Nuclear Physics Radioactivity Applications Lesson 43 by Owen Borville 1.19.2026
Some atomic nuclei are radioactive because they spontaneously decay and destroy some part of their mass and emit energetic rays (nuclear radioactivity).
Nuclear radiation, like x-rays, is ionizing radiation, because energy sufficient to ionize matter is emitted in each decay. The range (or distance travelled in a material) of ionizing radiation is directly related to the charge of the emitted particle and its energy, with greater-charge and lower-energy particles having the shortest ranges. Radiation detectors are based directly or indirectly upon the ionization created by radiation, as are the effects of radiation on living and inert materials.
The atomic nucleus is composed of protons and neutrons. Nucleons are two different particles found inside the nuclei: protons and neutrons that are very similar except that the proton is positively charged and the neutron is neutral. A mass unit convenient to atomic and nuclear processes is the unified atomic mass unit (u): 1 u = 1.6605 x 10-27 kg = 931.46 MeV/c^2.
A nuclide is a specific combination of protons and neutrons: Xn or X, where X is the symbol for the element, N (right subscript) is the number of neutrons, Z (left subscript) is the number of protons or atomic number, A (left superscript) is the mass number or the total number of protons and neutrons (nucleons). A = N + Z. The atomic mass of an element is the weighted average of the masses of its isotopes.
Nuclides having the same Z but different N are isotopes of the same element. The radius of a nucleus, r, is approximately r = r0A^1/3, where r0 = 1.2 fm. Nuclear volumes are proportional to A. There are two nuclear forces, the weak force and the strong force. Systematics in nuclear stability seen of the chart of the nuclides indicate that there are shell closures in nuclei for values of Z and N equal to the magic numbers, which correspond to highly stable nuclei.
When a parent nucleus decays, it produces a daughter nucleus following rules and conservation laws. There are three major types of nuclear decay: alpha (α), beta (β), and gamma (γ). Nuclear decay releases an amount of energy E related to the mass destroyed Δm by E = (Δm)c^2. (binding energy)
There are three forms of beta decay: β-, β+, electron capture. β- is an electron, β+ is an antielectron or positron, while ve represents an electron's neutrino, and ν̅ₑ is an electron's antineutrino.
In addition to all previously known conservation laws, two new ones are conservation of electron family number and conservation of the total number of nucleons. The gamma decay equation (γ) is a high-energy photon originating in a nucleus.
When a heavy nucleus decays into a lighter one, the lighter daughter nucleus can become the parent nucleus for the next decay, and so on, producing a decay series.
Half-life t1/2 is the time in which there is a 50 percent change that the nucleus will decay. The number of nuclei N as a function of time is N = N0e^-λt, where N0 is the number present at t = 0, and λ is the decay constant, related to the half-life by λ = 0.693/t1/2. If the decay constant λ is large, the half-life is small and vise-versa. Lifetime of a substance is T = 1/λ.
One of the applications of radioactive decay is radioactive dating, in which the age of a material is determined by the amount of radioactive decay that occurs. The rate of decay is called the activity R: R = ΔN/Δt. (Also -dN/dt =λN). The activity equation can be in linear form: ln (N) = -λt + ln (N0).
The SI unit for R is the becquerel (Bq), defined by 1 Bq = 1 decay/s. The radioactive decay law N = N0e^-λt uses the properties of radioactive substances to estimate the age of a substance.
Radioactive carbon-14 has the same chemistry as stable carbon-12, so it mixes into the ecosphere and eventually becomes part of every living organism. By comparing the abundance of Carbon-14 in an artifact with organic remains with the normal abundance in living tissue, it is possible to estimate the artifacts age.
R is also expressed in terms of curies (Ci), where 1 Ci = 3.70 x 10^10 Bq. The activity R of a source is related to N and t1/2 by R = 0.693N/t1/2.
Since N has an exponential behavior as in the equation N = N0e^-λt, the activity also has an exponential behavior, given by R = R0e^-λt, where Ro is the activity at t = 0.
