Notes on the Structure of the Atom

Historical Development of Atomic Theory

• The concept of the atom evolved through key scientific discoveries over time, transitioning from early philosophical ideas to modern quantum mechanical energy levels.

Democritus

• Proposed the origin of atomic theory approximately $2000$ years ago in ancient Greece.

• Believed that all matter consisted of extremely small, indivisible particles.

• Named these fundamental particles atoms, derived from the original Greek word atomos (meaning uncuttable or indivisible).

• Main limitation: Lacked experimental evidence, empirical data, or scientific tools to support his hypothesis.

John Dalton

• Revisited the atomic model in the early $19\text{th}$ century and built upon Democritus's foundational concept.

• Key Postulates of Dalton's Atomic Theory:

  • Proposed that atoms could not be divided into smaller pieces.

  • Stated that all atoms of a particular element are exactly identical in mass and properties.

  • Stated that atoms of different elements combine in fixed ratios to form compounds (e.g., $\text{Iron} + \text{Sulfur} \rightarrow \text{Iron sulfide}$).

• Model Name: His structure became known as the Billiard Ball Model, visualizing atoms as solid, uniform spheres.

J.J. Thomson

• Conducted experiments using the Cathode Ray Tube.

• Experimental Observation: The radiation beam deflected toward the positively charged plate, demonstrating that the particles in the beam possessed a negative electrical charge.

• Primary Discovery: Discovered the electron (the first recognized subatomic particle).

• Model Name: Proposed the Plum Pudding Model.

  • Visualized the atom as a sphere of diffuse positive charge with negatively charged electrons embedded evenly throughout, analogous to raisins or plums inside a plum pudding dessert.

Ernest Rutherford

• Conducted the famous Gold Foil Experiment alongside his university students.

• Experimental Procedure: Aimed a stream of positively charged alpha particles at an extremely thin sheet of gold foil.

• Experimental Observations:

  • Most alpha particles passed straight through the foil unaffected.

  • Approximately $1$ in every $8000$ alpha particles deflected backward at sharp angles or directly back toward the source.

• Scientific Deduction: The backward deflection indicated that the positively charged alpha particles were bouncing off a dense, highly concentrated, positively charged center.

• Primary Discovery: Discovered the atomic nucleus.

• Model Name: Led directly to the Planetary Model of the atom, where electrons orbit a small, dense positive center.

Niels Bohr

• Refined Rutherford's planetary representation to create the foundational model used in introductory chemistry.

• Proposed that electrons do not orbit randomly around the nucleus like planets orbiting the sun.

• Discovered that electrons exist only within specific, quantized regions termed energy levels (or electron shells).

• Model Name: The Bohr Model of the atom.

Atomic Structure and Subatomic Particles

• Atoms consist of three primary subatomic particles: protons, neutrons, and electrons.

Protons

• Symbol: $p^+$

• Charge: Positive ($+1$)

• Location: Inside the central nucleus.

• Relative Mass: Approximate mass of $1\text{ amu}$; contributes directly to the total atomic mass.

Neutrons

• Symbol: $n^0$

• Charge: Neutral ($0$ / no charge)

• Location: Inside the central nucleus.

• Relative Mass: Approximate mass of $1\text{ amu}$; contributes directly to the total atomic mass.

Electrons

• Symbol: $e^-$

• Charge: Negative ($-1$)

• Location: Reside outside the nucleus in defined energy levels.

• Relative Mass: Extremely small, approximately $\frac{1}{2000}\text{th}$ the mass of a proton or neutron ($\text{mass} \rightarrow 0\text{ amu}$).

• Because of their minute size, electrons do not contribute to the overall mass calculation of an atom.

Electrical Neutrality of Atoms

• Atoms in their baseline, ground state are electrically neutral.

• Electrical neutrality requires a perfect balance of positive and negative charges:   $\text{Number of protons} = \text{Number of electrons}$

Atomic Identification and Calculations

• Atomic Number:

  • The unique identification number assigned to each element on the periodic table.

  • Defined strictly by the number of protons contained in the nucleus:     $\text{Atomic Number} = \text{Number of protons}$

• Mass Number / Atomic Mass:

  • Defined as the total sum of protons and neutrons located within the nucleus:     $\text{Mass Number} = \text{Number of protons} + \text{Number of neutrons}$

  • To calculate the number of neutrons in an atom:     $\text{Number of neutrons} = \text{Mass Number} - \text{Atomic Number}$

• Decimal Rounding Rule:

  • Periodic tables display average atomic masses that frequently contain decimals.

