Notes on The Structure of the Atom and the Periodic Table

2.1 Composition of the Atom

• Atom: the basic structural unit of an element; the smallest unit that retains the chemical properties of that element.
• Subatomic particles:
  • Protons (p+): positively charged.
  • Neutrons (n): neutral.
  • Electrons (e¯): negatively charged.
• Nucleus:
  • A small, dense, positively charged region at the center of the atom containing protons and neutrons.
  • Protons: positively charged.
  • Neutrons: uncharged.
• Electrons: negatively charged particles located outside the nucleus; move rapidly in a relatively large volume; the nucleus is small and dense.
• Charge balance:
  • A neutral atom has the same number of protons and electrons.
  • Protons and electrons have charges equal in magnitude but opposite in sign.
• Symbolic representation of an element:
  • Let X be the element symbol; Z = atomic number (number of protons);
  • A = mass number = number of protons + number of neutrons = Z + N.
• Atomic calculations:
  • Number of neutrons: $N = A - Z$
  • Number of neutrons (alternative): $N = A - Z$ (same formula different wording)
• Determining the composition of an atom (practice): calculate protons, neutrons, and electrons for given isotopes.
• Isotopes:
  • Atoms of the same element with different masses; same number of protons; different numbers of neutrons.
  • Isotopes have identical chemical properties in many contexts; some isotopes are radioactive.
• Atomic mass and isotopes:
  • Atomic mass is the weighted average of the masses of all naturally occurring isotopes.
  • Example concept: chlorine consists of chlorine-35 and chlorine-37 in a natural ratio; the atomic mass is a weighted average reflecting isotope abundances.
  • Calculation method:
  • Step 1: Convert isotope abundances to decimals: $f_i$.
  • Step 2: Multiply each decimal by its isotope mass: $m_i$.
  • Step 3: Sum contributions: M =
    \sumi fi m_i.
• Dalton’s Atomic Theory (brief): introduction to atomic theory with postulates foundational to later development.

2.2 Development of Atomic Theory

• Dalton’s Atomic Theory (summary):
  1. All matter is composed of atoms.
  2. Atoms cannot be created, divided, destroyed, or converted to other atoms.
  3. Atoms of a given element have identical properties.
  4. Atoms of different elements have different properties.
• Additional postulates (containing the idea of compound formation):
  5. Atoms combine in simple whole-number ratios to form compounds.
  6. Chemical changes involve joining, separating, or rearranging atoms.
• Postulates 1, 4, 5, and 6 are still regarded as true today; postulates about indivisibility and identical properties are refined by later subatomic discoveries.
• Evidence for subatomic particles:
  • Electrons discovered via cathode-ray tube experiments.
  • Protons discovered by Goldhaber (positive charge, same magnitude as electrons, about 1837× heavier than an electron).
  • Neutrons postulated in the 1920s and demonstrated in 1932; nearly the same mass as the proton but zero charge.
• Evidence for the nucleus (Rutherford):
  • Gold foil experiment: most alpha particles passed through; some were deflected; a few were reflected back.
  • Conclusion: atoms are mostly empty space with a tiny, dense, positively charged nucleus containing protons and neutrons; most of the mass is in the nucleus.
• Models of the atom:
  • a) Early model with a positively charged sphere; b) Nucleus-centered model with electrons in surrounding space; electrons reside in mostly empty space surrounding a dense nucleus.

2.3 Light, Atomic Structure, and the Bohr Atom

• Rutherford’s model: a tiny, dense, positively charged nucleus surrounded by electrons; need a way to describe electron positions and energies.
• Spectroscopy and light:
  • Spectroscopy: study of information from absorption or emission of light by atoms; reveals electronic structure.
  • Electromagnetic radiation travels as waves; characterized by wavelength and energy.
• Electromagnetic spectrum (conceptual): high energy corresponds to short wavelength; low energy corresponds to long wavelength.
• Wavelengths and energy:
  • Wavelength concept: $\lambda$ is the distance between identical points on successive waves.
  • Each wavelength has a characteristic energy; relationship to energy and radiation is central to spectroscopy.
• The Bohr atom (historical model):
  • Electrons absorb energy to move to higher energy levels (excited states) and emit energy when relaxing to lower levels.
  • Emission of light is observed as a single wavelength corresponding to the energy difference between levels.
  • Spectral lines arise from electron transitions between allowed energy levels.
• Emission spectra:
  • Emission spectrum: light emitted when a substance is excited.
  • Hydrogen’s emission spectrum contributed to modern understanding of atomic structure.
• Bohr atom characteristics:
  • Electrons occupy fixed energy levels (quantized energy).
  • Energy promotion occurs via absorption; energy release via relaxation.
  • Energy differences can be calculated from the emitted/absorbed photon wavelength.
  • Ground state: lowest energy state.
  • Spectral lines result from transitions between permitted energy levels.
• Limitations of Bohr’s model:
  • Could not explain line spectra for atoms with more than one electron.
  • Modern theory uses atomic orbitals: regions in space with high probability of finding an electron; electrons move rapidly within orbitals.

