Electron Configuration - Lesson 3 Notes

Ground-State Electron Configuration

• Definition: The arrangement of electrons in an atom is called the atom's electron configuration.
• Stability principle: Low-energy systems are more stable; electrons tend to the arrangement with the lowest energy. The most stable arrangement is the ground-state electron configuration.
• Governing rules (principles): aufbau principle, Pauli exclusion principle, and Hund's rule.

The Aufbau Principle

• Statement: Each electron occupies the lowest energy orbital available.
• Practical step: Determine the order of atomic orbitals from lowest energy to highest energy using an aufbau diagram.
• Aufbau diagram:
  • In the diagram, each box represents an atomic orbital.
  • Orbital filling sequence (increasing energy):
    $6d \, 5f \, 7s \, 6p \, 5d \, 4f \, 6s \, 5p \, 4d \, 5s \, 4p \, 3d \, 4s \, 3p \, 3s \, 2p \, 2s$
  • Example question: Determine which sublevel has the greater energy, 4d or 5p?
  • Answer based on the sequence: 5p comes before 4d, so 4d has the greater energy than 5p.
• Important caveat: Atoms are not built up electron by electron in a literal, step-by-step fashion; the principle guides the overall filling order.

The Pauli Exclusion Principle

• Core idea: A maximum of two electrons can occupy a single atomic orbital, and only if the electrons have opposite spins.
• Visualization: Electrons in orbitals can be represented by arrows in boxes:
  • An upward arrow = electron spin in one direction
  • A downward arrow = electron spin in the opposite direction
  • Empty box = unoccupied orbital
  • One arrow (up or down) = orbital with one electron
  • Both arrows (↑ and ↓) = filled orbital with a pair of electrons of opposite spins
• Significance: Sets the maximum occupancy per orbital and dictates how electrons pair up in sublevels.

Hund's Rule

• Core idea: When electrons occupy equal-energy orbitals, they will fill each orbital singly with the same spin before any pairing occurs.
• Consequence: For equal-energy orbitals, single electrons fill first, one per orbital, before pairing.
• Example shown: Filling the three 2p orbitals with six electrons results in one electron in each of the three 2p orbitals before any pairing occurs.

Features of the Aufbau Diagram (Table 3)

• Key features:
  • All orbitals related to an energy sublevel are of equal energy.
  • In a multi-electron atom, the energy sublevels within a principal energy level have different energies.
  • In order of increasing energy, the sequence of energy sublevels within a principal energy level is: $s, p, d, f.$ For example, if $n=4$, the sequence is 4s
    ightarrow 4p
    ightarrow 4d
    ightarrow 4f.
  • Orbitals related to energy sublevels within one principal energy level can overlap orbitals related to energy sublevels within another principal level (e.g., 4s can be lower in energy than 3d).
• Examples from Table 3:
  • All three 2p orbitals are of equal energy.
  • The three 2p orbitals are of higher energy than the 2s orbital.
  • If $n=4$, the sequence is 4s, 4p, 4d, 4f.
  • The 4s orbital is lower in energy than the five 3d orbitals.

Electron Configuration Methods

Electron Arrangement Overview

• Two common methods to represent electron configurations:
  • Orbital diagrams (arrows in boxes)
  • Electron configuration notation (superscripts indicate electron counts in orbitals)

Orbital Diagrams

• Concept: Arrows in boxes labeled by principal quantum number and sublevel (e.g., 1s, 2s, 2p, etc.).
• Example: Ground-state carbon
  • 1s: two electrons
  • 2s: two electrons
  • 2p: one electron in each of two of the three 2p orbitals; the third 2p orbital is empty
• Neon example (overlap of orbitals): 1s, 2s, 2p orbitals shown overlapping for neon
• Sodium example: first ten electrons fill 1s, 2s, 2p; the eleventh electron goes into 3s
• Electron configuration notation for the same atoms is written succinctly (see below).

Electron Configuration Notation

• Definition: Notation designates the principal energy level and sublevel for each orbital and uses superscripts for electron count in that orbital.
• Example: Ground-state carbon configuration is written as
  • $1s^2\ 2s^2\ 2p^2$
• This notation implicitly implies the orbital distribution; e.g., for nitrogen, a common shorthand is $1s^2\ 2s^2\ 2p^3$ (the 2p subshell has three electrons distributed among its three degenerate orbitals as per Hund’s rule).
• Period-1 and Period-2 electron configurations (Table 4) illustrate the fill order for the first two periods.

