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21.3 Radioactive Decay

4 min read•june 25, 2024

is a fascinating process where unstable atomic nuclei break down, emitting particles and energy. This natural phenomenon comes in different forms, each with unique characteristics and applications in science and technology.

Understanding is crucial for grasping nuclear physics and chemistry. It helps explain how elements change over time, enables , and forms the basis for nuclear energy production and medical treatments.

Radioactive Decay Modes and Particles

Types of radioactive decay

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  • Alpha (α\alpha) decay involves the emission of an alpha particle (, 24He^4_2He) consisting of 2 protons and 2 neutrons from the atomic nucleus resulting in a decrease of the atomic number by 2 and mass number by 4
  • Beta (β\beta) decay occurs in two forms:
    • Beta minus (β−\beta^-) decay involves the emission of an from the atomic nucleus as a neutron converts into a proton, an electron, and an , increasing the atomic number by 1 while the mass number remains constant
    • Beta plus (β+\beta^+) decay involves the emission of a (antiparticle of an electron) from the atomic nucleus as a proton converts into a neutron, a positron, and a , decreasing the atomic number by 1 while the mass number remains constant
  • Gamma (γ\gamma) decay involves the emission of high-energy electromagnetic radiation (photons) from the atomic nucleus as an excited nucleus transitions to a lower energy state without changing the atomic number or mass number

Particles in nuclear decay

  • are helium nuclei (24He^4_2He) emitted during carrying a positive charge of +2, having a mass of approximately 4 atomic mass units (amu), and typically possessing kinetic energy in the range of 4-9 MeV
  • are electrons (e−e^-) or positrons (e+e^+) emitted during carrying a negative charge of -1 (electrons) or a positive charge of +1 (positrons), having a mass of approximately 1/1836 amu, and possessing varying kinetic energy with a maximum value depending on the specific decay
  • are high-energy photons emitted during with no charge, no mass, and energy typically in the range of keV to MeV
  • Radioactive decay releases energy due to the conversion of mass to energy (E=mc^2) carried away by the emitted particles and photons as the daughter nucleus achieves a lower mass and greater stability than the parent nucleus
  • are used to measure and analyze the particles and energy released during radioactive decay

Nuclear Decay Equations and Kinetics

Equations for nuclear decay

  • Alpha decay equation: ZAX→Z−2A−4Y+24He^A_ZX \rightarrow ^{A-4}_{Z-2}Y + ^4_2He where X is the parent nucleus, Y is the daughter nucleus, A is the mass number, and Z is the atomic number
  • Beta minus decay equation: ZAX→Z+1AY+e−+νˉe^A_ZX \rightarrow ^A_{Z+1}Y + e^- + \bar{\nu}_e where νˉe\bar{\nu}_e represents an electron antineutrino
  • Beta plus decay equation: ZAX→Z−1AY+e++νe^A_ZX \rightarrow ^A_{Z-1}Y + e^+ + \nu_e where νe\nu_e represents an electron neutrino
  • Gamma decay equation: ZAX∗→ZAX+γ^A_ZX^* \rightarrow ^A_ZX + \gamma where the asterisk (*) indicates an excited nuclear state

Half-life and decay kinetics

  • (t1/2t_{1/2}) is the time required for half of a given quantity of a radioactive substance to decay, which is constant for a specific radionuclide and can be calculated using the equation: t1/2=ln(2)λt_{1/2} = \frac{ln(2)}{\lambda}, where λ\lambda is the
  • Decay constant (λ\lambda) is the probability of decay per unit time and is related to by: λ=ln(2)t1/2\lambda = \frac{ln(2)}{t_{1/2}}
  • equation: N(t)=N0e−λtN(t) = N_0e^{-\lambda t} where N(t)N(t) is the quantity of the radionuclide at time tt, N0N_0 is the initial quantity of the radionuclide, λ\lambda is the decay constant, and tt is the elapsed time

