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Electronic Structure of Matter - Module 1 Notes (Science 9)

Overview

  • This module introduces the Electronic Structure of Matter for Science 9 (Alternative Delivery Mode). It covers the quantum mechanical model of the atom, how electrons are arranged, and how to read and use electron configurations, quantum numbers, and related concepts.
  • Core purpose: explain how the Quantum Mechanical Model describes energies and positions of electrons, predict probable electron locations (electron cloud), and extract information (period, group, valence, core electrons) from electron configurations.

Learning Competencies (What I Need to Know)

  • Explain how the Quantum Mechanical Model describes the energies and positions of electrons. (S9MT-IIa-22)
  • Predict the probable location of electrons in an atom (electron cloud; Heisenberg’s Uncertainty Principle).
  • Describe and write electron configurations for given elements.
  • Describe the set of quantum numbers and complete a given set for each element.
  • Extract data from electron configurations: period number, group number, number of paired and unpaired electrons, number of valence electrons, and number of core electrons.

Key Concepts and Models

  • Atomic models history (as background to the Quantum Mechanical Model)
    • Dalton’s Solid Sphere Model
    • Thomson’s Plum Pudding Model
    • Rutherford’s Nuclear Model
    • Bohr’s Planetary Model
    • Schrödinger’s Quantum Mechanical Model (Electron Cloud)
  • Differences among models
    • Rutherford: nucleus with electrons in surrounding space; mostly empty space in atom.
    • Bohr: electrons occupy fixed energy levels (orbitals) around a nucleus; energy quantization.
    • Schrödinger: electrons are described by wavefunctions; location is probabilistic, forming electron clouds/orbitals.
  • The Quantum Mechanical Model (QMM)
    • Electrons are found in regions of space around the nucleus called orbitals, described by probability densities.
    • Heisenberg’s Uncertainty Principle: you cannot simultaneously know the exact position and momentum of an electron with arbitrary precision.
    • The electron cloud represents the probability distribution of finding an electron around the nucleus.
  • Emission and absorption of energy
    • Electrons move between energy levels; absorbing energy raises an electron to a higher level; releasing energy occurs when returning to a lower level.
    • Atomic spectra and flame tests illustrate energy transitions and element identification.
    • Flame colors example (energy emitted by excited atoms):
    • Sodium (Na): Yellow
    • Copper (Cu): Green
    • Lithium (Li): Red (light red)
    • Lead (Pb): Pale Blue
    • Calcium (Ca): Brick Red
  • Light and energy relationships
    • Light is electromagnetic radiation; wavelength and frequency are inversely related: c = ext{(speed of light)} =
      u \, imes \, ext{(wavelength)} =
      u \, imes \, rac{c}{
      u} = rac{c}{ ext{wavelength}}
    • Energy of a photon: E = h
      u = rac{h c}{ ext{wavelength}}
    • Shorter wavelength corresponds to higher energy (and higher frequency).
  • Quantum numbers and orbitals
    • Principal quantum number: n (energy level, also called shell; K, L, M, N, O, P, Q correspond to n=1,2,3,4,5,6,7)
    • Angular momentum quantum number: l (shape of orbital; s: l=0, p: l=1, d: l=2, f: l=3)
    • Magnetic quantum number: ml (orientation of orbital; for p: ml \, \in {-1, 0, 1}; for d: ml \, \in {-2, -1, 0, 1, 2}; for f: ml \in {-3, -2, -1, 0, 1, 2, 3})
    • Spin quantum number: ms (electron spin; ms = \pm \tfrac{1}{2})
  • Sublevels and energy level capacity
    • Each principal energy level n consists of sublevels with shapes determined by l: 0 to n−1.
    • Each sublevel with angular momentum quantum number l has a number of orbitals equal to 2l+1 and can hold a total of 2(2l+1) electrons.
    • Maximum electrons in a principal energy level: 2n^2
    • Examples:
    • n=1: 1s → 2 electrons
    • n=2: 2s, 2p → 8 electrons total
    • n=3: 3s, 3p, 3d → 18 electrons total
    • n=4: 4s, 4p, 4d, 4f → 32 electrons total
  • Main energy level and sublevel naming
    • n = 1 is K, n = 2 is L, n = 3 is M, n = 4 is N, n = 5 is O, n = 6 is P, n = 7 is Q
  • Rules for electron configurations
    • Aufbau Principle: electrons occupy the lowest available energy level before filling higher levels.
    • Pauli Exclusion Principle: no two electrons can have the same set of four quantum numbers; thus each orbital can hold at most two electrons with opposite spins.
    • Hund’s Rule: in a sublevel, electrons fill each orbital singly before pairing, and all unpaired electrons in a sublevel have the same spin.
  • Electron configuration implications
    • Electron configuration allows determination of group number, period number, and valence electrons.
    • Valence electrons are generally those in the outermost principal energy level.
    • Core electrons are those in inner shells not in the outermost level.
  • Reading and interpreting electron configurations
    • Example: Sodium (Na) = 1s^2 \, 2s^2 \, 2p^6 \, 3s^1
    • Group number: 1; Valence electrons: 1; Period: 3
    • Energy level information can be summarized as: Energy Level 1: 2 electrons; Energy Level 2: 8 electrons; Energy Level 3: 1 valence electron (for Na)

