Atoms and Radioactivity Vocabulary Flashcards

Fundamental Concepts of Atomic Structure

• Definition of the Atom:

  • An atom is defined as the smallest continuous particle that forms an element.

  • All atoms of a specific element share identical chemical and physical properties that distinguish them from atoms of any other element.

• Atomic Structure and Volume Distribution:

  • Lithium Example ($Z = 3$, Group 1A, Period 2, alkali metal):

    • The physical surface of solid lithium metal consists of aligned spherical units repeating in a uniform pattern to create a solid crystal structure.

    • Despite appearing solid, most of an atom's volume is empty space.

    • Only a tiny fraction of the total atomic volume contains measurable mass.

    • Subatomic particles containing measurable mass possess diminishingly small masses.

  • The Nucleus:

    • Located at the center of the atomic volume as an infinitesimally small central core.

    • Contains virtually all the mass of the atom.

    • Composed of protons (which determine elemental identity) and neutrons (which contribute to mass and nuclear stability).

  • The Electron Cloud:

    • Surrounds the central nucleus across a vastly larger volume.

    • Contains electrons distributed randomly throughout the region surrounding the nucleus.

    • Ground-state lithium contains 3 protons in its nucleus paired with 3 surrounding electrons, creating an overall electrically neutral environment.

    • The electron cloud balances the nuclear charge and acts as an electrostatic shield against neighboring atomic nuclei.

• Relative Scale and Dimensions of Atomic Architecture:

  • Atomic Diameter: On the order of $10^{-10}\,m$ ($0.1\,nm$).

  • Nuclear Diameter: On the order of $10^{-15}\,m$.

  • Scale Ratio: The overall atomic diameter is roughly $10,000$ times larger than the diameter of its nucleus, meaning the nucleus occupies an extraordinarily small fraction of the total atomic volume.

Subatomic Particles and Physical Quantities

• Protons:

  • Mass: $1\,\text{atomic mass unit (amu)}$, corresponding to approximately $1.7 \times 10^{-24}\,g$

  • Charge: $+1$

  • Role: Determines the unique elemental identity of the atom.

• Neutrons:

  • Mass: Assigned a value of $1\,\text{atomic mass unit (amu)}$ ($\approx 1.7 \times 10^{-24}\,g$).

    • Technically, a neutron is slightly heavier/denser than a proton, but for general chemical accounting, their masses are treated as equivalent.

  • Charge: Neutral ($0$)

  • Role: Adds mass and structural stability to the atomic nucleus.

• Electrons:

  • Mass: Approximately $\frac{1}{1000}$ the mass of a proton or neutron.

    • Because it requires roughly $1,000$ electrons to equal the mass of a single proton, electron mass is considered negligible and rounded to $0\,\text{amu}$ in mass calculations.

  • Charge: $-1$

  • Role: Balances the positive nuclear charge generated by protons.

• Subatomic Composition of Lithium:

  • Nucleus contains 3 protons ($3\,\text{amu}$) and 4 neutrons ($4\,\text{amu}$).

  • Total nuclear subatomic particles = 7.

  • Total atomic mass = $7\,\text{amu}$.

Atomic Number, Mass Number, and Isotopes

• Atomic Number ($Z$):

  • Represents the total number of protons in the nucleus of an atom.

  • Printed as the top integer in each box on the periodic table.

  • Uniquely defines the elemental identity:

    • Carbon ($Z = 6$) must always contain exactly 6 protons.

    • An atom with 5 protons is Boron ($Z = 5$).

    • An atom with 7 protons is Nitrogen ($Z = 7$).

• Mass Number ($A$):

  • The integer sum of the total number of protons and neutrons in a specific individual atom:         $\text{Mass Number }(A) = \text{Protons} + \text{Neutrons}$

  • Individual atoms do not possess fractional neutrons, making mass numbers whole integers.

• Atomic Mass:

  • The weighted average mass of all naturally occurring variants (isotopes) of an element as found on Earth.

  • Printed at the bottom of each elemental box on the periodic table.

