Ionizing radiation

Ionizing radiation is high-energy radiation that includes x-rays and radioactive emissions such as alpha, beta, and gamma radiation. This article explains the composition of these radiation types and the physical properties used to distinguish them.

Interactions between ionizing radiation and matter are especially important in medicine. Key considerations include how radiation is attenuated and how deeply it penetrates tissue, as well as the biological effects, specifically how to distinguish harmless doses from those sufficient to achieve a therapeutic effect.

• Radioactive radiation: radiation emitted from an atomic nucleus
  • Particle radiation: Nuclear fragments (alpha radiation) or elementary particles (beta radiation) are emitted from the atomic nucleus.
  • Photon radiation (electromagnetic waves): Massless photons (gamma radiation) originate from processes within the atomic nucleus, such as radioactive decay or nuclear fusion.
• Radioactive elements
  • Light elements: atomic nuclei (nuclides) with an unstable ratio of neutrons to protons such as carbon-14
  • Heavy elements: Atomic nuclei with more than 83 protons (atomic number ≥ 84) are unstable. In the periodic table, all elements with an atomic number greater than bismuth (Z=83) are radioactive.
• Nuclear decay: transformation of an unstable nucleus into one or more daughter nuclei, e.g., ²²⁶Ra ⟶ ²²²Rn + ⁴He
• Decay series: a sequence of nuclear decays that begins with an unstable radionuclide and ends with the formation of a stable nucleus

Nuclear fission

• Definition: a nuclear reaction in which a large, heavy nucleus splits into two or more smaller, lighter nuclei
• Characteristics
  • Releases a large amount of energy.
  • Can be spontaneous or induced by the absorption of a low-energy neutron by the heavy nucleus
  • The process often releases additional neutrons, which can trigger further fission events, leading to a chain reaction.
  • The combined mass of the resulting smaller nuclei is less than the mass of the original heavy nucleus; the difference is converted into energy.
  • The basis for nuclear power generation

Nuclear fusion

• Definition: a nuclear reaction in which two or more light nuclei combine to form a single, heavier, and more stable nucleus
• Characteristics
  • Releases a tremendous amount of energy, even more than fission.
  • Occurs under conditions of extremely high temperature and pressure (e.g., in the core of the sun).
  • The mass of the resulting heavier nucleus is less than the total mass of the original light nuclei; the difference is converted into energy.
  • The energy source of stars (e.g., the Sun)

Particle radiation can be completely blocked by appropriate shielding; electromagnetic radiation can only be attenuated!

The terms radioactive radiation and ionizing radiation are not synonymous. Radioactive radiation originates from an atomic nucleus, while ionizing radiation refers to any radiation with enough energy to ionize matter, regardless of its origin!

Ionizing radiation includes all types of radiation with sufficient energy to remove electrons from an atom . These can be classified as follows:

Alpha radiation

• Characteristics: particle radiation composed of alpha particles, which are helium nuclei ( ⁴₂He) consisting of two protons and two neutrons
  • Origin: emitted by radioactive nuclides (alpha emitters) during alpha decay
  • Reaction: ^A_ZX ⟶ ^A-4_Z₋₂Y + ⁴₂He
• Energy : has a radiation weighting factor of 20, reflecting its high potential for tissue damage compared to beta or gamma radiation
• Effect: directly ionizing
• Range: approx. 5 μm in water (≈ tissue)
• Protective measures: can be blocked by a sheet of paper
• Medical application (example): nuclide therapy for bone metastases

Beta radiation

• Characteristics: two types of particle radiation
  • β⁺ radiation: consists of positrons
    • Origin: a proton in the nucleus converts into a neutron, a positron, and an electron neutrino; the positron and neutrino are emitted as radiation
    • Reaction β⁺: ^A_ZX ⟶ ^A_Z₋₁Y + e⁺ + νₑ
  • β⁻ radiation: consists of electrons
    • Origin: a neutron converts into a proton, an electron, and an electron antineutrino; the electron and antineutrino are emitted as radiation
    • Reaction β⁻: ^A_ZX ⟶ ^A_Z+1Y + e⁻ + ν̅ₑ
• Energy : the released energy is shared between the emitted particles. Beta decay produces a continuous energy spectrum rather than monoenergetic particles
• Effect: directly ionizing
• Range: approx. 5 mm in water (≈ tissue)
• Protective measures: can be blocked by an aluminum sheet a few millimeters thick
• Medical application (example): primarily for therapeutic purposes (e.g., ¹³¹I for radioiodine therapy)

Electron capture

• Characteristics: a type of radioactive decay related to β⁺ decay
  • Origin: the nucleus of an atom captures one of its own inner-shell electrons (typically from the K or L shell).
  • Nuclear transformation: inside the nucleus, the captured electron combines with a proton to form a neutron and an electron neutrino.
    • p⁺ + e⁻ ⟶ n⁰ + νₑ
  • Effect on nucleus
    • The atomic number (Z) decreases by 1.
    • The mass number (A) remains unchanged.
  • Emission: an electron neutrino is emitted from the nucleus.
    • The vacancy left by the captured electron is filled by an electron from a higher energy level, resulting in the emission of characteristic x-rays or an Auger electron.