2.4 The Periodic Law and the Periodic Table

• Periodic Law (Mendeleev and Meyer): properties of elements vary periodically with atomic numbers when elements are arranged in order of increasing atomic number.
• Classification of the elements:
  • Period: horizontal row; known lengths: 2, 8, 8, 18, 18, 32, 32 elements.
  • Group (family): vertical column; elements in a group share many similarities.
• Periodic table structure:
  • Metals: tend to lose electrons in chemical changes; located mainly on the left side.
  • Nonmetals: tend to gain electrons in chemical changes; located on the right side.
  • Metalloids: properties intermediate between metals and nonmetals.
• Information contained in the periodic table:
  • Atomic number (Z), symbol, name, and atomic mass.
  • Example layout shows Ca with 40.078 amu, etc. (illustrative)
• Atomic number and atomic mass definitions:
  • Atomic number: the number of protons in the nucleus; reflects nuclear charge.
  • Atomic mass: weighted average of the masses of all naturally occurring isotopes of an element.

2.5 Electron Arrangement and the Periodic Table

• Electron arrangement is key to understanding bonding and compound formation.
• Electron configuration: arrangement of electrons in atomic orbitals.
• Quantum mechanical atom: Schrödinger’s equations describe electrons in terms of probabilities, not fixed orbits.
• Sublevels and orbitals:
  • Principal energy levels: denoted by n (n = 1, 2, 3, …).
  • Each energy level can have one or more sublevels (subshells): s, p, d, f.
  • Each sublevel contains one or more atomic orbitals.
• Sublevel energy order: s < p < d < f
• Principal energy levels and sublevels:
  • n = 1: 1s
  • n = 2: 2s, 2p
  • n = 3: 3s, 3p, 3d
  • n = 4: 4s, 4p, 4d, 4f
• Orbitals:
  • An Atomic Orbital is a region within a sublevel that can hold a maximum of two electrons.
  • Orbital naming: 1s, 2s, 2p, 3s, 3p, etc.
  • Orbital shapes: s is spherically symmetrical; p has a dumbbell shape.
• Sublevels and orbitals per level:
  • Sublevel counts per n: 1s; 2s, 2p; 3s, 3p, 3d; 4s, 4p, 4d, 4f.
  • Number of orbitals in a subshell: s → 1; p → 3; d → 5; f → 7.
  • Maximum electrons per subshell: s → 2; p → 6; d → 10; f → 14.
• Electron configuration rules:
  • Aufbau Principle: electrons fill the lowest-energy orbitals available first.
  • In energy ordering, s < p < d < f.
  • Pauli Exclusion Principle: each orbital holds up to two electrons with opposite spins.
  • Hund’s Rule: within a subshell, electrons fill degenerate orbitals singly before pairing.
• Writing configurations:
  • Determine total electrons from atomic number.
  • Fill orbitals starting from 1s, following the order shown by the Aufbau diagram.
  • Use superscripts to denote electron count in each orbital (e.g., 1s^2 2s^2 2p^6 for Ne).
• Shorthand (noble-gas) configurations:
  • Use [NobleGas] to represent the core electrons and then add valence electrons: e.g., Na = [Ne] 3s^1.
  • The noble gas before Na is neon (Ne).
• Examples of shorthand configurations: Be, N, Na, Cl, Ag (illustrative sequences provided in slides).

