Nuclear Structure, Isotopes, and Purity: Study Notes

Structure of the Nucleus

• All particles in the nucleus are collectively called nucleons.
  • Nucleons include all protons and neutrons.
• As we progress up the periodic chart to larger atoms:
  • The normal number of neutrons increases, and the increase is faster than the increase in protons.
  • Hydrogen (Z = 1) normally has no neutrons.
  • From Helium (Z = 2) to Chlorine (Z = 17), the number of neutrons is normally balanced with the number of protons.
  • Beyond this point, atoms have progressively more neutrons than protons.
• Examples of extra neutrons beyond the protons:
  • Nickel: 2 “extra” neutrons
  • Copper: 5 “extra” neutrons
  • Bromine: 9 “extra” neutrons
  • Lead: 43 “extra” neutrons
  • Uranium: 54 “extra” neutrons
• Rationale:
  • Neutrons do not carry electric charge, so they do not electrostatically repel each other the way protons do.
  • The presence of more neutrons helps bind large nuclei; as nuclei get very large, having more neutrons relative to protons reduces the nuclear binding energy needed to hold the nucleus together.

Atomic Mass and Basic Particles

• The nucleon number is called the atomic mass, abbreviated A.
• Atomic mass is not the same as atomic weight.
• Important physical facts:
  • Radius of a typical atom ≈ 1 Å = 10^{-8} cm. Radius of a typical nucleus ≈ 0.0001 Å = 10^{-12} cm.
  • An atom is mostly empty space.
• Atomic Mass Unit (AMU):
  • Defined as 1/12 the mass of a carbon atom;
  • 1 amu = m(^{12}_{6}C)/12.
• Basic particles and their properties (as listed on the slides):
  • Electron: symbol e or e^{-}, mass ≈ 0.000549 amu, charge = -1.
  • Proton: symbol p^{+}, mass ≈ 1.00759 amu, charge = +1.
  • Neutron: symbol n, mass ≈ 1.00898 amu (listed on the slide); note a later correction lists 1.008139 amu. Charge = 0.
• Mass references in SI units and AMU (from the slide):
  • Electron mass: m_e = 9.10938 × 10^{-31} kg.
  • 1 amu = 1.66054 × 10^{-27} kg.
  • Proton mass: m_p ≈ 1.67263 × 10^{-27} kg (≈ 1.00759 amu).
  • Neutron mass: listed as n ≈ 1.00898 amu, with a later correction to ≈ 1.008139 amu.
  • Note: The slide shows a discrepancy for the neutron’s exact AMU value (1.008980 vs 1.008139 AMU).
• Quick takeaway:
  • Electron mass is ~1/2000 of a proton mass.
  • The nucleus is composed of protons and neutrons; mass and charge distributions differ markedly between these constituents.

Nuclear Notation and Nuclear Shorthand

• Nuclear identity is determined by the number of protons (Z).
  • Example: 6 protons → Carbon (C); 8 protons → Oxygen (O).
• Why Carbon-12 is written as Carbon-12 (12C) and not Carbon-6 (6C):
  • In nuclear shorthand, A denotes the mass number (protons + neutrons) and Z denotes the atomic number (protons).
  • Common notation: ^{A}_{Z}X, where X is the chemical symbol of the element.
  • Example: ^{12}_{6}C (Carbon-12).

Atomic Structure and Periodic Trends

• Within the nucleus, each proton has a +1 charge that balances the total negative charge of the electron shells. Mass, size, and weight of a proton are much larger than that of an electron (about 2000× larger).
• Atomic Mass Unit (AMU) defined as the mass of a proton; serves as the standard for comparing other particles.
• The Atomic Number Z:
  • Defines the chemical identity of the element.
  • Dmitri Mendeleev’s Law of Periodicity: properties of elements are periodic functions of their atomic weight (as Z increases). Periodic chart constructed on this basis.
• Nuclear shorthand components:
  • Z = number of protons (and typically electrons in a neutral atom).
  • N = number of neutrons; A = mass number = protons + neutrons = Z + N.
• Relationships:
  • Isotopes: same Z, different N (hence different A).
  • Isobars: different Z and N, but same A.
  • Isotones: same N, but different Z and A.
  • Isomers: same Z and A, but different energy/stability states (metastable states denoted by an m, e.g., 99mTc).
• Periodic Chart structure:
  • Groups (columns) show increasing Z left to right with similar chemical properties.
  • Periods (rows) show a repeating cycle of chemical properties.

Isotope, Isobar, Isotone, Isomer: Definitions and Examples

• Isotope: variation of atomic structure of an element where Z is constant but A and N differ.
  • Example: ^{12}{6}C vs ^{14}{6}C (both Carbon, same Z, different N).
• Isobar: nuclides with the same mass number A but different Z and N.
  • Example: ^{3}{2}He (Helium-3) and ^{3}{1}H (Tritium) both have A = 3 but different Z and N.
• Isotone: nuclides with the same neutron number N but different Z and A.
  • Example: ^{3}{2}He and ^{2}{1}H (deuterium) both have N = 1 neutron.
• Isomer: nuclides with the same Z and A but in different energy/stability states; metastable state denoted with a superscript m (e.g., ^{99m}_{43}Tc).
• Nuclide concept: there are known to exist over 1500 nuclides.