Gamma radiation

• Characteristics: electromagnetic wave
  • Typical origin: energy is released as photons when an atomic nucleus transitions from an excited state to its ground state (radiation is emitted from the atomic nucleus)
  • Reactions: [^A_ZX]* ⟶ ^A_ZX + γ
• Energy: electromagnetic, ionizing radiation that typically has higher energy than x-radiation
• Effect: indirectly ionizing
• Protective measures: materials with a high atomic number, such as lead
• Medical application (example): primarily for diagnostic purposes (e.g., ¹²³I or ⁹⁹ᵐTc for scintigraphy)

X-radiation

• Characteristics: electromagnetic wave
  • Typical origin: ionizing radiation generated by the rapid deceleration of high-energy electrons striking a metal anode (radiation originates from the atomic electron shell)
    • Characteristic x-radiation: a line spectrum that is characteristic of the anode material
    • Bremsstrahlung: a continuous braking radiation spectrum
      • High-energy electrons from the x-ray cathode are deflected and decelerated as they pass near the positively charged nuclei of the anode material. This deceleration causes them to lose kinetic energy, which is emitted as electromagnetic radiation (Bremsstrahlung). This process produces a continuous spectrum of x-ray energies.
      • The greater the anode voltage,
        • The greater the maximum energy and intensity of the x-ray photons
          • The maximum photon energy is achieved when an electron's entire kinetic energy is converted into a single photon, calculated by Eₘₐₓ = e × U
          • Eₘₐₓ = maximum photon energy, e = elementary charge ≈ 1.602 × 10⁻¹⁹ C, U = anode voltage
      • The higher the cutoff frequency of the x-radiation
      • The shorter the cutoff wavelength of the x-radiation
  • Reactions: not a nuclear process
• Energy
  • Corresponds to the energy of the photons; the unit is electron volt (eV)
  • Depending on the anode material and voltage, either “soft” (< 100 keV) or “hard” radiation (≥ 100 keV) is generated
• Effect: indirectly ionizing
• Half-value layer: the thickness of a material required to reduce the intensity of incident radiation by half
  • Body tissues attenuate x-rays to different degrees based on their density, resulting in differential exposure on an x-ray film .
• Protective measures: materials with a high atomic number, such as lead
• Medical application (example): diagnostic purposes (e.g., CT or conventional radiography)

Radioactive radiation is ionizing radiation emitted from an atomic nucleus and includes alpha, beta, and gamma radiation!

X-ray diagnostics
When x-rays pass through tissue, they are attenuated to different degrees depending on the tissue's properties (thickness, density, atomic number) and the radiation energy (soft or hard). The residual intensity of the x-rays after passing through the body is sufficient to expose a detector or film, which is used to visualize various structures.
Soft x-radiation (energy < 100 keV) has low penetration depth and is used for diagnosing tissues with high atomic numbers, such as bone, and in mammography to visualize subtle density differences (e.g., microcalcifications). Hard x-radiation (energy > 100 keV) has high penetration depth and is used in applications like conventional chest x-rays.

Positron emission tomography (PET)
PET is a noninvasive nuclear medicine procedure that provides functional information about disease processes. A patient receives a metabolically relevant molecule labeled with a positron (β+) emitter (e.g., ¹⁸F, ¹¹C, ¹³N, or ¹⁵O). Emitted positrons travel a short distance in tissue before annihilating with electrons; each annihilation produces two ∼511 keV γ photons emitted nearly 180° apart. PET scanners use coincidence detection and image reconstruction to localize those events and map the tracer distribution in the body. PET is used in cardiology (to assess coronary artery disease), oncology (to detect and stage tumors), and neurology (to diagnose conditions like Parkinson's disease or dementia).

To characterize radiation precisely, one must know not only its type but also its intensity. This can be described by radioactivity, which indicates how quickly a source decays. The number of nuclei indicates how many radioactive nuclei remain in a source. Both quantities decrease exponentially over time. Half-life is the most common parameter used to characterize this decay.