2.6 Valence Electrons and the Octet Rule

• Valence electrons: outermost electrons involved in bonding.
• Noble gases are highly stable because of a complete valence shell (full s and p sublevels).
• Octet rule: atoms tend to attain the electron configuration of the nearest noble gas by gaining, losing, or sharing electrons.
• Consequences for bonding:
  • Elements on the right tend to move toward the next noble gas (gain electrons).
  • Elements on the left tend to move toward the previous noble gas (lose electrons).
• Ions:
  • Cations: positively charged ions formed by loss of electrons, resulting in a configuration like the nearest noble gas.
  • Anions: negatively charged ions formed by gain of electrons, achieving the nearest noble gas configuration.
• Isoelectronic species: ions or atoms with the same number of electrons.
• Examples of common ion charges (predictable via the Octet Rule):
  • Ca, Sr → typically form Ca^{2+}, Sr^{2+}; S → S^{2-}; P → P^{3-} (illustrative representative-element charges).
• Transition metals: often form more than one stable ion; simple octet-rule predictions are less reliable for these elements.
• Applications:
  • Use the Octet Rule to predict possible charges and electron configurations in simple ionic compounds.
  • Determine which species are isoelectronic by counting electrons.

2.7 Trends in the Periodic Table

• Atomic size (atomic radius) trends:

  • Increases moving down a group (valence shell deeper, farther from nucleus).
  • Decreases across a period (increasing nuclear charge pulls electrons closer).

• Influence of nuclear charge and shielding on size.

• Ion size trends:

  • Cations are smaller than their parent atoms because of reduced electron-electron repulsion and effective nuclear charge.
  • Anions are larger than their parent atoms because added electrons increase repulsion and reduce effective nuclear attraction.
  • Ions with higher positive charges are smaller; isoelectronic ions vary in size depending on nuclear charge.

• Ionization energy:

  • Energy required to remove an electron from an isolated atom.
  • Trend: ionization energy generally decreases down a group (outer electrons farther from the nucleus and more shielded).
  • Trend: ionization energy generally increases across a period (outer electrons held more tightly by higher nuclear charge).

• Electron affinity:

  • Energy released when a single electron is added to an isolated atom.
  • Large electron affinity indicates a tendency to form anions and gain electrons.
  • Trend: electron affinity generally decreases down a group and generally increases across a period (though there are exceptions).

• Relevance and connections:

  • Trends help predict reactivity, bonding, and compound formation.
  • Periodic classification (groups and periods) maps to electronic structure and observed chemical behavior.

• Quick recap of key quantitative ideas:

  • Maximum electrons in a principal energy level: $2n^2$.
  • Number of orbitals in a subshell: $s\to 1,\ p\to 3,\ d\to 5,\ f\to 7$.
  • Maximum electrons per subshell: $2,\ 6,\ 10,\ 14$ for $s,\ p,\ d,\ f$ respectively.
  • Atomic size and shielding concepts relate to group and period positions.

• Connections to real-world chemistry:

  • Electron configuration explains bonding patterns, chemical reactivity, and properties like conductivity and ion formation.
  • Periodic trends underpin the design of materials, catalysis, and understanding of elements’ roles in compounds.

• Notes on numerical references and typical values (for reference only):

  • Proton mass: $m<em>p \approx 1.0073\ \text{amu} \quad\text{or}\quad m</em>p \approx 1.6726\times 10^{-24}\ \text{g}$
  • Neutron mass: $m<em>n \approx 1.0087\ \text{amu} \quad\text{or}\quad m</em>n \approx 1.6749\times 10^{-24}\ \text{g}$
  • Electron mass: $m<em>e \approx 5.4858\times 10^{-4}\ \text{amu} \quad\text{or}\quad m</em>e \approx 9.1094\times 10^{-28}\ \text{g}$
  • Atomic number: $Z =\text{number of protons}$
  • Mass number: $A = Z + N$
  • Number of neutrons: $N = A - Z$
  • Energy of a photon: $\Delta E = \frac{h c}{\lambda}$
  • Principal energy level capacity: $2n^2$
  • Sublevel ordering: s < p < d < f
  • Orbitals per subshell: $s:1,\ p:3,\ d:5,\ f:7$
  • Maximum electrons per subshell: $s:2,\ p:6,\ d:10,\ f:14$
  • Electron configurations use the Aufbau principle, Pauli exclusion, and Hund’s rule.