Exam Review Notes: Nuclear Chemistry and Radioisotopes

Protons, Neutrons, and Electrons

Subatomic particles and basic properties
- Proton: charge +1; mass ≈ 1 amu; located in the nucleus
- Neutron: charge 0; mass ≈ 1 amu; located in the nucleus
- Electron: charge −1; mass ≈ 0 amu; located outside the nucleus (electron cloud)
- Rationale: nucleus contains protons and neutrons (nucleons); electrons occupy orbitals around the nucleus and determine chemical behavior

Isotopes, Atomic Mass, and Mass Number

Definitions
- Isotope: atoms of the same element with different numbers of neutrons
- Mass number (A): A = Z + N, where Z = number of protons, N = number of neutrons
- Atomic (decimal) mass on the periodic table is a weighted average of all isotopes of the element, reflecting natural abundances
Interpretation of a given isotope table (conceptual):
- Mass number applies to the specific isotope (not to all isotopes of the element)
- Protons determine the element; neutrons contribute to mass and stability; electrons balance charge in neutral atoms

Carbon Isotopes and Radioactivity

Carbon has three stable/radioactive isotopes commonly discussed:
- Carbon-12: Protons = 6; Neutrons = 6
- Carbon-13: Protons = 6; Neutrons = 7
- Carbon-14: Protons = 6; Neutrons = 8
Carbon-14 is radioactive due to an unstable nucleus (excess neutrons relative to stability for this nuclide)
Note: mass numbers are 12, 13, 14, with identical proton count (6) but different neutron counts

Nuclear Decay of Carbon-14

Decay mode: beta emission (β−)
- Balanced reaction (beta decay):
  ^{14}{6}C ightarrow ^{14}{7}N + e^{-} + ar{
  u}_e
Half-life of Carbon-14: $T_{1/2} = 5730 ext{ years}$
Example problem: a fossilized tree shows 6.25% of Carbon-14 remaining
- 6.25% = 1/16 ≈ (1/2)^4, so 4 half-lives have passed
- Time elapsed: $t = 4 imes T_{1/2} = 4 imes 5730 ext{ yr} = 22{,}920 ext{ yr}$
Conceptual takeaway: fraction remaining after n half-lives is $rac{1}{2^n}$ ; elapsed time scales with the half-life

Atomic Mass vs. Isotope Mass and Average Atomic Mass

Isotope mass: exact mass of a specific isotope (e.g., boron-11 has a mass of exactly $11 ext{ amu}$ for that nuclide)
Periodic table mass: a weighted average reflecting natural abundances of all isotopes of the element (e.g., boron average ≈ $10.81 ext{ amu}$ , not equal to any single isotope mass)
Important distinction: use exact isotope mass for a single nuclide; use average mass for elemental properties and comparisons

Copper Isotopes and Average Atomic Mass

Naturally occurring copper isotopes and abundances:
- Cu-63: abundance ≈ 69%
- Cu-65: abundance ≈ 31%
Average atomic mass calculation:
$ext{Avg mass} = (63 imes 0.69) + (65 imes 0.31) = 63.62 ext{ amu}$

Nuclear Emission Processes (Overview)

Alpha emission (α): a helium nucleus is emitted
- Example form (common representation):
 $^{A}{Z}X ightarrow ^{A-4}{Z-2}Y + ^{4}_{2} ext{He}$
Beta emission (β−): a neutron converts to a proton with emission of an electron and an antineutrino
- Form: ^{A}{Z}X ightarrow ^{A}{Z+1}Y + e^{-} + ar{
  u}_e
Gamma emission (γ): emission of high-energy photons from a excited nucleus, no change in Z or A
- Form: $^{A}{Z}X^{*} ightarrow ^{A}{Z}X + obreak ext{γ}$
Electron capture (EC): a proton captures an inner-shell electron to become a neutron, nucleus shifts to a lower Z
- Form: $^{A}{Z}X + e^{-} ightarrow ^{A}{Z-1}Y + u_e$
General notes from the slide set include example reactions: Ra-222 → Rn-218 + He-4 (alpha decay), Co-59 + n → … (beta pathways), Mo + e− (electron capture) and pathways involving gamma emission

Radiation Health Effects and Shielding (External vs Internal)

External exposure (radiation source outside the body): ranking from least to most harmful based on penetrating power
- Alpha particles: least penetrating; stopped by skin or a sheet of paper
- Beta particles: moderate penetrating; can be stopped by plastic, clothing, or light shielding
- Gamma rays: highly penetrating; require dense shielding (lead or concrete, roughly 10 cm or more depending on energy)
- Key principle: more penetrating radiation is generally more harmful externally
Shielding guidelines (external protection):
- Alpha: paper or thin clothing is typically sufficient
- Beta: plastic, glass, or lightweight metal shielding
- Gamma: thick shielding such as lead or concrete (≈ 10 cm or more as a general guideline)
Internal exposure (emissions inside the body, e.g., via inhalation, ingestion, implantation): ranking is opposite
- Inside the body, high-LET (often more localized) alpha radiation can cause significant damage despite being less penetrating externally
- In this context, alpha particles are most harmful internally; beta particles are intermediate; gamma rays are least harmful internally (though they still pose risk)