• Radioactivity (A): the number of nuclei that decay per unit time
  • Formula: A(t) = N(t) × λ = A₀ × e⁻ˡᵗ
    • Unit: Bq (Becquerel, 1 Bq = 1 decay/s)
    • A(t) = activity at time t, A₀ = initial activity, N(t) = number of nuclei at time t, λ = decay constant, e ≈ 2.718
• Number of nuclei (N): the number of radioactive nuclei in a source
  • Formula: N(t) = N₀ × e⁻ˡᵗ
    • N(t) = number of nuclei at time t, N₀ = initial number of nuclei, λ = decay constant, e ≈ 2.718
• Half-life (t_1/2): the time required for half of the radioactive nuclei in a sample to decay
  • Formula: t_1/2 = ln(2) / λ
    • Unit: s (second)
    • t_1/2= half-life, λ = decay constant, ln(2) ≈ 0.693
• Mean lifetime (τ): the average time a radioactive nucleus exists before it decays
  • Formula: τ = 1 / λ
    • Unit: s (second)
    • τ = mean lifetime, λ = decay constant
• Decay curves
  • A plot of the number of undecayed nuclei (N) or activity (A) versus time results in an exponential decay curve
  • A semi-log plot, which graphs the natural logarithm of activity (ln A) versus time, produces a straight line
  • The slope of this line is equal to the negative of the decay constant (-λ)

The energy of elementary particles is very small, so it is often given in the unit electron volt (eV): 1 eV ≈ 1.602 × 10⁻¹⁹ J.

Example calculation: half-life

A radioactive element has a decay constant of 0.0005 s⁻¹. What is the half-life of this element?

• Required: half-life t_1/2
• Given: decay constant λ
  • The half-life can be calculated with the formula t_1/2 = ln(2) / λ
  • ln(2) corresponds to a numerical value of approx. 0.693
  • t_1/2= 0.693 / (0.0005 s⁻¹) = 1386 s (≈ 23.1 min)
  • The half-life of the element is approximately 23 minutes.

Example calculation: radioactivity

A radioactive element has a decay constant of 0.0078 s⁻¹. How many atomic nuclei of the element are still present after 30 minutes if the initial quantity is 10¹⁵ nuclei?

• Required: the number of nuclei after 30 minutes, N(t)
• Given: initial number of nuclei N₀, time of decay t, decay constant λ
  • The equation for radioactive decay is N(t) = N₀ × e⁻ˡᵗ
  • For this case, t = 30 min = 1800 s. Then N(1800 s) = 10¹⁵ × e^-(0.0078 s⁻¹ × 1800 s) = 10¹⁵ × e⁻¹⁴·⁰⁴ ≈ 10¹⁵ × 8.025 × 10⁻⁷ ≈ 8.0 × 10⁸
  • After 30 minutes, approximately 8.0 × 10⁸ atomic nuclei are still present.

When radiation interacts with matter, its intensity is reduced, or attenuated. The specific type of interaction depends on whether the radiation consists of charged particles (like alpha and beta radiation) or electromagnetic waves (like gamma and x-radiation). The following principles apply mainly to electromagnetic radiation.

Attenuation law and half-value layer

The further radiation travels through matter, the more it is attenuated. Attenuation also depends on the type of matter and the radiation's energy. The exponential decrease in radiation intensity is described by the attenuation law, but attenuation is also often expressed as the half-value layer.

• Attenuation law for radiation: when radiation passes through matter, absorption and scattering effects cause an exponential decrease in its intensity.
  • Attenuation of radiation intensity
    • Formula: I = I₀ × e⁻^μd
      • Unit of intensity (I): W/m² (watts per square meter)
      • I = intensity after interaction, I₀ = initial intensity, μ = linear attenuation coefficient, d = layer thickness
      • The attenuation coefficient is strongly dependent on the atomic number of the irradiated matter (approximately μ ∝ Z⁴), meaning absorption increases significantly with the atomic number of an element
  • Attenuation of radiation energy with distance: the inverse-square law applies to the intensity of radiation from a point source
    • Formula: intensity ∝ 1/r²
      • r = distance from the source
• Half-value layer (HVL): the thickness of a material required to reduce the radiation intensity by half
  • Formula: HVL = ln(2)/μ
    • Unit: m
    • HVL = half-value layer, μ = linear attenuation coefficient

Radiation from uncharged particles (e.g., photons in gamma radiation) is attenuated less by matter than radiation from charged particles (e.g., alpha radiation)!