Principal Energy Levels and Sublevels (n, l, orbitals, capacity)

  • There are main energy levels (n) from 1 to 7 with corresponding sublevels and maximum electrons per level:
    • n = 1: sublevels: 1 (s) → 2 electrons; orbitals: 1
    • n = 2: sublevels: s, p → 8 electrons; orbitals: 4 (1 + 3)
    • n = 3: sublevels: s, p, d → 18 electrons; orbitals: 9 (1 + 3 + 5)
    • n = 4: sublevels: s, p, d, f → 32 electrons; orbitals: 16 (1 + 3 + 5 + 7)
    • n = 5: sublevels: s, p, d, f (and potentially g in higher models) → 50 electrons; orbitals: 25
    • n = 6: sublevels: s, p, d, f → 72 electrons; orbitals: 36
    • n = 7: sublevels: s, p, d, f → 98 electrons; orbitals: 49
  • Capacity formula reminder: ext{Max electrons in level } n = 2n^2
  • Shapes and examples of orbitals: s (sphere), p (dumbbell with 3 orientations), d, f (more complex shapes)

Quantum Numbers and Orbitals

  • Four quantum numbers:

    • Principal quantum number: n — energy level; allowed values: n = 1, 2, 3, \, \,
    • Angular momentum quantum number: l — orbital shape; allowed values: l = 0, 1, 2, 3, \, \, (for s, p, d, f)
    • Magnetic quantum number: ml — orientation of orbital; allowed values: ml \, \in \{-l, -l+1, \, \ldots, l-1, l}
    • Spin quantum number: ms — electron spin; allowed values: ms = \pm \tfrac{1}{2}

  • Examples of orbital designations

    • s orbital: l = 0, often written as s orbital (e.g., 1s, 2s)
    • p orbital: l = 1; p orbitals have 3 orientations: m_l \in \{-1, 0, 1}
    • d orbital: l = 2; 5 orientations: m_l \in \{-2, -1, 0, 1, 2}
    • f orbital: l = 3; 7 orientations: m_l \in \{-3, -2, -1, 0, 1, 2, 3}

  • Table: relationship among quantum numbers

    • Example: For 3s electron: n = 3, l = 0, ml = 0, ms = \pm\tfrac{1}{2}
    • For 2p electron: n = 2, l = 1, ml \in {-1, 0, 1}, ms = \pm\tfrac{1}{2}

  • Representation of electron configurations and quantum number rules

    • Aufbau Principle: electrons fill lowest energy orbitals first
    • Pauli Exclusion Principle: each orbital can hold at most two electrons with opposite spins
    • Hund’s Rule: orbitals of the same sublevel are singly occupied before pairing

Reading and Using Electron Configurations

  • Example configurations and what they tell you
    • Sodium: 1s^2\ 2s^2\ 2p^6\ 3s^1
    • Group: 1; Period: 3; Valence electron: 1; Core electrons: 10
  • How to derive information from a configuration
    • Identify the outermost shell (highest principal quantum number n with electrons)
    • Count valence electrons (electrons in outermost shell)
    • Determine the number of unpaired electrons (based on occupancy of orbitals in the outermost sublevel)
    • Determine the group and period as per periodic table rules

Relation to Spectra, Emission, and Real-World Relevance

  • Why emission spectra matter: electrons transition between levels emit photons with specific energies, producing line spectra.
  • Flame tests as qualitative demonstration of energy transitions in elements (element-specific colors).
  • The quantum model explains why electrons are not in fixed orbits but in probability regions (orbitals), leading to the concept of electron clouds.

Activities and Practice (Summary of What You’ll Do in the Module)

  • Activity 1: Identify atomic models from a box (Rutherford Nuclear Model, Thomson Plum Pudding, Bohr Planetary, Dalton Solid Sphere, Schrödinger Electron Cloud).
  • Activity 2: Probability activity using a circle pattern to model electron distribution; asks about how the number of items (electrons) changes with radius and the concept of highest probability region.
  • Activity 3: Amazing Electron – match electron configurations to elements; distribute electrons into main energy levels accordingly; identify elements from configurations.
  • Activity 4: My Quantum Numbers – fill in n, l, ml, ms for given elements; determine the orbital names.
  • Activity 5: Complete the electron configuration data table; determine period, group, valence electrons, unpaired and paired electrons; solve related items.
  • Additional activities include more practice on writing electron configurations, determining valence electrons, and answering concept-based questions.