The mass defect of the nucleus is the difference between the total mass of a nucleus and the sum of the masses of all its constituent nucleons. Δm = Z(mp) + (A - Z) (mn) - m(nuc), where Z is the number of protons, (mp) is the proton mass, A is atomic number, (A-Z) is number of neutrons, (mn) is the neutron mass, m(nuc) is the mass of the nucleus.
The binding energy (BE) of a nucleus is the energy needed to separate it into individual proton and neutrons (see image). The binding energy is equal to the amount of energy released in forming the nucleus, or the mass defect multiplied by the speed of light squared. A graph of binding energy per nucleon (BEN) versus atomic number A implies that nuclei divided or combined release an enormous amount of energy. The binding energy of a nucleon in a nucleus is analogous to the ionization energy of an electron in an atom. Patterns in the binding energy per nucleon, BE/A, reveal details of the nuclear force. The larger the BE/A, the more stable the nucleus. The binding energy of a nucleon is BEN = BE (binding energy)/A (mass number)
Tunneling is a quantum mechanical process of potential energy barrier penetration. The concept was first applied to explain alpha α decay, but tunneling is found to occur in other quantum mechanical systems.
Applications of Nuclear Physics include Diagnostics and Medical Imaging.
Radiopharmaceuticals are compounds that are used for medical imaging and therapeutics. Radiopharmaceuticals are drugs that help locate and study diseased tissue in the body. The process of attaching a radioactive substance is called tagging. Radioactive tags are used to identify cancer cells in bones, brain tumors, and Alzheimer's disease, and to monitor the function of body organs, blood flow, heart muscle activity, and iodine uptake in the thyroid gland.
One common imaging device is the Anger camera, which has a lead collimator, radiation detectors, and an analysis computer. Tomography performed with γ-emitting radiopharmaceuticals is called SPECT and has the advantages of x-ray CT scans coupled with organ-and function-specific drugs. PET is a similar technique that uses β+ emitters and detects the two annihilation γ rays, which aid to localize the source.
The biological effects of ionizing radiation are due to two effects it has on cells: interference with cell reproduction, and destruction of cell function. The radiation dose unit called the rad is defined in terms of the ionizing energy deposited per kilogram of tissue: 1 rad = 0.01 J/kg.
The SI unit for radiation dose is the gray (Gy), which is defined to be 1 Gy = 1 J/kg = 100 rad. To account for the effect of the type of particle creating the ionization, we use the relative biological effectiveness (RBE) or quality factor (QF) and define a unit called the roentgen equivalent man (rem) as rem = rad x RBE.
The particles that have short ranges or create large ionization densities have RBEs greater than unity. The SI equivalent of the rem is the sievert (Sv) = Gy x RBE and 1 Sv = 100 rem.
Sources of radiation include that emitted by Earth due to the isotopes of uranium, thorium, and potassium. Natural radiation sources come from cosmic rays, rocks, soils, and building materials, and artificial sources from medical and dental diagnostic tests.
Whole body, single exposure doses of 0.1 Sv or less are low doses while those of 0.1 to 1 Sv are moderate, and those over 1 Sv are high doses, causing radiation effects. Effects due to low doses are not observed, but their risk is assumed to be directly proportional to those of high doses, (linear hypothesis). Long term effects are cancer deaths at the rate of 10/10^6 rem*y and genetic defects at roughly one-third this rate. World-wide average radiation exposure from natural radon (in rocks, soil, water) is about 3 mSv, or 300 mrem. Radiation protection utilizes shielding, distance, and time to limit exposure.
Radiotherapy is the use of ionizing radiation to treat ailments, now limited to cancer therapy. The sensitivity of cancer cells to radiation enhances the ratio of cancer cells killed to normal cells killed, which is called the therapeutic ratio. Doses for various organs are limited by the tolerance of normal tissue for radiation. Treatment is localized in one region of the body and spread out in time.