  • When calculating specific subatomic particle counts, round the given atomic mass to the nearest whole integer to find the mass number.

Standard Element Notation

• Elements are represented symbolically using standard nuclear notation:   $\mathbf{^{mass}_{Atomic\,Number}X}$

• Example notations:

  • Cadmium ($\text{Cd}$): Atomic Number = $48$, Mass Number = $112.41$ (rounds to $112$).

  • Protons ($p^+$): $48$

  • Neutrons ($n^0$): $112 - 48 = 64$

  • Electrons ($e^-$): $48$

  • Neon ($\text{Ne}$): Atomic Number = $10$, Mass Number = $20.1797$ (rounds to $20$).

  • Protons ($p^+$): $10$

  • Neutrons ($n^0$): $20 - 10 = 10$

  • Electrons ($e^-$): $10$

  • Germanium ($\text{Ge}$): Atomic Number = $32$, Mass Number = $74$.

  • Protons ($p^+$): $32$

  • Neutrons ($n^0$): $74 - 32 = 42$

  • Electrons ($e^-$): $32$

  • Sodium ($\text{Na}$): Atomic Number = $11$, Mass Number = $22.990$ (rounds to $23$).

  • Protons ($p^+$): $11$

  • Neutrons ($n^0$): $23 - 11 = 12$

  • Electrons ($e^-$): $11$

  • Magnesium ($\text{Mg}$): Atomic Number = $12$, Mass Number = $24.305$ (rounds to $24$).

  • Protons ($p^+$): $12$

  • Neutrons ($n^0$): $24 - 12 = 12$

  • Electrons ($e^-$): $12$

Constructing Bohr Models

• Bohr models visually depict the arrangement of protons, neutrons, and electrons within an atom.

Steps for Drawing a Bohr Model

1. Draw a central circle to represent the nucleus. Label the exact quantities of protons and neutrons inside using the notation $p^+$ and $n^0$.

2. Draw concentric rings around the central nucleus as needed to represent energy levels. Add dots onto these rings to represent electrons ($e^-$).

3. Apply electron distribution constraints per energy level:

   • $1\text{st}$ energy level (innermost): Holds a maximum of $2e^-$

   • $2\text{nd}$ energy level: Holds a maximum of $8e^-$

   • $3\text{rd}$ energy level: Holds a maximum of $8e^-$

4. School Bus Rule:

   • Electrons populate open energy levels like passengers boarding a bus.

   • Each electron fills an empty single position ("seat") around the energy level ring before double-pairing with another electron.

   • Electrons pair up only when no vacant single positions remain on that specific energy level.

Isotopes

• Definition: Isotopes are atoms of the same element that possess the exact same number of protons (same atomic number) but differ in their total number of neutrons.

Properties and Impact on Atomic Mass

• Because neutrons contribute significant mass ($1\text{ amu}$ each) without affecting electrical charge, changing the neutron count changes the total mass of the atom.

• Isotopes explain why atomic mass values listed on the periodic table are decimals: the listed value represents a weighted average of all naturally occurring isotopes of that element.

Naming and Notation Standards

• Symbol-Mass Format: Written as Element-Mass Number (e.g., $\text{Oxygen-17}$ or $\text{Carbon-14}$).

• Mass-Symbol Format: Written as Mass Number-Symbol (e.g., $17\text{-oxygen}$).

• Isotope Examples:

  • Carbon Isotopes:

  • $\text{Carbon-12}$ ($\text{C-12}$): $6\text{ protons}$, $6\text{ neutrons}$, Mass Number = $12$

  • $\text{Carbon-13}$ ($\text{C-13}$): $6\text{ protons}$, $7\text{ neutrons}$, Mass Number = $13$

  • $\text{Carbon-14}$ ($\text{C-14}$): $6\text{ protons}$, $8\text{ neutrons}$, Mass Number = $14$

  • Hydrogen Isotopes:

  • $\text{Hydrogen-1}$ (Protium): $1\text{ proton}$, $0\text{ neutrons}$, Mass Number = $1$

  • $\text{Hydrogen-2}$ (Deuterium): $1\text{ proton}$, $1\text{ neutron}$, Mass Number = $2$

  • $\text{Hydrogen-3}$ (Tritium): $1\text{ proton}$, $2\text{ neutrons}$, Mass Number = $3$

Ions

• Definition: An ion is formed when a neutral atom either gains or loses one or more valence electrons, creating an imbalance between protons and electrons and producing a net electrical charge.

