Radiological physics: radioactivity

2/3 times the rest energy of the electron, because the energy of the incoming photon must surpass 4 times the rest energy of the electron, half goes to producing the electron/positron pair, and the other half is split between the particles

Minimum kinetic energy of participating particles following triplet production?

Ionization energy or potential

Minimum energy to remove an electron from an atom

~4 eV (alkali metals) to 24.6 eV (Helium gas)

Range of ionization energy with examples

Near ultraviolet radiation; Visible light; Infrared photons; Microwaves; Radiowaves

Examples of non-ionizing radiation

Charged particles that deposit energy in absorber in one step via Coulomb interactions

Directly ionizing particles overview & mechanism

Neutral particles that deposit energy in absorber in two steps by releasing a charged particle that behaves as a directly ionizing particle

Indirectly ionizing particles overview & mechanism

electron and positron

Examples of directly ionizing particles with light mass

negative pion

Example of directly ionizing particle with intermediate mass

proton, alpha particle, carbon 12 ion, neon-20 ion

Examples of directly ionizing particles with heavy mass

Photons (x-ray and gamma ray) and neutrons

Examples of indirectly ionizing particles

Linear energy transfer: the mean amount of energy that a given ionizing radiation departs into the absorbing medium per unit path length

LET meaning

LET

What specifies the quality of an ionizing radiation beam?

Sparsely: LET < 10 keV/um; Densely: LET > 10 keV/um

Difference between sparsely and densely ionizing radiation?

Energy lost by an energetic charged particle moving through an absorber per unit path length

stopping power

gamma rays; x rays; high energy electrons (~10 keV)

Examples of low LET radiation

low energy electrons (~1 keV); neutrons (~ 14 MeV); protons (~ 2 MeV); carbon ions (~ 100 MeV); heavy ions

Examples of high LET radiation

0.3 keV/um

Approximate LET of gamma rays (Co-60)

0.3 keV/um @ 3 MeV up to 2 keV/um @ 250 kVp

Approximate LET of x rays

0.25 keV/um @ 1 MeV up to 12.3 keV/um @ 1 keV

Approximate LET of electrons

12 keV/um @ 14 MeV

Approximate LET of neutrons

17 keV/um @ 2 MeV

Approximate LET of protons

160 keV/um @ 100 MeV

Approximate LET of carbon ions

100-2000 keV/um

Approximate LET of heavy ions

E1 - E2 = h * frequency of photon

Energy of photon released by electron jumping from higher E1 to lower E2

Minimum energy required to release an electron from a metal via the photoelectric effect (symbol e*phi)

Work function meaning and symbol

KE = energy of photon - work function

Max kinetic energy of electron ejected from metal via photoelectric effect

a few eV

Approximate work function of metals

Visible light (400-700 nm) and near ultraviolet (80-400 nm)

Types of light with energy on the order of work function of metals

Atomic: outer orbital electron ejected by high energy photon (energy > binding energy); Surface: free electron in a metal ejected by visible or near UV photon (energy > work function)

Difference between atomic and surface photoelectric effects

Ratio dN/dA for number of particles dN entering a volume with cross-sectional area dA (phi often measured in 1/cm2)

Particle fluence meaning, symbol and units

Ratio dE/dA for radiant energy dE incident on a volume with cross-sectional area dA (psi often measured in MeV/cm2)

Energy fluence meaning, symbol and units

psi = dE/dA = E * dN/dA = E * particle fluence

Energy fluence of monoenergetic beam

The ionization threshold is medium dependent

Why does the distinction between ionizing and non-ionizing radiation depend on the medium?

Number of protons and number of electrons in an atom

Atomic number Z

Number of nucleons in atom symbol

Atomic mass number A

M measured in MeV (per c^2 but usually reported as MeV informally) is the rest mass of the nucleus

Nuclear mass symbol, units and meaning

Curly M measured in amu is the mass of the nucleus and orbital electrons (the binding energy of the electrons is ignored)

Atomic mass symbol, units and meaning

1 amu is 1/12 the mass of a Carbon-12 atom (not nucleus)

Definition of atomic mass unit

For all elements except Carbon-12, the atomic mass in amu differs slightly from the integer atomic mass number

How does the atomic mass in amu relate to the atomic mass number?