Radiometric Dating

Principles of radiometric dating

  • Radiometric dating is based on the radioactive decay of unstable and compares the ratio of a radioactive isotope to its decay product in a sample, assuming that the initial ratio is known and that the sample has remained a closed system (no loss or gain of )
  • is used for dating organic materials up to ~50,000 years old based on the decay of to nitrogen-14 with a half-life of approximately 5,730 years
  • is used for dating rocks and minerals based on the decay of to (half-life of 4.47 billion years) and to (half-life of 704 million years)
  • is used for dating rocks and minerals based on the decay of to with a half-life of 1.28 billion years
  • Radiometric dating is applied to determine the age of fossils, rocks, and archaeological artifacts, reconstruct past climates and environments, study the evolution of life on Earth, and investigate the formation and history of the Earth and solar system

Nuclear Stability and Energy

Nuclear stability and isotopes

  • is determined by the ratio of neutrons to protons in the nucleus, with stable nuclei generally having a specific range of neutron-to-proton ratios
  • Isotopes are atoms of the same element with different numbers of neutrons, which can affect their stability and radioactive properties
  • describe the sequential decay of unstable isotopes, forming a chain of decay products until a stable isotope is reached

Nuclear reactions

  • is the splitting of heavy atomic nuclei into lighter nuclei, releasing energy and often neutrons that can sustain a chain reaction
  • is the combining of light atomic nuclei to form heavier nuclei, releasing large amounts of energy in the process

Key Terms to Review (44)