Common Concepts and Real-World Connections

  • Heisenberg’s Uncertainty Principle in simple terms: exact position and momentum cannot be known simultaneously with arbitrary precision; this underpins the probabilistic nature of the electron cloud.
  • The Quantum Mechanical Model does not specify precise electron paths but describes probability regions (orbitals) with shapes (s, p, d, f).
  • The electron configuration of an element provides information about its chemical properties, especially valence electrons and reactivity.
  • The historical context explains why modern chemistry relies on quantum mechanical principles rather than strictly fixed orbits.

Important Formulas and Numerical References (LaTeX)

  • Energy-momentum-wavelength relation for photons:
    • E = h\nu = \frac{hc}{\lambda}
    • c = \lambda \nu
  • Maximum electrons in a principal energy level:
    • N_{ ext{max}} = 2n^2
  • Sublevel orbital counts and capacities (per sublevel):
    • s: 2 electrons (1 orbital), p: 6 electrons (3 orbitals), d: 10 electrons (5 orbitals), f: 14 electrons (7 orbitals)
  • Magnetic and spin quantum numbers (illustrative):
    • m_l \in {-l, -l+1, \ldots, l-1, l}
    • m_s \in {+\tfrac{1}{2}, -\tfrac{1}{2}}
  • Quantum number relationships (conceptual):
    • Aufbau: electrons fill the lowest energy levels first
    • Pauli: no two electrons share the same set of quantum numbers
    • Hund: electrons fill degenerate orbitals singly before pairing

Quick Reference: Element Electron Configurations (Examples)

  • Sodium (Na): 1s^2\ 2s^2\ 2p^6\ 3s^1
  • Potassium (K): 1s^2\ 2s^2\ 2p^6\ 3s^2\ 3p^6\ 4s^1
  • Neon (Ne): 1s^2\ 2s^2\ 2p^6
  • Boron (B): 1s^2\ 2s^2\ 2p^1
  • Aluminum (Al): 1s^2\ 2s^2\ 2p^6\ 3s^2\ 3p^1
  • Chlorine (Cl): 1s^2\ 2s^2\ 2p^6\ 3s^2\ 3p^5

Connections to Assessment and Study Skills

  • Use the electron configuration to determine period (row) and group (column) on the periodic table.
  • Identify valence electrons as the outermost electrons; count unpaired electrons to infer magnetic properties and possible bonding behavior.
  • Practice with the four quantum numbers to understand electron placement in orbitals and to solidify the Aufbau/Pauli/Hund rules.
  • Be prepared to translate between orbital notation (e.g., 2p^6) and full energy level descriptions (e.g., energy level 2 with s and p sublevels).

Ethical and Practical Implications

  • Understanding electronic structure underpins technologies such as spectroscopy, semiconductors, and materials science.
  • Accurate models enable predictions about chemical reactivity, bonding, and material properties, which have broad real-world applications including medicine, electronics, and environmental science.

Quick Answer Key (Selected Items)

  • Uncertainty Principle origin: Heisenberg
  • Region around nucleus where electrons are found: Electron cloud / Atomic orbital
  • Highest-energy sublevel presence per principle level: s, p, d, f as n increases
  • Maximum electrons in the second shell: 8
  • Principal energy level naming: 1\rightarrow K, 2\rightarrow L, 3\rightarrow M, 4\rightarrow N, 5\rightarrow O, 6\rightarrow P, 7\rightarrow Q
  • Aufbau/Hund/Pauli rules (summary): follow lowest energy first; no two electrons share the same set of four quantum numbers; fill singly before pairing in a sublevel
  • Orbitals present in the 3rd principal energy level: 9 orbitals; 3s, 3p, 3d
  • Electron configuration for potassium: 1s^2\ 2s^2\ 2p^6\ 3s^2\ 3p^6\ 4s^1
  • Valence electrons of group 2 element: 2
  • Lowest principal quantum number n: 1

References from the Module

  • Text: Science – Grade 9, Module 1: Electronic Structure of Matter (DepEd, 2020) with guidance on the Quantum Mechanical Model, electron configurations, and related activities.
  • Flame test data and example colors (Sodium, Copper, Lithium, Lead, Calcium) as real-world demonstrations of energy emission.
  • Activity and assessment items (multiple-choice and short-answer formats) to reinforce the concepts of quantum numbers, orbitals, and electron configurations.
  • Contact and publication details for further reference are provided in the module.