Radiation intensity decreases in proportion to the inverse square of the distance r from the source (intensity ∝ 1/r²). For example, standing 2 m away from an x-ray source instead of 1 m reduces the intensity to one-quarter (1/2² = 1/4). At a distance of 10 m, the intensity is only one-hundredth (1/10² = 1/100)!

Example calculation

The radiation of a laser decreases in muscle tissue according to an exponential attenuation law. The absorption coefficient of the tissue is 750 cm⁻¹. After what distance through the tissue does approximately 1/10th of the original intensity remain?

• Required: layer thickness d
• Given: absorption coefficient μ and intensity ratio I/I₀ = 1/10
  • The attenuation formula is I = I₀ × e⁻^μd
  • 1/10 = e⁻⁷⁵⁰ᵈ = ln(0.1) = -750 × d → d = ln(0.1) / -750 ≈ -2.3026 / -750 ≈ 0.00307 cm = 0.0307 mm ≈ 31 μm
  • The radiation intensity drops to 1/10th of its initial value after traveling approximately. 31 μm through the tissue.

Special interaction of gamma rays

• Attenuation of photon (γ-quantum) energy when passing through matter occurs via
  • Photoelectric effect
    • A photon's energy is completely absorbed by an atom, causing an inner-shell electron to be ejected
    • Dominant for photons in the low-energy range of a few keV
  • Compton effect
    • A photon collides with an outer-shell electron, transferring part of its energy to the electron and scattering in a new direction with reduced energy
    • Dominant for photons in the medium-energy range of a few 100 keV to a few MeV
  • Pair production
    • In the electric field of a nucleus, a high-energy photon is converted into an electron-positron pair. The positron later annihilates with another electron.
    • Requires photon energy of at least 1.022 MeV and becomes more probable with increasing energy

• Dose: the amount of radiation absorbed by an object
• Dosimetry: the method for measuring radiation dose
• Absorbed dose (D): the radiation energy absorbed per unit mass
  • Formula: D = E/m
    • Unit: Gy (Gray); 1 Gy = 1 J/kg
    • D = absorbed dose, E = absorbed energy, m = irradiated mass
• Equivalent dose (H): allows for comparison of the biological effects of different types of radiation by multiplying the absorbed dose by a radiation weighting factor.
  • Formula: H = D × w_R
    • Unit: Sv (Sievert); 1 Sv = 1 J/kg
    • H = equivalent dose, D = absorbed dose, w_R = radiation weighting factor
    • The weighting factor w_R is 1 for beta and gamma radiation/x-rays, and 20 for alpha radiation
• Dose rate: the absorbed or equivalent dose delivered per unit time
  • Formula: dose rate = D/t or H/t
    • Unit: Gy/s or Sv/s
    • D = absorbed dose, H = equivalent dose, t = time

Radiation exposure
Every person is exposed to natural background radiation, which amounts to approx. 2–3 mSv/year. Medical procedures can involve much higher doses: a chest x-ray (2 views) corresponds to approx. 0.1 mSv, while a CT scan of the chest results in an exposure of approx. 5–7 mSv. Acute doses above 250 mSv are considered harmful, though this cell-damaging effect is used therapeutically to destroy cancer cells. Radiation therapy utilizes doses of 20–80 Gy, and radioiodine therapy can use doses of 100–400 Gy. For perspective, a radiation dose of 1 Gy causes approximately 5000 DNA damage events per cell! See also: DNA damage.

Since the energy of individual radioactive decays is minuscule, the unit "electron volt" (eV) is often used. The conversion to joules (J) is: 1 eV ≈ 1.602 × 10⁻¹⁹ J!

Example calculation

A person is exposed to continuous, weak gamma radiation. Each decay event deposits 10⁻¹² J of energy. What is the absorbed dose received by this 80 kg person in one month (30 days), if they are exposed to 10,000 decay events per day?

• Required: absorbed dose D
• Given: mass m, time t, number of decay events per day, energy per event E_event
  • The total number of decay events in 30 days is 10,000 day⁻¹ × 30 days = 300,000
  • The total energy absorbed is E = 300,000 × 10⁻¹² J = 3 × 10⁻⁷ J.
  • The absorbed dose (D) is calculated using the formula D = E/m = (3 × 10⁻⁷ J) / 80 kg = 3.75 × 10⁻⁹ J/kg ≈ 3.8 nGy
  • The absorbed dose of radiation received by the person per month is therefore approximately. 3.8 nGy.