Notes: Atomic Spectra and Energy Levels; Sublevels and Orbitals; Electron Configurations; Periodic Trends

5.2 Atomic Spectra and Energy Levels

  • Learning goal: Explain how atomic spectra correlate with the energy levels in atoms.

  • White light behavior:

    • When white light (from Sun or a bulb) passes through a prism or raindrops, it forms a continuous spectrum (a rainbow).

    • When atoms of elements are heated, they also emit light, but the resulting spectrum is not continuous.

  • Photons:

    • Light emitted from a lamp or heated atoms is a stream of particles called photons.

    • A photon is a packet of energy with both particle and wave characteristics, traveling at the speed of light.

    • Energy-wavelength relationship: high-energy photons have short wavelengths; low-energy photons have long wavelengths.

    • Photons are critical in technologies (e.g., lasers) and medical applications (e.g., X-rays, gamma rays for diagnosis and tumor treatment).

  • Atomic spectra:

    • When light from heated elements is passed through a prism, it produces an atomic spectrum: a set of lines of specific colors separated by dark regions (FIGURE 5.3).

    • This line spectrum indicates that only certain wavelengths of light are emitted by an element, giving each element a unique spectrum.

    • Contrast with continuous spectrum from white light, which contains all wavelengths.

  • Electron energy levels:

    • Spectral lines are associated with changes in electron energies.

    • Each electron in an atom has a specific energy, described by the principal quantum number n (n = 1, 2, 3, …).

    • Lower energy levels are closer to the nucleus; higher energy levels are farther away.

    • Energy levels are quantized; the energy of an electron can only take specific values, not intermediate ones.

    • When energy is absorbed, an electron moves to a higher energy level (excited state).

    • An excited electron is less stable and will fall to a lower energy level, emitting a photon with energy equal to the difference between levels (
      ΔE).

    • If the emitted energy is in the visible range, we see colors of visible light (e.g., sodium streetlights yellow, neon lights red).

  • Energy transitions and spectra:

    • The colors observed in atomic spectra are due to transitions between discrete energy levels.

    • The line spectrum of each element is unique due to its specific energy-level spacings.

  • Engage 5.4 question (conceptual): Why does light emitted by heated elements form atomic spectra whereas white light produces a continuous spectrum?

    • Answer: Heated elements emit photons only at certain energies corresponding to allowed electron transitions, producing discrete lines. White light contains a broad range of energies, leading to a continuous spectrum.

  • Sample problem (5.2) highlights:

    • a) When does an electron move to a higher energy level? → When it absorbs energy equal to the difference between energy levels.

    • b) When an electron drops to a lower energy level, how is energy lost? → Energy equal to the difference between energy levels is emitted as a photon.

  • Key formulas (in context):

    • Photon energy: E=hν=hcλE = h\nu = \frac{hc}{\lambda}

    • Energy difference for a transition: ΔE=E<em>upperE</em>lower\Delta E = E<em>{upper} - E</em>{lower}


5.3 Sublevels and Orbitals

  • Learning goal: Describe the sublevels and orbitals for electrons in an atom.

  • Electron capacity of an energy level:

    • The maximum number of electrons in energy level n is given by 2n22n^2.

    • Examples:

    • n = 1: 2 electrons

    • n = 2: 8 electrons

    • n = 3: 18 electrons

    • n = 4: 32 electrons

  • Sublevels within an energy level:

    • Each energy level contains one or more sublevels, where electrons share the same energy.

    • Sublevels are labeled s, p, d, and f.

    • The number of sublevels in energy level n equals n.

    • Examples:

    • n = 1: 1 sublevel → 1s

    • n = 2: 2 sublevels → 2s and 2p

    • n = 3: 3 sublevels → 3s, 3p, 3d

    • n = 4: 4 sublevels → 4s, 4p, 4d, 4f

    • Higher energy levels (n ≥ 5, 6, 7) also have as many sublevels as n, but only s, p, d, f are needed for the 118 known elements.

  • Visual ordering of sublevels by energy within a given level:

    • Order of increasing energy: s < p < d < f

    • Within an energy level, the s sublevel has the lowest energy, followed by p, then d, then f (when present).

  • Shapes and properties of orbitals:

    • Orbitals are three-dimensional regions where electrons are most likely to be found (probability distributions).

    • s orbitals: spherical; there is one s orbital per energy level (e.g., 1s, 2s, 3s, …).

    • p orbitals: three dumbbell-shaped orbitals per energy level (starting at n = 2: 2p, 3p, …); oriented along x, y, z axes (2px, 2py, 2pz, etc.).