• Isotopic Notation:

  • Depicted by placing the mass number ($A$) as a superscript to the upper-left of the atomic symbol ($\text{X}$) and the atomic number ($Z$) as a subscript to the lower-left:         ${}_{Z}^{A}\text{X}$

  • Example (Carbon-12): ${}^{12}_{6}\text{C}$

    • Protons = $6$

    • Neutrons = $12 - 6 = 6$

• Isotopes:

  • Atoms of the same element that possess identical atomic numbers (protons) but differing numbers of neutrons, yielding distinct mass numbers.

  • Isotopes of Carbon:

    • Carbon-12 (${}^{12}_{6}\text{C}$): 6 protons, 6 neutrons ($99\%$ natural abundance).

    • Carbon-13 (${}^{13}_{6}\text{C}$): 6 protons, 7 neutrons ($\approx 1\%$ natural abundance).

    • Carbon-14 (${}^{14}_{6}\text{C}$): 6 protons, 8 neutrons ($<1\%$ natural abundance).

    • Weighted Average Atomic Mass: $12.01\,\text{amu}$, reflecting the overwhelming abundance of Carbon-12 alongside trace heavier isotopes.

• Isotopic Abundance Analysis Examples:

  • Gallium ($Z = 31$, reported atomic mass = $69.72\,\text{amu}$):

    • Composed primarily of two natural isotopes: Gallium-69 (${}^{69}_{31}\text{Ga}$, 38 neutrons) and Gallium-71 (${}^{71}_{31}\text{Ga}$, 40 neutrons).

    • Natural relative proportions are roughly $60\%$ Gallium-69 and $40\%$ Gallium-71:             $0.60 \times 69 + 0.40 \times 71 = 69.72\,\text{amu}$

  • Sodium ($Z = 11$, reported atomic mass = $22.99\,\text{amu}$):

    • Atomic number = $11$ ($11$ protons, $11$ electrons in a neutral atom).

    • Sodium-25 Isotope (${}^{25}_{11}\text{Na}$):

      • Mass number = $25$

      • Protons = $11$

      • Neutrons = $25 - 11 = 14$

      • Electrons = $11$

• Practice Identifications:

  • Atomic number $13$: Aluminum ($\text{Al}$, Group 3A, Period 3).

  • Atomic number $19$: Potassium ($\text{K}$, Group 1A, Period 4, alkali metal).

  • Atomic number $16$: Sulfur ($\text{S}$, Group 6A, Period 3).

  • An Oxygen atom ($Z = 8$) containing 9 neutrons has a mass number of $8 + 9 = 17$ (${}^{17}_{8}\text{O}$).

Types of Nuclear Radiation

• Nuclear Radiation Definition:

  • Radiation emitted directly from the nucleus of an unstable atom.

  • Driven by nuclear instability resulting from unfavorable neutron-to-proton ratios.

  • Radioactive Decay: The process wherein an unstable parent isotope spontaneously emits particles or electromagnetic energy to attain a stable nuclear state.

  • Radioisotopes: Specific isotopes that undergo radioactive decay.

• Five Primary Forms of Radiation:

  1. Alpha Particle ($\alpha$):

     • Composition: 2 protons and 2 neutrons (identical to a Helium-4 nucleus without electrons).

     • Charge: $+2$

     • Mass: $4\,\text{amu}$

     • Notation: ${}^{4}_{2}\text{He}$ or $\alpha$

  2. Beta Particle ($\beta$):

     • Composition: A high-energy electron ejected from the nucleus.

     • Origin: Generated when a nuclear neutron converts into a proton by expelling a negatively charged particle.

     • Charge: $-1$

     • Mass: $0\,\text{amu}$ (negligible electron mass).

     • Notation: ${}^{0}_{-1}\text{e}$ or $\beta$

  3. Gamma Ray ($\gamma$):

     • Composition: Massless high-energy photon of electromagnetic radiation outside the visible spectrum.

     • Charge: $0$

     • Mass: $0\,\text{amu}$

     • Notation: ${}^{0}_{0}\gamma$ or $\gamma$

     • Behavior: Emitted during nuclear decay transitions; carries no mass or electric charge.