Food irradiation is the treatment of food with ionizing radiation. Irradiating food can destroy insects and bacteria by creating free radicals and radiolytic products that can break apart cell membranes. Food irradiation has produced no observable negative short-term effects for humans, but its long term effects are unknown.
Nuclear fusion is a reaction in which two nuclei are combined to form a larger nucleus. Energy is released when light nuclei are fused to form medium-mass nuclei. Fusion is the source of energy in stars, with the proton-proton cycle, being the principle sequence of energy-producing reactions in our Sun. Fusion also explains the process of nucleosynthesis in stars and the creation of heavy elements. The amount of energy released by a fusion reaction is called the Q value.
Attempts to utilize controlled fusion as an energy source on Earth are related to deuterium and tritium, and the reactions play important roles. Nuclear fusion explains the reaction between deuterium and tritium that produces a fusion. Ignition is the condition under which the controlled fusion is self-sustaining, but this has not yet been achieved. Break-even, in which the fusion energy output is as great as the external energy input, has nearly been achieved.
Magnetic confinement and inertial confinement are the two methods being developed for heating fuel to sufficiently high temperatures, at sufficient density, and for sufficiently long times to achieve ignition. The first method uses magnetic fields and the second method uses the momentum of impinging laser beams for confinement.
Nuclear fission is a reaction in which a nucleus is split. Fission releases energy when heavy nuclei are split into medium-mass nuclei. The sum of the masses of the product nuclei are less than the masses of the reactants. Energy changes in a nuclear fission reaction can be understood in terms of the binding energy per nucleon curve.
Self-sustained fission is possible, because neutron-induced fission also produces neutrons that can induce other fissions, n + AX > FF1 + FF2 + xn, where FF1 and FF2 are the two daughter nuclei, or fission fragments, and x is the number of neutrons produced. A minimum mass, called the critical mass, should be present to achieve criticality. More than a critical mass can produce supercriticality.
The production of new or different isotopes by nuclear transformation is called breeding, and reactors designed for this purpose are called breeder reactors.
Some atomic nuclei are radioactive because they spontaneously decay and destroy some part of their mass and emit energetic rays (nuclear radioactivity).
Nuclear radiation, like x-rays, is ionizing radiation, because energy sufficient to ionize matter is emitted in each decay. The range (or distance travelled in a material) of ionizing radiation is directly related to the charge of the emitted particle and its energy, with greater-charge and lower-energy particles having the shortest ranges. Radiation detectors are based directly or indirectly upon the ionization created by radiation, as are the effects of radiation on living and inert materials.
The atomic nucleus is composed of protons and neutrons. Nucleons are two different particles found inside the nuclei: protons and neutrons that are very similar except that the proton is positively charged and the neutron is neutral. A mass unit convenient to atomic and nuclear processes is the unified atomic mass unit (u): 1 u = 1.6605 x 10-27 kg = 931.46 MeV/c^2.
A nuclide is a specific combination of protons and neutrons: Xn or X, where X is the symbol for the element, N (right subscript) is the number of neutrons, Z (left subscript) is the number of protons or atomic number, A (left superscript) is the mass number or the total number of protons and neutrons (nucleons). A = N + Z. The atomic mass of an element is the weighted average of the masses of its isotopes.
Nuclides having the same Z but different N are isotopes of the same element. The radius of a nucleus, r, is approximately r = r0A^1/3, where r0 = 1.2 fm. Nuclear volumes are proportional to A. There are two nuclear forces, the weak force and the strong force. Systematics in nuclear stability seen of the chart of the nuclides indicate that there are shell closures in nuclei for values of Z and N equal to the magic numbers, which correspond to highly stable nuclei.
When a parent nucleus decays, it produces a daughter nucleus following rules and conservation laws. There are three major types of nuclear decay: alpha (α), beta (β), and gamma (γ). Nuclear decay releases an amount of energy E related to the mass destroyed Δm by E = (Δm)c^2. (binding energy)
There are three forms of beta decay: β-, β+, electron capture. β- is an electron, β+ is an antielectron or positron, while ve represents an electron's neutrino, and ν̅ₑ is an electron's antineutrino.