    • d orbitals: five orbitals per energy level (e.g., 3d, 4d, …); more complex shapes; 5 d orbitals.

    • f orbitals: seven orbitals per energy level (e.g., 4f, 5f, …); complex shapes; not needed beyond certain periods.

  • Orbital capacity by type:

    • s: 1 orbital → up to 2 electrons

    • p: 3 orbitals → up to 6 electrons

    • d: 5 orbitals → up to 10 electrons

    • f: 7 orbitals → up to 14 electrons

  • Orbital examples and terminology:

    • 2s and 2p: in energy level n = 2; 2s has 1 orbital; 2p has 3 orbitals.

    • 3d: contains 5 d orbitals.

    • 4f: contains 7 f orbitals.

  • Orbital diagrams and probability density:

    • An orbital diagram uses boxes to represent orbitals; each orbital can hold a maximum of two electrons with opposite spins.

    • s orbitals are spherical and increase in size with higher n (e.g., 1s, 2s, 3s).

    • p orbitals have three lobes along orthogonal axes; shapes are consistent across energy levels, but volume increases with n.

  • Hund’s rule and electron arrangement:

    • Within a sublevel, electrons occupy degenerate orbitals singly with the same spin before pairing (lowest energy state is achieved with maximum unpaired electrons).

    • Example with carbon (Z = 6): 1s^2 2s^2 2p^2; electrons singly occupy available 2p orbitals before pairing (in the same sublevel).

    • Engage 5.10: When to use Hund’s rule in orbital diagrams?

  • Periodic table implications:

    • The sublevel structure (s, p, d, f) corresponds to blocks on the periodic table:

    • s block: Group 1A and 2A; includes H and He; outermost electrons occupy s orbitals.

    • p block: Groups 13–18; six electrons max in each period's p block (3 p orbitals).

    • d block: Transition metals; first appears after Ca; 10 elements per period (5 d orbitals); d block sublevel is n - 1.

    • f block: Lanthanides and actinides; 14 elements per block (7 f orbitals); f block sublevel is n - 2.

  • Sample problems and practice problems:

    • Determine the type and number of orbitals in given sublevels (e.g., 3p has 3 orbitals; 4d has 5 orbitals).

    • Exercises cover counting orbitals, sublevels, and electrons per sublevel, and comparing shapes and capacities.

  • Core example: The n = 2 energy level consists of 2s (1 s orbital) and 2p (3 p orbitals) → total 4 orbitals (2 + 6 = 8 electrons).


5.4 Orbital Diagrams and Electron Configurations

  • Learning goal: Draw the orbital diagram and write the electron configuration for an element.

  • Orbital diagrams illustrate the filling order of electrons by energy: lowest energy orbitals fill first (e.g., 1s then 2s then 2p, etc.).

  • Visual example of filling order (partial view):

    • 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p

  • Steps to draw an orbital diagram:

    • Step 1: Draw boxes for the orbitals in increasing energy for the element (e.g., for carbon, 1s, 2s, 2p).

    • Step 2: Place electrons with opposite spins in filled orbitals (paired arrows).

    • Step 3: Fill the last occupied sublevel with electrons in separate orbitals (Hund’s rule) before pairing.

  • Example: Orbital diagram for nitrogen (Z = 7) follows: 1s^2, 2s^2, 2p^3 with the three 2p electrons in separate 2p orbitals (↑ in each) before pairing occurs.

  • Core Chemistry Skill: Writing Electron Configurations

    • Electron configuration notation lists sublevels in order of increasing energy with electron counts as superscripts.

    • Example: Electron configuration for carbon: 1s^2 2s^2 2p^2; abbreviated form: [He]2s^2 2p^2.

  • Period 1 (H and He):

    • 1s orbital is filled first; H: 1s^1; He: 1s^2. Orbital diagrams show paired arrows in 1s for He.

  • Period 2 (Li to Ne):

    • Fill order: 1s, 2s, then 2p.

    • Boron to neon: 2p orbitals fill singly first (Hund’s rule) until 2p becomes half-filled, then electrons begin pairing to complete 2p.

    • Abbreviated configurations use [He] as the noble-gas core: Li → [He]2s^1; Be → [He]2s^2; B → [He]2s^2 2p^1; etc.

  • Period 3 (Na to Ar):

    • Fill 3s and 3p; 3d is not filled in Period 3.

    • Abbreviated configurations use [Ne] core: Na → [Ne] 3s^1; Mg → [Ne]3s^2; Al → [Ne]3s^2 3p^1; etc.