Alpha Decay: Alpha decay is a type of radioactive decay where an atomic nucleus emits an alpha particle, which is a helium nucleus consisting of two protons and two neutrons. This process occurs in heavy, unstable nuclei as a means of achieving a more stable configuration.
Alpha particles: Alpha particles are a type of ionizing radiation consisting of two protons and two neutrons bound together. They are emitted from the nucleus of certain radioactive elements during alpha decay.
Alpha Particles: Alpha particles are a type of ionizing radiation consisting of two protons and two neutrons, emitted during the radioactive decay of certain elements. They are the largest and most heavily charged particles released in radioactive processes and have a limited range in matter.
Antineutrino: An antineutrino is the antimatter counterpart of the neutrino, a neutral, weakly interacting subatomic particle. Antineutrinos are produced in certain nuclear processes and play a crucial role in understanding nuclear equations and radioactive decay.
Argon-40: Argon-40 is a stable isotope of the noble gas argon, consisting of 18 protons and 22 neutrons in its nucleus. It is significant in understanding radioactive decay processes because it is produced as a byproduct of the decay of potassium-40, which is a radioactive isotope that undergoes beta decay. Argon-40 plays a crucial role in radiometric dating techniques, especially in determining the ages of geological formations and archaeological artifacts.
Beta (β) decay: Beta (β) decay is a type of radioactive decay in which a beta particle (electron or positron) is emitted from an atomic nucleus. This process changes the atomic number of the nucleus, effectively transforming one element into another.
Beta Decay: Beta decay is a type of radioactive decay in which a nucleus emits an electron (or a positron) and an antineutrino (or a neutrino) to transform one type of nucleon into another. This process changes the number of protons in the nucleus, resulting in the transformation of one element into another.
Beta particles: Beta particles are high-energy, high-speed electrons or positrons emitted during the radioactive decay of an atomic nucleus. These particles play a significant role in transforming unstable isotopes into more stable forms and can impact biological systems due to their penetrating ability.
Carbon-14: Carbon-14 is a radioactive isotope of carbon with a nucleus containing 6 protons and 8 neutrons. It is used extensively in radiometric dating techniques to determine the age of various materials, as it undergoes radioactive decay over time.
Carbon-14 Dating: Carbon-14 dating is a radiometric dating method used to determine the age of organic materials by measuring the radioactive decay of the carbon-14 isotope. It is a key technique in the field of archaeology and geology for establishing the chronology of historical and geological events.
Daughter nuclide: A daughter nuclide is the product that remains after a radioactive isotope undergoes decay. It can be either stable or continue to undergo further radioactive decay.
Decay Constant: The decay constant, denoted by the Greek letter lambda (λ), is a fundamental parameter that describes the rate of radioactive decay for a given radioactive isotope. It represents the probability of a radioactive nucleus decaying per unit of time and is a crucial concept in understanding the behavior of radioactive materials.
Electron: An electron is a subatomic particle that carries a negative electric charge and is found in all atoms. Electrons play a crucial role in the evolution of atomic theory and in the process of radioactive decay.
Electron capture: Electron capture is a process in which an atomic nucleus absorbs an inner orbital electron, leading to the conversion of a proton into a neutron and the emission of a neutrino. This process reduces the atomic number by one while keeping the mass number unchanged.
Exponential Decay: Exponential decay is a process where a quantity decreases at a rate proportional to its current value, resulting in a rapid reduction over time. This phenomenon is often observed in radioactive decay, where unstable nuclei lose energy by emitting radiation. The rate of decay can be mathematically expressed with the equation $$N(t) = N_0 e^{-kt}$$, where $$N(t)$$ is the remaining quantity at time $$t$$, $$N_0$$ is the initial quantity, and $$k$$ is the decay constant.
Gamma Decay: Gamma decay is a type of radioactive decay in which an unstable atomic nucleus emits a high-energy electromagnetic radiation known as a gamma ray. This process occurs when a nucleus transitions from a higher energy state to a lower energy state, releasing the excess energy in the form of a gamma photon.
Gamma Rays: Gamma rays are a type of high-energy electromagnetic radiation, similar to X-rays, that are emitted during radioactive decay. They have the highest frequency and shortest wavelength in the electromagnetic spectrum, making them highly penetrating and capable of causing significant biological damage.
Gamma rays (γ): Gamma rays ($\gamma$) are high-energy electromagnetic waves emitted from the nucleus of an atom during radioactive decay. They have no mass and no charge but can penetrate most materials.
Half-life: Half-life is the time required for half of the radioactive nuclei in a sample to decay. It is a characteristic property of each radioactive isotope.
Half-life: Half-life is the time it takes for a radioactive substance to decay to half of its original amount. It is a fundamental concept in nuclear chemistry that describes the exponential decay of radioactive isotopes and is crucial for understanding the behavior of radioactive materials.
Helium Nucleus: The helium nucleus, also known as an alpha particle, is a positively charged particle consisting of two protons and two neutrons. It is a stable and naturally occurring form of the helium atom that is released during certain types of radioactive decay processes.
Isotopes: Isotopes are variants of a particular chemical element that have the same number of protons but different numbers of neutrons. This results in different atomic masses for the isotopes of an element.