1 amu = 931.5 MeV

Approximate value of 1 amu in MeV

It is energetically favourable for neutrons to decay via beta negative decay because protons have less mass (lower rest energy) than neutrons

Why and how do free neutrons decay into protons?

For an atom (Z, A), nuclear mass is the atomic mass less Z * electron mass

How do the nuclear and atomic masses relate?

The summed mass of the nucleons minus the nuclear mass (which weighs less) is the mass deficit. The energy equivalent of the mass deficit is the binding energy of the nucleus

How does the nuclear mass relate to the sum of the masses of the nucleons that compose the nucleus?

The positive work required to disassemble a nucleus into its individual components: Z protons and (A−Z) neutrons.; The energy liberated when Z protons and (A−Z) neutrons are brought together to form the nucleus

Interpret the binding energy of the nucleus

Find the difference between the summed mass of the nucleons and the nuclear mass

How can the nuclear binding energy by found?

On the order of 8 MeV per nucleon, but varies with the number of nucleons

Approximate binding energy per nucleon

N_A = 1 g/amu

Convenient units to describe Avogadro's number?

Recall that one mol of atoms with atomic mass A weighs "A" grams, then divide the number of atoms in one mol (N sub A) by the mass of one mol (A)

Convenient derivation for number of atoms N sub a per mass m of an element?

Z/A=1 for H, then decreases to 0.5 for He and decreases slowly as higher Z elements need more neutrons (i.e. higher A per Z) to stabilize the repulsive force between protons as the strong force weakens with larger nuclei

Trend in Z/A as Z increases?

Known as the standard atomic weight, averages the atomic mass of all stable isotopes given their natural relative abundances

Mean atomic mass meaning?

X with prior sub Z and superscript A

Convention for labelling atomic symbol X with Z and A

A few femtometers

Approximate distance where strong force is active?

Nuclide refers to all atomic forms of all elements, whereas isotope is limited to all atomic forms of a single element (same Z)

Relation between terms isotope and nuclide?

Nuclides with common atomic mass A

Isobar

Nuclides with common number of neutrons

Isotone

Common atomic number and atomic mass number (different excitation)

Isomer

Or metastable, refers to a nucleus that remains in an excited state for some time, denoted with an m beside the nuclide like barium-137m

Isomeric state and notation

Stable nuclides have higher binding energies

Relation between binding energy per nucleon and stability?

Generally increases sharply to approximately A=20, then peaks at approximately A=60 and decreases slowly. That is, fusion is more likely for low A and fission is more likely for large A

Trend in binding energy per nucleon as number of nucleons increases? Consequence with respect to converting mass into energy?

Fusion of small nuclei into a larger nucleus releases some energy

Fusion

Fission of a larger nucleus into smaller nuclei releases some energy

Fission

Alpha decay; Beta decay; Gamma decay; Spontaneous fission (SF); Proton emission (PE) decay; Neutron emission (NE) decay

Categories of radioactive decay

Positive, negative, electron capture

Types of beta decay

gamma decay and internal conversion

Types of gamma decay

Total energy; Momentum; Charge; Atomic mass number

Conserved quantities in nuclear transformations

Equal to the decrease in rest energy of the neutral atom from parent P to daughter D

What is the total energy of the particles released by nuclear transformation?

Q = {M(P) - [M(D)+m]}c^2 where M and m are nuclear rest masses (of parent P and daughter D) and the emitted particle in amu. Must use nuclear and not atomic masses since the electron masses do not always cancel!!

Decay (or disintegration) energy symbol and calculation

Radioactive decay is only possible when Q > 0 (i.e. the processes are exoergic or exothermic) and the energy equivalent of Q is shared as KE between the daughter and emitted particles

Decay energy interpretation

Unstable parent emits alpha particle and sheds two orbital electrons to become neutral. The alpha particle then captures another two electrons from its surroundings to become neutral as well

Alpha decay process

Helium-4

Alpha particle composition

28.3 MeV

Nucleus binding energy of alpha particle

KE is 4 to 9 MeV but barrier is 30 MeV, so quantum tunnelling must occur

For an alpha particle emitted via alpha decay, what is the typical KE and Coulomb barrier on surface of parent nucleus?

Lighter nuclides have lower nuclear binding energies, making them less stable, whereas larger nuclides struggle to quantum tunnel through the Coulomb barrier

Why does alpha decay usually occur with alpha particles rather than lighter or heavier nuclides?