Noble-Gas Notation

• Concept: Use the electron configuration of the preceding noble gas in brackets to shorten the configuration of the element.
• Examples:
  • Sodium: [Ne]3s^1
  • Neon: [Ne] (complete inner shell)
• How to apply: Represent the inner-shell configuration with the noble gas symbol that completes the previous period, followed by the remaining electrons in the outer orbitals.
• Period 3 (Table 5) examples (complete vs noble-gas shorthand):
  • Sodium (11): 1s^2 2s^2 2p^6 3s^1 → [Ne]3s^1
  • Magnesium (12): 1s^2 2s^2 2p^6 3s^2 → [Ne]3s^2
  • Aluminum (13): 1s^2 2s^2 2p^6 3s^2 3p^1 → [Ne]3s^2 3p^1
  • Silicon (14): 1s^2 2s^2 2p^6 3s^2 3p^2 → [Ne]3s^2 3p^2
  • Phosphorus (15): 1s^2 2s^2 2p^6 3s^2 3p^3 → [Ne]3s^2 3p^3
  • Sulfur (16): 1s^2 2s^2 2p^6 3s^2 3p^4 → [Ne]3s^2 3p^4
  • Chlorine (17): 1s^2 2s^2 2p^6 3s^2 3p^5 → [Ne]3s^2 3p^5
  • Argon (18): 1s^2 2s^2 2p^6 3s^2 3p^6 → [Ne]3s^2 3p^6 or [Ar] as shorthand
• Important note: The inner-shell configuration of sodium is identical to neon's configuration (Ne); using noble-gas notation compresses the same idea.
• Use of noble-gas notation can extend to all elements by appending outer-shell electron configurations to the previous noble gas core.

Valence Electrons

• Definition: Valence electrons are the electrons in the atom's outermost orbitals (typically those in the highest principal energy level).
• Examples:
  • Sulfur: Electron configuration $[Ne]3s^2 3p^4$ → valence electrons = 6
  • Cesium: Electron configuration $[Xe]6s^1$ → valence electrons = 1
• Significance: Valence electrons largely determine an element’s chemical properties and bonding behavior.

Electron-Dot Structures (Lewis Dot Structures)

• Concept: A visual shorthand for valence electrons around the element’s symbol.
• Rules:
  • Dots represent valence electrons.
  • Place dots one at a time on the four sides of the symbol, pairing them as needed until all valence electrons are shown.
• Example: Second-period elements (Table 6) show how valence electrons are arranged.
• Tin (Sn) example (from the problem-solving steps):
  • Tin has atomic number 50; electron configuration (noble-gas core) is $[Kr]5s^2 4d^{10} 5p^2$
  • The valence electrons are the electrons in the orbitals related to the atom’s highest principal energy level (5th level): 5s^2 and 5p^2 → 4 valence electrons.
  • Electron-dot structure: place four dots around the Sn symbol to represent these four valence electrons.

Practice Problems (Selected from the Lesson)

• 19. Write ground-state electron configurations for the following elements:
  • a. bromine (Br)
  • b. strontium (Sr)
  • c. antimony (Sb)
  • d. rhenium (Re)
  • e. terbium (Tb)
  • f. titanium (Ti)
• 20. A chlorine atom in its ground state has seven electrons in the third energy level. How many of these occupy p orbitals? How many of the total 17 electrons in chlorine occupy p orbitals?
• 21. When a sulfur atom reacts with other atoms, electrons in the atom's third energy level are involved. How many such electrons does sulfur have?
• 22. An element has the ground-state electron configuration $[Kr]5s^2 4d^5 5p$. It is used in semiconductors and alloys. What element is it?
• 23. CHALLENGE: In its ground state, an atom has two electrons in all orbitals related to the atom's highest energy level for which n = 6. Using noble-gas notation, write the electron configuration for this element, and identify the element.
• 24. Draw electron-dot structures for the following elements: a. magnesium; b. thallium; c. xenon
• 25. An atom has a total of 13 electrons. What is the element, and how many electrons are shown in its electron-dot structure?
• 26. CHALLENGE: This element exists solid at room temperature and normal pressure and is found in emerald gemstones. It is known to be one of: carbon, germanium, sulfur, cesium, beryllium, or argon. Identify the element from its electron-dot structure.
• 27. Apply the Pauli exclusion principle, aufbau principle, and Hund's rule to write the electron configuration and draw the orbital diagram for:
  • a. silicon
  • b. fluorine
  • c. calcium
  • d. krypton
• 28. Define valence electron.
• 29. Illustrate and describe the sequence in which ten electrons occupy the five orbitals related to the atom's d sublevel.
• 30. Extend the aufbau sequence through an element that has not yet been identified, but whose atoms would completely fill 7p orbitals. How many electrons would such an atom have? Write its electron configuration using noble-gas notation for the previous noble gas, radon.
• 31. Interpret Scientific Illustrations: Which is the correct electron-dot structure for selenium? Explain (options shown in the figure: a, b, c, d).

Check Your Progress — Summary

• The arrangement of electrons in an atom is called the atom's electron configuration.
• Electron configurations are defined by the aufbau principle, the Pauli exclusion principle, and Hund's rule.
• An element's valence electrons determine the chemical properties of the element.
• Electron configurations can be represented using:
  • orbital diagrams
  • electron configuration notation
  • electron-dot structures
• Practice and problem-solving strategies are provided to apply these concepts to specific elements and to extend understanding to more complex configurations.

Demonstrate Understanding (End-of-Section Questions)

• 27. Apply the three principles to write electron configurations and draw orbital diagrams for silicon, fluorine, calcium, and krypton.
• 28. Define valence electron.
• 29. Illustrate and describe the sequence in which ten electrons occupy the five orbitals related to the d sublevel.
• 30. Extend the aufbau sequence to an undetermined element that would completely fill 7p orbitals. How many electrons would such an atom have? Write its electron configuration using the previous noble gas (radon) notation.
• 31. Interpret the correct electron-dot structure for selenium from provided diagrams.

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