 emits alpha particles of two distinct energies along with gamma photons of 180 keV.

This example demonstrates that different decay pathways can lead to daughter nuclei in either the ground state or excited states, depending on how the available energy is distributed between the emitted particle and the daughter nucleus.

Example: decay of magnesium-27

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Worked Example: Magnesium-27 Beta Decay

A nucleus of magnesium-27 undergoes beta-minus emission to form aluminium-27 in an excited state. The aluminium-27 nucleus may then emit one or two gamma photons as it returns to its ground state.

Observation:

Analysis shows that three different gamma photon energies can be emitted during this process.

Explanation:

This indicates that the excited aluminium-27 nucleus can follow different decay pathways:

A direct transition from a higher excited state to the ground state, emitting a single higher-energy gamma photon
A cascade through intermediate energy levels, emitting two lower-energy gamma photons in sequence
A transition from a different excited state to the ground state

Conclusion: Each pathway produces characteristic gamma photon energies. The observation of three possible gamma energies reveals the structure of the nuclear energy levels in aluminium-27.

Metastable states

Most excited nuclei return to their ground state very rapidly, typically with half-lives much shorter than 10⁻¹² seconds. However, some excited nuclei remain in an excited state for much longer periods. These long-lived excited states are called metastable states.

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Definition of Metastable State:

A metastable state is an excited nuclear energy level with a half-life longer than 1 nanosecond (1 ns = 10⁻⁹ s). The term "metastable" is used for excited nuclei that return to their ground state with a half-life exceeding 1 ns.

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A metastable nucleus is often denoted with an "m" after the mass number, such as barium-137m.

Example: caesium-137 decay

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Worked Example: Caesium-137 Decay to Metastable Barium-137

Caesium-137 decays by beta-minus emission to form barium-137. In 94.6% of decays, the barium-137 nucleus is produced in a metastable excited state rather than the ground state.

Decay equations:

$^{137}_{55}\text{Cs} = ^{137m}_{56}\text{Ba} + ^{0}_{-1}\beta + ^{0}_{0}\bar{\nu}_{e}$

$^{137m}_{56}\text{Ba} = ^{137}_{56}\text{Ba} + \gamma$

Key property:

The excited barium-137m nuclei are slow to return to their ground state, doing so with a half-life of 153 seconds. During this transition, they emit gamma photons of energy 0.662 MeV.

Significance: This relatively long half-life means the barium-137m exists in the excited state long enough to be physically and chemically separated from the caesium-137 parent nuclei before it decays. This property makes metastable states particularly valuable for practical applications.

Medical applications of metastable isotopes

Metastable states have important applications in nuclear medicine. The key advantage is that if the parent nuclei can be separated from the excited daughter nuclei, then radioactive material that emits only gamma rays can be produced. This material can then be introduced into a patient for medical diagnosis.

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The gamma radiation penetrates body tissues and can be detected externally by a gamma camera without exposing the patient to the more harmful beta particles emitted by the parent nuclei.

Technetium-99m

The most commonly used medical radioisotope is technetium-99m. The parent nuclide is molybdenum-99, which undergoes beta-minus emission to form technetium-99m. The technetium-99m then undergoes a transition to its ground state, emitting a gamma photon of energy 140 keV.

Key properties that make technetium-99m suitable as a medical tracer:

1. Pure gamma emitter

Once separated from molybdenum-99, technetium-99m emits only gamma radiation, not beta or alpha particles. This minimizes the radiation dose to the patient.

2. Appropriate half-life

With a half-life of 6 hours, technetium-99m exists long enough to allow sufficient time for the tracer to reach the organ under investigation and for the gamma camera to build an image. However, the half-life is short enough to minimize radiation exposure and ensure the patient is not significantly radioactive when they return home.

3. Suitable gamma energy

The 140 keV gamma photons have energy high enough to penetrate body tissues and be detected externally, but low enough to produce substantially lower levels of ionisation compared with higher-energy gamma emitters. This makes the procedure safer for patients.

4. Long-lived parent

Molybdenum-99, produced by fission of uranium-235 in nuclear reactors, has a half-life of 66 hours. This allows it to be transported over long distances from the reactor facility to hospitals, where it is then used in a molybdenum-technetium generator to extract the technetium-99m.

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The technetium-99m can be chemically incorporated into various molecules to create tracers that target different areas of the body. As the tracer travels through the body, it emits gamma radiation, which is detected by the gamma camera. This maps the functions of the body and helps diagnose disorders.

Summary

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Key Points to Remember:

Nuclear excited states are higher energy configurations of the nucleus that form when a daughter nucleus is created with excess energy following alpha or beta decay.
Nuclei in excited states return to the ground state (lowest energy level, defined as 0.0 MeV) by emitting gamma photons with specific, characteristic energies determined by the energy differences between nuclear levels.
Metastable states are excited states with half-lives longer than 1 nanosecond, allowing time for physical and chemical separation from parent nuclei.
Energy level diagrams represent nuclear excited states as horizontal lines, with transitions shown by arrows indicating gamma emission as the nucleus cascades down to the ground state.
Medical applications, particularly technetium-99m, exploit metastable states to create pure gamma-emitting tracers with appropriate half-lives and energies for safe diagnostic imaging.

Nuclear excited states (AQA A-Level Physics): Revision Notes