Isotopes: Isotopes are atoms of the same element that have the same number of protons but different numbers of neutrons in their nuclei. This difference in the number of neutrons results in variations in the atomic mass of the isotopes, while their chemical properties remain largely the same.
Lead-206: Lead-206 is a stable isotope of lead that is the final product of the radioactive decay chain of uranium-238. It is the most abundant isotope of lead found in nature and is considered a non-radioactive, or stable, isotope.
Lead-207: Lead-207 is a stable isotope of the element lead, with 82 protons and 125 neutrons in its nucleus. It is the final product of the radioactive decay chain of uranium-235, making it an important isotope in the study of radiometric dating and the age of the Earth.
Neutrino: A neutrino is an electrically neutral, weakly interacting elementary particle. It is one of the fundamental particles in the Standard Model of particle physics and plays a crucial role in the understanding of radioactive decay processes.
Nuclear Fission: Nuclear fission is the process of splitting heavy atomic nuclei, such as those of uranium or plutonium, into smaller nuclei. This process releases a large amount of energy and is the basis for nuclear power generation and nuclear weapons.
Nuclear Fusion: Nuclear fusion is the process in which two or more atomic nuclei collide at very high speeds and temperatures to form a new, heavier nucleus. This release of energy is the fundamental source of power for stars, including our own Sun.
Nuclear stability: Nuclear stability refers to the condition of an atomic nucleus that is neither undergoing radioactive decay nor experiencing significant changes in its structure. Stable nuclei have balanced numbers of protons and neutrons, which helps them maintain their integrity over time. This stability is crucial because it determines the longevity of isotopes and their potential to undergo transformations, affecting everything from energy production to the behavior of materials in nuclear reactions.
Parent nuclide: A parent nuclide is an unstable atomic nucleus that undergoes radioactive decay to form a daughter nuclide. It is the original nuclide before the decay process begins.
Positron: A positron is the antiparticle of the electron, possessing the same mass as an electron but with a positive charge. When a positron encounters an electron, they can annihilate each other, producing gamma-ray photons. This interaction is key in understanding certain types of radioactive decay and nuclear equations that involve particle interactions.
Positron emission (β+ decay: Positron emission (β+ decay) is a type of radioactive decay in which a proton inside a nucleus is converted into a neutron, releasing a positron and a neutrino. It reduces the atomic number by one while keeping the mass number constant.
Potassium-40: Potassium-40 is a radioactive isotope of the element potassium that undergoes radioactive decay. It is a naturally occurring radioisotope found in the environment and within living organisms, making it relevant to the topics of radioactive decay and the biological effects of radiation.
Potassium-Argon Dating: Potassium-argon dating is a radiometric dating method used to determine the age of rocks and minerals by measuring the ratio of the radioactive isotope of potassium (40K) to its decay product, the stable isotope of argon (40Ar). This method is particularly useful for dating geological materials that are millions of years old.
Radiation Detectors: Radiation detectors are devices used to measure and identify different types of ionizing radiation, such as alpha, beta, gamma, and X-rays. These instruments play a crucial role in monitoring and understanding radioactive decay processes.
Radioactive decay: Radioactive decay is the spontaneous transformation of an unstable atomic nucleus into a lighter nucleus, accompanied by emission of particles, radiation, or both. This process results in the release of energy.
Radioactive Decay: Radioactive decay is the spontaneous process by which an unstable atomic nucleus loses energy by emitting radiation in the form of particles or electromagnetic waves. This process transforms the original nucleus into a more stable configuration, eventually leading to the formation of a stable isotope.
Radioactive decay series: A radioactive decay series is a sequence of radioactive decays that proceed until a stable, non-radioactive isotope is formed. Each step in the series involves the transformation of one element into another through alpha or beta decay.
Radioactive Series: A radioactive series, also known as a decay chain or radioactive cascade, is a sequence of radioactive decays in which an unstable atomic nucleus undergoes a series of transformations, emitting radiation in the form of alpha or beta particles, until it reaches a stable configuration. This process is a fundamental aspect of radioactive decay and is crucial in understanding the behavior of radioactive materials.
Radiocarbon dating: Radiocarbon dating is a technique used to determine the age of organic materials by measuring the decay of carbon-14 isotopes. It is widely employed in fields like archaeology and geology to date ancient artifacts and fossils.
Radiometric dating: Radiometric dating is a technique used to date materials such as rocks or carbon by comparing the relative abundance of specific radioactive isotopes. It relies on the known rates of decay of these isotopes to determine age.
Uranium-235: Uranium-235 is a naturally occurring isotope of the element uranium that is fissile, meaning it can sustain a nuclear chain reaction. It is the primary isotope used in nuclear reactors and nuclear weapons due to its unique nuclear properties.
Uranium-238: Uranium-238 is a naturally occurring, radioactive isotope of the element uranium. It is the most stable isotope of uranium, with a half-life of approximately 4.5 billion years, making it a crucial component in the study of nuclear equations and radioactive decay.
Uranium-Lead Dating: Uranium-lead dating is a radiometric dating method used to determine the age of rocks and minerals by measuring the decay of radioactive uranium isotopes into lead isotopes. It is a powerful tool for understanding the geological history of the Earth and the solar system.
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21.4 Transmutation and Nuclear Energy