  4. Positron:

     • Composition: A positively charged electron-like particle.

     • Origin: Generated when an unstable nuclear proton loses its positive charge and converts into a neutron.

     • Charge: $+1$

     • Mass: $0\,\text{amu}$

     • Notation: ${}^{0}_{1}\text{e}$

     • Behavior: Collides with ambient electrons to undergo annihilation, secondarily producing gamma rays.

  5. Neutron Emission:

     • Composition: A free neutron ejected directly from an unstable nucleus.

     • Charge: $0$

     • Mass: $1\,\text{amu}$

     • Notation: ${}^{1}_{0}\text{n}$

Penetrating Power, Energy, and Damage Potential

• Penetration Capabilities:

  • Alpha Particles:

    • Most massive particles; rapidly impeded by collisions with matter.

    • Lowest penetration depth; blocked by paper or a few outer layers of skin/epithelium.

  • Beta Particles and Positrons:

    • Low mass; capable of penetrating biological tissue and passing through the human body.

    • Stopped by thin metal barriers such as aluminum foil.

  • Gamma Rays:

    • Massless short-wavelength electromagnetic radiation.

    • Extremely high penetration; easily passes through human tissue and aluminum.

    • Requires dense, thick shielding such as solid lead to prevent passage.

  • Neutrons:

    • Unique uncharged particle behavior coupled with high momentum.

    • Most penetrating form of radiation evaluated; requires thick structural shielding such as $30\text{ inch}$ concrete walls (e.g., reactor cooling tanks).

• Biological Tissue Damage Potential:

  • Alpha Particles: Most damaging form of radiation upon tissue contact due to high mass and charge, causing severe localized ionization damage despite low penetration.

  • Beta Particles: Significantly less damaging to tissue per interaction than alpha particles.

  • Gamma Rays: Lower localized damage density than alpha or beta particles, despite high penetration.

  • Neutrons: Least damaging per particle interaction despite having the highest penetration capability.

• X-rays vs. Gamma Rays:

  • X-rays and gamma rays share identical electromagnetic energy and short wavelength characteristics.

  • Key Distinction: Gamma rays originate inside the atomic nucleus via radioactive nuclear decay. X-rays originate outside the nucleus from electron shell energy transitions. Therefore, X-rays are not classified as nuclear radiation.

Radiotherapy and Clinical Applications

• Direct Radioactive Seed Implantation (Lung Cancer Therapy):

  • A bronchoscope places a sealed radioactive source (seed) directly inside a lung tumor.

  • Employs short-range, high-energy emitters (such as alpha emitters).

  • Clinical Advantage: Delivers extreme, localized radiation damage directly into tumor cells while limited penetration prevents damage to surrounding healthy lung tissue or exposure to external individuals.

• Focused External Gamma Radiosurgery (Gamma Knife / Cobalt-60 Helmet):

  • Used for inaccessible tumors, such as brain tumors.

  • Employs arrayed Cobalt-60 radioisotope sources embedded inside a headpiece.

  • Built-in shielding filters out emitted beta particles while permitting gamma rays to pass.

  • Multiple low-dose gamma beams arrayed across $180^{\circ}$ to $360^{\circ}$ converge simultaneously at the precise focal point of the tumor.

  • Clinical Advantage: Focuses a lethal cumulative dose at the tumor site while keeping radiation intensity low through surrounding healthy brain tissue.

Balancing Nuclear Equations

• Fundamental Conservation Rules:

  1. Conservation of Mass Number ($A$): The sum of mass numbers on the reactant side must equal the sum of mass numbers on the product side.

  2. Conservation of Atomic Number ($Z$): The sum of atomic numbers on the reactant side must equal the sum of atomic numbers on the product side.