In addition to all previously known conservation laws, two new ones are conservation of electron family number and conservation of the total number of nucleons. The gamma decay equation (γ) is a high-energy photon originating in a nucleus.
When a heavy nucleus decays into a lighter one, the lighter daughter nucleus can become the parent nucleus for the next decay, and so on, producing a decay series.
Half-life t1/2 is the time in which there is a 50 percent change that the nucleus will decay. The number of nuclei N as a function of time is N = N0e^-λt, where N0 is the number present at t = 0, and λ is the decay constant, related to the half-life by λ = 0.693/t1/2. If the decay constant λ is large, the half-life is small and vise-versa. Lifetime of a substance is T = 1/λ.
One of the applications of radioactive decay is radioactive dating, in which the age of a material is determined by the amount of radioactive decay that occurs. The rate of decay is called the activity R: R = ΔN/Δt. (Also -dN/dt =λN). The activity equation can be in linear form: ln (N) = -λt + ln (N0).
The SI unit for R is the becquerel (Bq), defined by 1 Bq = 1 decay/s. The radioactive decay law N = N0e^-λt uses the properties of radioactive substances to estimate the age of a substance.
Radioactive carbon-14 has the same chemistry as stable carbon-12, so it mixes into the ecosphere and eventually becomes part of every living organism. By comparing the abundance of Carbon-14 in an artifact with organic remains with the normal abundance in living tissue, it is possible to estimate the artifacts age.
R is also expressed in terms of curies (Ci), where 1 Ci = 3.70 x 10^10 Bq. The activity R of a source is related to N and t1/2 by R = 0.693N/t1/2.
Since N has an exponential behavior as in the equation N = N0e^-λt, the activity also has an exponential behavior, given by R = R0e^-λt, where Ro is the activity at t = 0.
The mass defect of the nucleus is the difference between the total mass of a nucleus and the sum of the masses of all its constituent nucleons. Δm = Z(mp) + (A - Z) (mn) - m(nuc), where Z is the number of protons, (mp) is the proton mass, A is atomic number, (A-Z) is number of neutrons, (mn) is the neutron mass, m(nuc) is the mass of the nucleus.
The binding energy (BE) of a nucleus is the energy needed to separate it into individual proton and neutrons (see image). The binding energy is equal to the amount of energy released in forming the nucleus, or the mass defect multiplied by the speed of light squared. A graph of binding energy per nucleon (BEN) versus atomic number A implies that nuclei divided or combined release an enormous amount of energy. The binding energy of a nucleon in a nucleus is analogous to the ionization energy of an electron in an atom. Patterns in the binding energy per nucleon, BE/A, reveal details of the nuclear force. The larger the BE/A, the more stable the nucleus. The binding energy of a nucleon is BEN = BE (binding energy)/A (mass number)
Tunneling is a quantum mechanical process of potential energy barrier penetration. The concept was first applied to explain alpha α decay, but tunneling is found to occur in other quantum mechanical systems.
Applications of Nuclear Physics include Diagnostics and Medical Imaging.
Radiopharmaceuticals are compounds that are used for medical imaging and therapeutics. Radiopharmaceuticals are drugs that help locate and study diseased tissue in the body. The process of attaching a radioactive substance is called tagging. Radioactive tags are used to identify cancer cells in bones, brain tumors, and Alzheimer's disease, and to monitor the function of body organs, blood flow, heart muscle activity, and iodine uptake in the thyroid gland.
One common imaging device is the Anger camera, which has a lead collimator, radiation detectors, and an analysis computer. Tomography performed with γ-emitting radiopharmaceuticals is called SPECT and has the advantages of x-ray CT scans coupled with organ-and function-specific drugs. PET is a similar technique that uses β+ emitters and detects the two annihilation γ rays, which aid to localize the source.
