JC

Electron Arrangement and Periodic Trends

Electron Arrangement and Quantum Numbers

  • Electrons as Waves: Edwin Schrödinger, a mathematician and physicist, discovered that electrons behave more like waves than particles.
    • He developed the concept of a wave function (derived from the complex Schrödinger equation though not shown here) to describe the organization of electrons around the nucleus within the electron cloud.
  • Orbitals: Schrödinger's wave function disproved the Bohr model's idea of electrons existing in set, circular orbits.
    • Instead, electrons are found in orbitals, which are regions of space surrounding the nucleus, not circular paths.
    • Orbitals represent the highest region of probability of finding an electron at a particular point in 3D space, acting like a 3D density map.

Quantum Numbers

  • Definition: Orbitals are characterized by a series of numbers and letters called quantum numbers.
    • A set of four quantum numbers provides the relative position of an electron in an atom at any given time.
    • Each electron in an atom has a unique set of four quantum numbers (Pauli Exclusion Principle).
  • Four Quantum Numbers: To designate an electron's position, all four quantum numbers are required.
    1. Principal Quantum Number (n):
      • Designated by the letter n.
      • Defines the shell in which a particular orbital is found.
      • Values are positive integers (1, 2, 3, ext{etc.}).
      • Each shell (n=1, n=2, ext{etc.}) has different energies and sizes.
        • Smaller n values correspond to smaller shells, lower energy, and fewer possible electrons.
        • Larger n values correspond to larger shells, higher energy, and more possible electrons.
      • All subsequent quantum numbers' possible values are derived from the principal quantum number. Always start with n.
    2. Secondary Quantum Number (l):
      • Designated by a cursive-looking l (formally called the azimuthal quantum number).
      • Indexes energy differences between orbitals within the same shell.
      • Determines the shape of the orbital (also called subshell).
      • Values are integers ranging from 0 up to (n-1).
        • Example: If n=2, possible l values are 0 and (2-1)=1. So, l=0 or l=1.
      • Letter Designations for Shapes:
        • l=0: s orbital (sphere shape)
        • l=1: p orbital (figure 8 or dumbbell shape)
        • l=2: d orbital (more complex shapes)
        • l=3: f orbital (even more complex shapes)
    3. Magnetic Quantum Number (m_l):
      • Designated by ml. (The full notation is actually ml)
      • Determines the number of orbitals available for electrons within a subshell.
      • Values are integers ranging from -l to +l (including zero).
        • Example: If l=1, possible m_l values are -1, 0, +1. This indicates three orbitals.
        • If l=0, possible m_l value is 0. This indicates one orbital.
    4. Spin Quantum Number (m_s):
      • Designated by m_s.
      • Indicates the direction of spin of an electron.
      • Values can only be +1/2 or -1/2.
      • This quantum number arises from the Pauli Exclusion Principle.

Pauli Exclusion Principle

  • Principle Statement: No two electrons in the same atom can have the exact same set of all four quantum numbers (n, l, ml, ms).
  • Electron Capacity of Orbitals: Each orbital can hold a maximum of two electrons.
    • If two electrons occupy the same orbital (meaning they have the same n, l, m_l values), they must have opposite spins.
    • One electron will have ms = +1/2 (e.g., spin up), and the other will have ms = -1/2 (e.g., spin down).
  • Orbital Electron Capacities (derived from l and m_l values):
    • s subshell (l=0): 1 orbital (m_l=0) imes 2 electrons/orbital = 2 electrons maximum.
    • p subshell (l=1): 3 orbitals (m_l=-1, 0, +1) imes 2 electrons/orbital = 6 electrons maximum.
    • d subshell (l=2): 5 orbitals (m_l=-2, -1, 0, +1, +2) imes 2 electrons/orbital = 10 electrons maximum.
    • f subshell (l=3): 7 orbitals (m_l=-3, -2, -1, 0, +1, +2, +3) imes 2 electrons/orbital = 14 electrons maximum.