Categorization of Ions

• Cation:

  • Formed when an atom loses one or more electrons.

  • Results in more positive protons than negative electrons.

  • Holds an overall positive charge ($+$).

  • Mnemonic: "Cats have paws -> Cations are paws-itive."

• Anion:

  • Formed when an atom gains one or more electrons.

  • Results in more negative electrons than positive protons.

  • Holds an overall negative charge ($-$).

  • Mnemonic: "Anion looks like onion -> Ogres have layers like onions -> Anions are A-Negative-Ion."

Ion Charge Calculations

• Magnesium ($\text{Mg}$) loses $1$ electron:

  • Protons = $12$, Electrons = $11$

  • Calculated Charge: $12 - 11 = +1$

  • Resulting Ion: $\text{Mg}^{+1}$ (Cation)

• Oxygen ($\text{O}$) gains $2$ electrons:

  • Protons = $8$, Electrons = $10$

  • Calculated Charge: $8 - 10 = -2$

  • Resulting Ion: $\text{O}^{-2}$ (Anion)

• Nitrogen ($\text{N}$) gains $3$ electrons:

  • Protons = $7$, Electrons = $10$

  • Calculated Charge: $7 - 10 = -3$

  • Resulting Ion: $\text{N}^{-3}$ (Anion)

• Sodium ($\text{Na}$) loses $1$ electron:

  • Protons = $11$, Electrons = $10$

  • Calculated Charge: $11 - 10 = +1$

  • Resulting Ion: $\text{Na}^{+1}$ (Cation)

Comprehensive Practice Problems

Carbon ($\text{C}$)

• Atomic Number: $6$

• Number of Protons: $6$

• Number of Neutrons: $6$

• Atomic Mass: $12\text{ amu}$

• Number of Electrons: $6$

• Isotope Scenario: If an atom of Carbon has $3$ extra neutrons, its new mass number is $12 + 3 = 15$ ($\text{Carbon-15}$).

• Ion Scenario: If Carbon gains $3$ electrons, its resulting charge is $6 - 9 = -3$ ($\text{C}^{-3}$ Anion).

Nitrogen ($\text{N}$)

• Atomic Number: $7$

• Number of Protons: $7$

• Number of Neutrons: $7$

• Atomic Mass: $14\text{ amu}$

• Number of Electrons: $7$

• Ion Scenario: If Nitrogen loses $2$ electrons, its resulting charge is $7 - 5 = +2$ ($\text{N}^{+2}$ Cation).

• Isotope Scenario: If Nitrogen has $4$ extra neutrons, its new mass number is $14 + 4 = 18$ ($\text{Nitrogen-18}$).

Aluminum ($\text{Al}$)

• Atomic Number: $13$

• Number of Protons: $13$

• Number of Neutrons: $14$ ($27 - 13 = 14$

• Atomic Mass: $27\text{ amu}$ (rounded from $26.98\text{ amu}$)

• Number of Electrons: $13$

• Electron Shell Configuration: $1s^2 2s^2 2p^6 3s^2 3p^1$

• Isotope Scenario: If Aluminum has $2$ extra neutrons, its new mass number is $27 + 2 = 29$ ($\text{Aluminum-29}$).

• Ion Scenario: If Aluminum gains $2$ electrons, its resulting charge is $13 - 15 = -2$ ($\text{Al}^{-2}$ Anion).

Sulfur ($\text{S}$)

• Atomic Number: $16$

• Number of Protons: $16$

• Number of Neutrons: $16$ ($32 - 16 = 16$

• Atomic Mass: $32\text{ amu}$ (rounded from $32.06\text{ amu}$)

• Number of Electrons: $16$

• Ion Scenario: If Sulfur gains $2$ electrons, its resulting charge is $16 - 18 = -2$ ($\text{S}^{-2}$ Anion).

• Isotope Scenario: If Sulfur has $1$ extra neutron, its new mass number is $32 + 1 = 33$ ($\text{Sulfur-33}$).