The biological effects of ionizing radiation are due to two effects it has on cells: interference with cell reproduction, and destruction of cell function. The radiation dose unit called the rad is defined in terms of the ionizing energy deposited per kilogram of tissue: 1 rad = 0.01 J/kg.
The SI unit for radiation dose is the gray (Gy), which is defined to be 1 Gy = 1 J/kg = 100 rad. To account for the effect of the type of particle creating the ionization, we use the relative biological effectiveness (RBE) or quality factor (QF) and define a unit called the roentgen equivalent man (rem) as rem = rad x RBE.
The particles that have short ranges or create large ionization densities have RBEs greater than unity. The SI equivalent of the rem is the sievert (Sv) = Gy x RBE and 1 Sv = 100 rem.
Sources of radiation include that emitted by Earth due to the isotopes of uranium, thorium, and potassium. Natural radiation sources come from cosmic rays, rocks, soils, and building materials, and artificial sources from medical and dental diagnostic tests.
Whole body, single exposure doses of 0.1 Sv or less are low doses while those of 0.1 to 1 Sv are moderate, and those over 1 Sv are high doses, causing radiation effects. Effects due to low doses are not observed, but their risk is assumed to be directly proportional to those of high doses, (linear hypothesis). Long term effects are cancer deaths at the rate of 10/10^6 rem*y and genetic defects at roughly one-third this rate. World-wide average radiation exposure from natural radon (in rocks, soil, water) is about 3 mSv, or 300 mrem. Radiation protection utilizes shielding, distance, and time to limit exposure.
Radiotherapy is the use of ionizing radiation to treat ailments, now limited to cancer therapy. The sensitivity of cancer cells to radiation enhances the ratio of cancer cells killed to normal cells killed, which is called the therapeutic ratio. Doses for various organs are limited by the tolerance of normal tissue for radiation. Treatment is localized in one region of the body and spread out in time.
Food irradiation is the treatment of food with ionizing radiation. Irradiating food can destroy insects and bacteria by creating free radicals and radiolytic products that can break apart cell membranes. Food irradiation has produced no observable negative short-term effects for humans, but its long term effects are unknown.
Nuclear fusion is a reaction in which two nuclei are combined to form a larger nucleus. Energy is released when light nuclei are fused to form medium-mass nuclei. Fusion is the source of energy in stars, with the proton-proton cycle, being the principle sequence of energy-producing reactions in our Sun. Fusion also explains the process of nucleosynthesis in stars and the creation of heavy elements. The amount of energy released by a fusion reaction is called the Q value.
Attempts to utilize controlled fusion as an energy source on Earth are related to deuterium and tritium, and the reactions play important roles. Nuclear fusion explains the reaction between deuterium and tritium that produces a fusion. Ignition is the condition under which the controlled fusion is self-sustaining, but this has not yet been achieved. Break-even, in which the fusion energy output is as great as the external energy input, has nearly been achieved.
Magnetic confinement and inertial confinement are the two methods being developed for heating fuel to sufficiently high temperatures, at sufficient density, and for sufficiently long times to achieve ignition. The first method uses magnetic fields and the second method uses the momentum of impinging laser beams for confinement.
Nuclear fission is a reaction in which a nucleus is split. Fission releases energy when heavy nuclei are split into medium-mass nuclei. The sum of the masses of the product nuclei are less than the masses of the reactants. Energy changes in a nuclear fission reaction can be understood in terms of the binding energy per nucleon curve.
Self-sustained fission is possible, because neutron-induced fission also produces neutrons that can induce other fissions, n + AX > FF1 + FF2 + xn, where FF1 and FF2 are the two daughter nuclei, or fission fragments, and x is the number of neutrons produced. A minimum mass, called the critical mass, should be present to achieve criticality. More than a critical mass can produce supercriticality.
The production of new or different isotopes by nuclear transformation is called breeding, and reactors designed for this purpose are called breeder reactors.