Electron Configurations

  • Definition: Electron configurations and orbital diagrams describe how electrons are distributed among the various orbitals within an atom.
  • Ground State: The most stable arrangement of electrons, where electrons occupy the lowest energy subshells/orbitals possible.
  • Aufbau Principle: For elements with many electrons, the ground state electron configuration is determined by filling orbitals from the lowest energy level upwards.
    • The filling order (e.g., 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, ext{etc.}) can be visualized with a diagram of energy levels and subshells, following diagonal arrows.
  • Notation: An electron configuration is written as: (n) ( ext{orbital type})^{ ext{number of electrons}} (e.g., 1s^2).
  • Periodic Table Method: The periodic table is organized to directly reflect the Aufbau Principle and electron configurations.
    • Blocks: The table is divided into s-, p-, d-, and f-blocks, corresponding to the subshell receiving the last electron.
      • s-block: Groups 1 and 2 (and Helium).
      • p-block: Groups 13-18 (excluding Helium).
      • d-block: Groups 3-12 (transition metals).
      • f-block: Lanthanides and Actinides (usually placed below the main table).
    • Periods (n value): Each horizontal row (period) number corresponds to the principal quantum number (n) for the s and p blocks.
      • For the d-block, the n value is the period number minus 1 (e.g., 4^{th} period d-block is 3d).
      • For the f-block, the n value is the period number minus 2 (e.g., 6^{th} period f-block is 4f).
    • Number of Electrons: Counting elements across a block in a given period gives the number of electrons in that subshell.
      • s-block is 2 elements wide (2 electrons).
      • p-block is 6 elements wide (6 electrons).
      • d-block is 10 elements wide (10 electrons).
      • f-block is 14 elements wide (14 electrons).
  • Steps to Write Full Electron Configurations using the Periodic Table:
    1. Locate the element on the periodic table.
    2. Start at Hydrogen (1s^1) and move across the periods, filling subshells in order.
    3. For each subshell, write its designation (ns, np, (n-1)d, (n-2)f) and the number of electrons as a superscript (equal to the number of elements counted in that subshell for that period).
    4. Stop when the element is reached.
    5. Self-check: The sum of superscripts (electrons) must equal the atomic number (for a neutral atom).
  • Examples:
    • Hydrogen (H, Z=1): 1s^1
    • Helium (He, Z=2): 1s^2
    • Nitrogen (N, Z=7): 1s^2 2s^2 2p^3
    • Calcium (Ca, Z=20): 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2
    • Chlorine (Cl, Z=17): 1s^2 2s^2 2p^6 3s^2 3p^5
    • Vanadium (V, Z=23): 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^3
  • Homework Question 3: Provide the complete electron configuration for Phosphorus (P) and Titanium (Ti).

Noble Gas Configurations (Abbreviated Electron Configurations)

  • Purpose: To shorten long electron configurations, especially for heavier elements.
  • Method: Utilize the electron configuration of the closest previous noble gas.
    1. Identify the element.
    2. Locate the noble gas in the period before the element's period.
    3. Place the noble gas symbol in square brackets (e.g., [Ne]). This core represents the filled electrons up to that noble gas.
    4. Write the remaining electron configuration for the subshells after that noble gas, up to the element.
  • Valence Electrons: The electrons written after the noble gas core are called valence electrons. These are the outermost electrons and determine the element's chemical reactivity.
  • Example: Sulfur (S, Z=16):
    • Previous noble gas is Neon (Ne, Z=10).
    • Neon's configuration: 1s^2 2s^2 2p^6
    • Sulfur's full configuration: 1s^2 2s^2 2p^6 3s^2 3p^4
    • Sulfur's noble gas configuration: [Ne] 3s^2 3p^4 (The 3s^2 3p^4 are the valence electrons).

Exceptions to Electron Configurations (Chromium and Copper)

  • Reason: These elements (and others in their groups) exhibit electron configurations that lead to more energetically stable half-filled or completely filled d subshells.
  • Chromium (Cr, Z=24):
    • Expected: [Ar] 4s^2 3d^4
    • Actual: [Ar] 4s^1 3d^5
    • Explanation: One electron from the 4s subshell moves to the 3d subshell, resulting in a half-filled 3d^5 subshell. A half-filled d subshell (one electron in each of the five d orbitals) is more energetically stable than a d^4 subshell with an empty orbital.
  • Copper (Cu, Z=29):
    • Expected: [Ar] 4s^2 3d^9
    • Actual: [Ar] 4s^1 3d^{10}
    • Explanation: One electron from the 4s subshell moves to the 3d subshell, resulting in a fully filled 3d^{10} subshell. A completely filled d subshell is highly energetically stable.
  • Other Elements: Similar exceptions occur for other elements in their respective groups, such as Molybdenum (Mo, Z=42) and Silver (Ag, Z=47).