  3. If the total atomic number changes, the elemental symbol must be updated to match the new atomic number.

• Common Phrasing Formats:

  • "$X$ nucleus decays to produce $Y$"

  • "$X$ nucleus undergoes beta decay to produce $Y$"

  • "$X$ nucleus emits a beta particle resulting in $Y$"

  • "$Y$ absorbs $X$ to become $Z$"

• Demonstration Reactions:

  • Alpha Decay of Radium-224:         ${}^{224}_{88}\text{Ra} \rightarrow {}^{220}_{86}\text{Rn} + {}^{4}_{2}\text{He}$

    • Mass check: $224 = 220 + 4$

    • Atomic number check: $88 = 86 + 2$ (Element 86 = Radon, $\text{Rn}$)

  • Positron Emission of Nitrogen-13:         ${}^{13}_{7}\text{N} \rightarrow {}^{13}_{6}\text{C} + {}^{0}_{1}\text{e}$

    • Mass check: $13 = 13 + 0$

    • Atomic number check: $7 = 6 + 1$ (Element 6 = Carbon, $\text{C}$)

  • Beta Decay of Nitrogen-13:         ${}^{13}_{7}\text{N} \rightarrow {}^{13}_{8}\text{O} + {}^{0}_{-1}\text{e}$

    • Mass check: $13 = 13 + 0$

    • Atomic number check: $7 = 8 + (-1)$ (Element 8 = Oxygen, $\text{O}$)

  • Gamma Emission of Cobalt-60:         ${}^{60}_{27}\text{Co} \rightarrow {}^{60}_{27}\text{Co} + {}^{0}_{0}\gamma$

    • Mass and atomic numbers remain unchanged.

• Step-by-Step Practice Problems:

  • Problem 1: Beta decay of Iodine-129:         ${}^{129}_{53}\text{I} \rightarrow {}^{129}_{Z}\text{X} + {}^{0}_{-1}\text{e}$

    • Mass balance: $A = 129 - 0 = 129$

    • Atomic number balance: $53 = Z + (-1) \Rightarrow Z = 54$

    • Periodic table check: Element 54 = Xenon ($\text{Xe}$).

    • Balanced Equation: ${}^{129}_{53}\text{I} \rightarrow {}^{129}_{54}\text{Xe} + {}^{0}_{-1}\text{e}$

  • Problem 2: Parent nuclide undergoing alpha emission to form Berkelium-239 ($Z = 97$):         ${}^{A}_{Z}\text{X} \rightarrow {}^{239}_{97}\text{Bk} + {}^{4}_{2}\text{He}$

    • Mass balance: $A = 239 + 4 = 243$

    • Atomic number balance: $Z = 97 + 2 = 99$

    • Periodic table check: Element 99 = Einsteinium ($\text{Es}$).

    • Balanced Equation: ${}^{243}_{99}\text{Es} \rightarrow {}^{239}_{97}\text{Bk} + {}^{4}_{2}\text{He}$

  • Problem 3: Decay producing Samarium-146 ($Z = 62$) via alpha decay:         ${}^{A}_{Z}\text{X} \rightarrow {}^{146}_{62}\text{Sm} + {}^{4}_{2}\text{He}$

    • Mass balance: $A = 146 + 4 = 150$

    • Atomic number balance: $Z = 62 + 2 = 64$

    • Periodic table check: Element 64 = Gadolinium ($\text{Gd}$).

    • Balanced Equation: ${}^{150}_{64}\text{Gd} \rightarrow {}^{146}_{62}\text{Sm} + {}^{4}_{2}\text{He}$

  • Problem 4: Alpha decay of Thorium-225 ($Z = 90$):         ${}^{225}_{90}\text{Th} \rightarrow {}^{A}_{Z}\text{X} + {}^{4}_{2}\text{He}$

    • Mass balance: $A = 225 - 4 = 221$

    • Atomic number balance: $Z = 90 - 2 = 88$

    • Periodic table check: Element 88 = Radium ($\text{Ra}$).

    • Balanced Equation: ${}^{225}_{90}\text{Th} \rightarrow {}^{221}_{88}\text{Ra} + {}^{4}_{2}\text{He}$

  • Problem 5: Beta decay of Cesium-137 ($Z = 55$):         ${}^{137}_{55}\text{Cs} \rightarrow {}^{A}_{Z}\text{X} + {}^{0}_{-1}\text{e}$

    • Mass balance: $A = 137$

    • Atomic number balance: $55 = Z - 1 \Rightarrow Z = 56$

    • Periodic table check: Element 56 = Barium ($\text{Ba}$).