Half-Life Calculation Guidelines and Key Formulas

Core formula: Total time = (number of half-lives) × (half-life time) or $t = n imes T_{1/2}$
Key relationships:
- Final amount = Initial amount ÷ 2^n
- Initial amount = Final amount × 2^n
- Always compare total time with the half-life time to determine n when given t
- Total time is always larger than or equal to the half-life time for at least one half-life to pass; initial amount > final amount for decay scenarios
Example: solve half-life from a pair of amounts and time
- If 1.0 g decays to 0.125 g in 90 years:
- 0.125 = 1.0 ÷ 2^n ⇒ 2^n = 8 ⇒ n = 3
- $T_{1/2} = rac{t}{n} = rac{90}{3} = 30 ext{ years}$
- If final amount is achieved after a given time with a known starting amount, use the same multiplication/division by powers of 2

Medical Radioisotopes: Diagnosis vs. Treatment

Medical applications of radioisotopes
- Diagnosis (imaging): trace amounts are used to image organs; short half-lives are preferred to minimize radiation exposure
- Treatment: higher doses aimed at destroying diseased or cancerous tissue; targeted to specific organs or tissues; often longer half-lives (days to weeks) to sustain dose
Brachytherapy (internal radiotherapy) specifics
- Permanent (low dose-rate) brachytherapy implant: radioactive seeds implanted into a target area (e.g., prostate) with ultrasound guidance
- Typical seed count: about 40 to 100 seeds implanted depending on treatment plan
- Seeds remain in place permanently and become biologically inert after months, providing localized high-dose radiation with limited damage to surrounding tissues
Pd-103 brachytherapy components
- Pd-103 seeds or sources are often delivered on ion-exchange beads placed into Ti capsules and can be part of Au/Cu alloy carriers
- Pd-103 half-life ≈ 17 days

Pd-103: Case Study, Timing, and Safety Considerations

What does Pd-103 mean?
- Pd-103 is one isotope of palladium with mass number 103
Why is Pd-103 radioactive?
- It has an unstable nucleus, leading to radioactive decay (emitting gamma radiation and/or particles over time)
Key timing for safety and patient family exposure
- After about 3–5 half-lives, most radioactivity decays away
- For Pd-103 (half-life ≈ 17 days), 5 half-lives ≈ 85 days ≈ ~3 months; this is why patients are advised about exposure to others (especially children) for several months after implantation
Specific calculation example: 3 months corresponds to roughly 5 half-lives
- Amount remaining ≈ Initial × (1/2)^5 ≈ Initial × 1/32 ≈ 3.125%
Electron capture recap (for context):
- Electron capture is a mode of decay where a nucleus captures an inner-shell electron, converting a proton to a neutron in the process
Practical takeaway: long-term radiation safety in brachytherapy hinges on knowing half-lives, dose delivery, and decay timelines to minimize risk to others while delivering effective treatment

Valence Electrons, Ion Formation, and the Octet Rule

Valence electron concept: electrons in the outermost shell determine chemical properties
Common-group rule: number of valence electrons typically equals the group number for main-group elements (exceptions for transition metals)
Examples of valence electrons (per page):
- Calcium: 2 valence electrons
- Oxygen: 6 valence electrons
- Chlorine (Chloride): 7 valence electrons
- Krypton: 8 valence electrons
- Arsenic: 5 valence electrons
- Aluminum: 3 valence electrons
Charge on ions via the octet rule (stability when an atom attains 8 valence electrons):
- Calcium → Ca^{2+} (loses 2 electrons)
- Oxygen → O^{2-} (gains 2 electrons)
- Chlorine → Cl^{-} (gains 1 electron)
- Krypton → does not form a typical ion (noble gas, stable with full octet)
- Arsenic → As^{3-} (gains 3 electrons) or forms other ionic states depending on context
- Aluminum → Al^{3+} (loses 3 electrons)
Summary of the octet rule: main-group atoms are most stable with 8 electrons in their valence shell; transition metals may deviate from this rule

Medical Applications for Radioisotopes: Diagnosis and Therapeutic Use

Diagnosis:
- Radioisotopes concentrate in specific organs, enabling imaging of diseased states
- Administered in trace amounts; very short half-lives reduce long-term exposure
Treatment:
- Higher doses are used to destroy diseased or cancerous tissue
- Targeted to affected organ; tissues that divide rapidly (e.g., cancer cells) are more affected
- Often employ slightly longer half-lives (days to weeks) to sustain therapeutic dose

Brachytherapy: Seeds, Capsule, and Materials

Seed construction and materials
- Pd-103 seeds may be embedded on ion-exchange beads
- Seed components can include Ti capsules and Au/Cu alloy constructions for shielding and structural integrity
Practical aspects
- Implantation guided by imaging (e.g., ultrasound)
- Number of seeds and placement are customized per patient
- Seeds become biologically inert after months while delivering a high, localized dose during that period

Quick Reference Formulas and Facts (Summary)

Beta decay balance (example): ^{14}{6}C ightarrow ^{14}{7}N + e^{-} + ar{
u}_e
Half-life concept: $t = n imes T_{1/2}$ where n is the number of half-lives
Fraction remaining after n half-lives: $ext{Fraction} = rac{1}{2^n}$
Average mass with isotopic abundances: $$ ext{Avg mass} =

ight( ext{mass}1 imes ext{abundance}1
ight) + ext{mass}2 imes ext{abundance}2 + \