Periodic Table Organization and Trends

  • Organization: The periodic table is a chart displaying elements with similar chemical properties in vertical columns (groups) and horizontal rows (periods).
    • Elements are primarily arranged by increasing atomic number (and atomic mass).
  • Element Classifications:
    • Main Group Elements: Elements in columns 1A - 8A (or 1, 2, 13-18).
    • Transition Elements: Elements in columns 3B - 12B (or 3-12 - the d-block).
    • Lanthanides and Actinides: The f-block elements usually shown below the main table; often radioactive and unstable.
  • Special Group Names:
    • Alkali Metals: Group 1A (1).
    • Alkaline Earth Metals: Group 2A (2).
    • Halogens: Group 7A (17).
    • Noble Gases: Group 8A (18).
  • Metals, Nonmetals, and Metalloids:
    • Metals: To the left of the stair-step line.
      • Properties: Shiny solids, good conductors of electricity and heat, ductile, malleable.
    • Nonmetals: To the right of the stair-step line.
      • Properties: Dull appearance, brittle, poor conductors (good insulators).
    • Metalloids: Elements along the stair-step line (e.g., Boron, Silicon, Germanium, Arsenic, Antimony, Tellurium).
      • Properties: Exhibit properties intermediate between metals and nonmetals.
      • Example: Silicon is widely used as a semiconductor.

Periodic Trends (Main Group Elements Only)

  • Periodicity: Elements with similar properties occur at regular intervals; electron arrangement dictates chemical properties, not just mass.
  • Disclaimer: These trends primarily apply to main group elements. Transition metals (d-block) often do not follow these trends due to the complexities of their d-orbitals.

1. Valence Electrons

  • Definition: Electrons in the outermost energy level (n) of an atom, critical for chemical reactions and bonding.
  • Trend: The group number (using the A-group designation, e.g., 1A through 8A) directly correlates to the number of valence electrons.
    • Group 1A: 1 valence electron.
    • Group 2A: 2 valence electrons.
    • Group 3A: 3 valence electrons, etc., up to Group 8A with 8 valence electrons.

2. Atomic Radius

  • Definition: The size of an atom.
  • Trend Down a Group (Vertical):
    • Increases: As you move down a group, n (principal quantum number) increases, meaning electrons occupy shells further from the nucleus, leading to larger atomic sizes.
    • More electron shells mean more electron-electron repulsions, contributing to larger size.
  • Trend Across a Period (Horizontal, Left to Right):
    • Decreases: As you move across a period, the effective nuclear charge (interaction between the nucleus and valence electrons) increases.
    • The increasing positive charge of the nucleus attracts the electrons more strongly, pulling them closer and resulting in a smaller atomic size.
  • Overall Trend: Smallest elements are at the top right of the periodic table; largest are at the bottom left.

3. Ionization Energy (IE)

  • Definition: The energy required to remove an electron from a neutral atom to form a positively charged cation.
  • Process: Always remove the outermost (valence) electrons, as they are furthest from the nucleus and least tightly held.
  • Resulting Cation: A cation will be smaller than its neutral atom because electron repulsion decreases, and the remaining electrons are pulled closer by the same number of protons.
  • Trend: Lower ionization energy means electrons are easier to remove.
    • Decreases Down a Group: Valence electrons are further from the nucleus and experience more shielding, making them easier to remove.
    • Increases Across a Period: Effective nuclear charge increases, holding valence electrons more tightly, making them harder to remove.
  • Metals vs. Nonmetals: Metals generally have low ionization energies because they readily lose electrons.

4. Electron Affinity (EA)

  • Definition: The energy change that occurs when an electron is added to a neutral atom to form a negatively charged anion.
    • Larger (more negative) EA values indicate a greater tendency for an atom to gain an electron and a more stable anion.
  • Trend: Generally, electron affinity becomes more negative (favorable) across a period and less negative (less favorable) down a group.
  • Nonmetals vs. Metals:
    • Nonmetals: Tend to have large, negative electron affinities.
      • This is especially true for halogens like Fluorine (1s^2 2s^2 2p^5), which can gain one electron to achieve a stable, noble gas configuration (1s^2 2s^2 2p^6).
    • Metals: Tend to have positive or less negative electron affinities.
      • It typically requires energy to add an electron to a metal's valence shell.
  • Summary: Metals readily lose electrons (low IE); nonmetals readily gain electrons (high/negative EA).