Alpha decay begins at Z > 82 and transitions to spontaneous fission at Z > 92 and eventually becomes the predominant mode of decay in the heaviest elements

For what Z does alpha decay begin to occur? When does it transition to spontaneous fission?

10 to 100 mm in air, 10 to 100 um in tissue

Typical range of alpha particle emitted via alpha decay in air and tissue

Q sub alpha is the sum of the daughter and alpha particle binding energies, less that of the parent (since the total number of neutrons and protons is constant, this can be found directly from decay energy Q). It implies the total binding energy of the daughter must be larger than the parent by at least the binding energy of an alpha particle

Decay energy of alpha decay wrt binding energies of constituent nuclei? Why can this be used directly and what is the implication?

Radium-226 into radon-222 (which also alpha decays, into polonium-218)

Example of alpha decay

Radium-226 decays into a chain of products that undergo alpha and beta decay with or without emission of gamma rays. The thick encapsulation stops the alpha and beta particles, and enables treatment with gamma particles with an effective energy close to cobalt-60

Mechanism of sealed radium-226 as treatment source

Radium-226 has a low inherent activity with self absorption of gamma rays, and if encapsulation is damaged, radon-222 gas can leak out

Reason that sealed radium-226 is not efficient and not used clinically as treatment source today

Proton converts to neutron and emits an positron and neutrino

Beta positive decay process

Neutron converts to proton and emits an electron and anti-neutrino

Beta negative decay process

The nucleus captures an orbital electron and transforms a proton into a neutron with the emission of a neutrino

Electron capture process

Beta negative decay or direct emission of a neutron if extremely neutron rich

Possible decay paths for neutron-rich nuclides

Beta positive decay; electron capture; or direct emission of a proton if extremely proton-rich (but this is less likely than neutron emission)

Possible decay paths for proton-rich nuclides

It does not directly, rather the daughter nucleus is sometimes in a stable or metastable state that de-excites in two ways: emits gamma rays; or by internal conversion

How do alpha and beta decay produce gamma rays?

mostly alpha and beta decay; neutron capture (and other nuclear reactions)

Source of excited nuclides that undergo gamma decay and internal conversion

Excited nucleus de-excites by emitting the energy as a gamma ray

Gamma decay process

Excited nucleus transfers the excitation energy to one of its atomic orbital electrons. The vacancy is replaced by another electron which causes characteristic x-ray or Auger electron emission

Internal conversion process

Given the de-excitation energy Q, some portion goes to overcoming the binding energy of the electron and the remainder goes to the gamma ray

Energy of gamma ray emitted by internal conversion

No, they have a continuous KE distribution with the max KE corresponding to the beta decay energy (neglecting the KE from the daughter nucleus) because the emitted (anti) neutrino shares the decay energy

Are beta particles monoenergetic?

Yes, the KE of the alpha particle is directly shared with the daughter (negligible)

Are alpha particles monoenergetic?

Because electrons are attracted to the nucleus

Why do electrons from beta negative decay have a higher distribution at lower KE then positrons from beta positive decay?

Effective energy is 1/3 of the maximum (i.e. the decay energy)

Effective energy of beta decay energy spectra for internal dosimetry calculation?

High gamma ray energy; high specific activity; relatively long half life; large specific air-kerma rate constant. All met by cobalt-60

Most important characteristics of radionuclides used in external beam radiotherapy and the nuclide that meets them

Energy is ~1.25 MeV, specific activity is ~300 Ci/g, 5.26 year half life

Effective energy, specific activity and half life of cobalt-60 gamma rays

Nuclear mass of parent must exceed that of daughter by at least one electron mass; Atomic mass of parent must exceed that of daughter

Condition of nuclear and atomic masses for beta negative decay

Nuclear mass of parent must exceed that of daughter by at least one electron mass; Atomic mass of parent must exceed that of daughter by at least two electron masses

Condition of nuclear and atomic masses for beta positive decay

KE of emitted electron/positron; KE of emitted neutrino/anti-neutrino; Energy of emitted gamma ray photons or conversion electrons with characteristic x-rats and Auger electrons; and (negligibly) recoil KE of daughter

Beta decay energy goes to

cesium-137 to barium-137

Example of beta negative decay

Radionuclides that undergo beta positive decay, useful for PET imaging

Positron emitter meaning and application