Nuclear Notation: Variations and Examples

• Notation typically shown as A Z X or ^{A}_{Z}X (A = mass number, Z = atomic number, X = chemical symbol).
• Example notations from the slides:
  • ^{12}_{6}C, carbon-12 (often written as 12C in shorthand).
  • The slide also references a compact form like 126C or 126C depending on formatting, but the standard is ^{A}{Z}X.

Isotopes, Isobars, Isotones, Isomers: Summary Points

• Isotopes share Z but have different A and N.
• Isobars share the same A but have different Z and N.
• Isotones share the same N but have different Z and A.
• Isomers share the same Z and A but differ in energy/stability (metastable state with m).
• Nuclide terminology includes all four families and the concept of nuclides in general.

Line of Stability

• The nucleus configuration tends to favor an equal number of protons and neutrons (N ≈ Z) for stability in lighter elements.
• Exception highlighted in the slide: Chlorine (Z = 17) is the point at which, after, extra neutrons are needed to keep the nucleus bound.
• Practically, stable nuclides lie near the line where N ≈ Z for light elements and shift toward N > Z as Z increases.

Radionuclidic and Radiochemical Purity: Definitions

• Radionuclidic purity:
  • The percentage of the element’s sample that is the desired isotope (regardless of chemical form).
  • Example: For a sample containing 235U and 238U, radionuclidic purity would consider only the 235U component if that is the desired isotope.
• Radiochemical purity:
  • The percentage of the element that is in the desired chemical form containing the desired radionuclide.
  • If the element is present in multiple chemical forms or as multiple radionuclides, radiochemical purity accounts for the fraction in the targeted chemical form and radionuclide.

Practical Example: 99Mo decaying to 99mTc and onward

• Isotope decay path described in the slide:
  • 99Mo → 99mTc → 99Tc (by decay paths releasing energy).
  • The metastable isotope 99mTc can be used to form imaging agents (e.g., 99mTc-HDP).
• Provided sample composition (as given on the slides):
  • 1% 99Mo
  • 4% total 99Tc, distributed as:
  • 2% 99Tc-HDP
  • 1% 99Tc-O2^{-}
  • 1% 99Tc-O4^{-}
  • 1% 99mTc-O2
  • 1% 99mTc-O4^{-}
  • 93% 99mTc-HDP
• Question: What is the radionuclidic purity of the sample for 99mTc and the radiochemical purity of the sample?
• Calculations (as given in the slides):
  • Radionuclidic purity for 99mTc = 1% (99mTc-O2) + 1% (99mTc-O4^{-}) + 93% (99mTc-HDP) = 95%
  • Radiochemical purity = 93% (99mTc-HDP) = 93%
• Takeaway:
  • Radionuclidic purity focuses on the isotope content regardless of chemical form.
  • Radiochemical purity focuses on the chemical form and specific radionuclide present in that form.

Key Equations and Numbers (at a glance)

• Mass relationships:
  • A = Z + N
  • Isotope notation: ^{A}_{Z}X (or A Z X in other formats).
• Atomic mass unit (AMU) definition:
  • 1 \, ext{amu} = rac{m(^{12}_{6} ext{C})}{12}
  • 1 \, ext{amu} \, ext{is defined as 1/12 the mass of Carbon-12}.
• Typical scales:
  • Atom radius ≈ 1 \,Å = 10^{-8} cm.
  • Nucleus radius ≈ 0.0001 \,Å = 10^{-12} cm.
  • Atom is mostly empty space.
• Particle masses (as listed):
  • Electron: $m_e = 9.10938\times 10^{-31}\ ext{kg} \quad (\approx 0.000549\ \text{amu})$
  • Proton: $m_p \approx 1.007590\ \text{amu} \quad (\approx 1.67263\times 10^{-27}\ \text{kg})$
  • Neutron: listed as $m_n \approx 1.008980\ \text{amu}$ on one slide, but later noted as $1.008139\ \text{amu}$ (the slide mentions both values).
• Isotope/Isobar/Isotone/Isomer concepts (recap):
  • Isotope: same Z, different N/A.
  • Isobar: same A, different Z/N.
  • Isotone: same N, different Z/A.
  • Isomer: same Z and A, different energy state; metastable indicated by m (e.g., 99mTc).
• Line of Stability (summary): stability generally favors N ≈ Z for light elements; after Chlorine (Z = 17), extra neutrons are needed for stability.

Connections to broader concepts

• The variation in neutron numbers explains stability trends and the existence of many nuclides (over 1500 known nuclides).
• Isotopes have nearly identical chemical behavior (same Z) but different nuclear properties due to A and N.
• Radiopharmaceuticals rely on radionuclidic purity (correct isotope) and radiochemical purity (correct chemical form) to ensure safe and effective medical imaging.
• Understanding the line of stability helps predict which nuclides are stable versus radioactive, guiding both fundamental physics and practical applications in medicine and energy.