    • Balanced Equation: ${}^{137}_{55}\text{Cs} \rightarrow {}^{137}_{56}\text{Ba} + {}^{0}_{-1}\text{e}$

Radiation Units and Half-Life Calculations

• Radioactivity Units:

  • Becquerel (Bq): Fundamental SI unit defined as 1 radioactive emission per second ($1\,\text{Bq} = 1\,\text{decay/s}$). Approximately equals the rate of emission from $1\,\text{g}$ of Radium.

  • Curie (Ci): Standard clinical/scientific unit proportional to the Becquerel.

  • RAD: Unit measuring absorbed radiation dose.

  • Measurement Quantities: Radioisotopes are typically quantified in milligrams ($\text{mg}$), grams ($\text{g}$), micrograms ($\mu\text{g}$), or kilograms ($\text{kg}$) and measured empirically using a Geiger counter.

• Half-Life ($t_{1/2}$):

  • Definition: The time required for exactly $50\%$ ($1/2$) of the radioactive nuclei in a sample to undergo decay into stable product nuclei.

  • Radioactive decay follows a constant, first-order exponential decay rate.

  • General Half-Life Equation:         $N_t = N_0 \times \left(\frac{1}{2}\right)^n = \frac{N_0}{2^n}$         where $N_t$ is remaining activity/mass, $N_0$ is initial activity/mass, and $n$ is the number of half-lives elapsed:         $n = \frac{\text{Total Elapsed Time } (t)}{\text{Half-Life Duration } (t_{1/2})}$

• Cobalt-60 Decay Model Example ($N_0 = 10\,\text{g}$, $t_{1/2} = 5.27\,\text{years}$):

  • 0 Half-Lives ($0\,\text{years}$): $100\%$ remaining = $10\,\text{g}$

  • 1 Half-Life ($5.27\,\text{years}$): $50\%$ remaining = $5\,\text{g}$

  • 2 Half-Lives ($10.54\,\text{years}$): $25\%$ remaining = $2.5\,\text{g}$

  • 3 Half-Lives ($15.81\,\text{years}$): $12.5\%$ remaining = $1.25\,\text{g}$

  • 4 Half-Lives ($21.08\,\text{years}$): $6.25\%$ remaining = $0.625\,\text{g}$

  • 5 Half-Lives ($26.35\,\text{years}$): $3.125\%$ remaining = $0.3125\,\text{g}$

• Quantitative Calculation Examples:

  • Problem 1: Technetium-99m Cardiac Imaging

    • Given: Initial activity $N_0 = 25\,\text{mCi}$, $t_{1/2} = 6\,\text{hours}$, total elapsed time $t = 30\,\text{hours}$.

    • Step 1: Calculate number of elapsed half-lives ($n$):             $n = 30\,\text{hours} \times \frac{1\,\text{half-life}}{6\,\text{hours}} = 5\,\text{half-lives}$

    • Step 2: Calculate remaining activity ($N_t$):             $N_t = \frac{25\,\text{mCi}}{2^5} = \frac{25\,\text{mCi}}{32} = 0.78125\,\text{mCi} \approx 0.78\,\text{mCi}$

  • Problem 2: Non-Integer Half-Life Decay of Phosphorus-32

    • Given: Initial mass $N_0 = 10\,\text{g}$, $t_{1/2} = 10\,\text{days}$, total elapsed time $t = 35\,\text{days}$.

    • Step 1: Calculate number of elapsed half-lives ($n$):             $n = 35\,\text{days} \times \frac{1\,\text{half-life}}{10\,\text{days}} = 3.5\,\text{half-lives}$

    • Step 2: Evaluate the exponential term $2^n$:             $2^{3.5} \approx 11.3137$

    • Step 3: Calculate remaining mass ($N_t$):             $N_t = \frac{10\,\text{g}}{2^{3.5}} = \frac{10\,\text{g}}{11.3137} \approx 0.884\,\text{g}$