  • Practice prompts and sample problems emphasize drawing orbital diagrams for various elements and writing complete and abbreviated configurations.

  • Periodic context for filling order:

    • Period 4 and beyond: 4s fills before 3d (4s < 3d in energy), and this pattern repeats with higher shells (e.g., 5s before 4d, 6s before 5d, etc.).

    • After filling 4s, electrons begin to populate 3d, continuing until Zn (30) completes the 3d block, then 4p fills from Ga to Kr.

  • Notable exceptions:

    • Chromium (Cr) and Copper (Cu) exhibit atypical configurations to achieve stability via half-filled (Cr) or fully filled (Cu) d subshells:

    • Cr: [Ar] 4s^1 3d^5 (one 4s electron, five 3d electrons)

    • Cu: [Ar] 4s^1 3d^{10} (one 4s electron, ten 3d electrons)

    • Other higher-d and f-sublevel exceptions exist but are less prominent here.

  • Sample Problem 5.6: Using sublevel blocks to write electron configurations (Cl as example)

    • Locate Cl (Period 3, Group 7A, Z = 17).

    • Fill blocks across a period: 1s, 2s 2p, 3s 3p.

    • For Cl, last occupied sublevel is 3p with 5 electrons: 1s^2 2s^2 2p^6 3s^2 3p^5, abbreviated as [Ne]3s^2 3p^5.

  • Self-test and practice problems reinforce the connection between block filling and electron configurations.


5.5 Electron Configurations and the Periodic Table

  • Learning goal: Write the electron configuration for an atom using the sublevel blocks on the periodic table.

  • Sublevel blocks on the periodic table map to electron sublevels:

    • s block: hydrogen and helium, plus Group 1A and Group 2A elements; final electrons occupy s orbitals; period indicates which s orbital (1s, 2s, 3s, …).

    • p block: Groups 13–18 (3A–8A); six electrons maximum per period’s p block (3 p orbitals); period indicates which p sublevel (2p, 3p, …).

    • d block: Transition elements; first appears after Ca (Z = 20); 10 elements per period; d sublevel is one less than the period number (n - 1). Example: Period 4 → 3d; Period 5 → 4d.

    • f block: Inner transition elements; 14 elements per block (7 f orbitals); elements with Z > 57 (La) begin filling 4f; the f sublevel is two less than the period number (n - 2). Example: Period 6 → 4f; Period 7 → 5f.

  • Writing electron configurations using sublevel blocks:

    • Start at H and move across the periodic table, recording each filled sublevel block in order until the element is reached.

    • Example: Chlorine (Cl, Z = 17) is in Period 3 and Group 17 (3p block). Filling order by period:

    • Period 1: 1s

    • Period 2: 2s and 2p (2s^2 2p^6)

    • Period 3: 3s and 3p (3s^2 3p^5)

    • The final configuration for Cl using sublevel blocks is: 1s^2 2s^2 2p^6 3s^2 3p^5; abbreviated as [Ne]3s^2 3p^5.

  • Self-test 5.6: Exercises using sublevel blocks to write configurations for elements like argon and cobalt (among others).

  • Writing and recognizing electron configurations for periods 4 and above:

    • The order of filling shows 4s fills before 3d; this causes the unusual sequence observed when constructing configurations across periods 4, 5, and 6.

    • After 4s is filled, 3d begins to fill, then 4p, followed by 5s, 4d, and so on for subsequent periods.

  • Exceptions recap:

    • Cr and Cu show deviations from the simple aufbau order to achieve extra stability via half-filled or filled d subshells, as described above.

  • Practice prompts cover:

    • Complete vs abbreviated configurations

    • Matching configurations to element symbols

    • Analyzing sublevel blocks for various periods

    • Determining electrons in indicated sublevels


5.6 Trends in Periodic Properties

  • Learning goal: Use electron configurations to explain periodic property trends.

  • Key periodic properties:

    • Valence electrons: determine chemical behavior and bonding.

    • Atomic size (atomic radius): tends to decrease across a period and increase down a group.

    • Ionization energy: energy required to remove an electron; generally increases across a period and decreases down a group.

    • Metallic character: tends to decrease across a period and increase down a group.

  • Conceptual framework:

    • Periodic properties show regular, repeating (periodic) trends as you move from one group to the next within a period and as you go to the next period.

    • Analogy: Seasonal changes (Spring, Summer, Autumn, Winter) illustrate how properties rise and fall in a repeating pattern each year.


NOTE ON STRUCTURE AND EXAM PREP:

  • Core ideas span the link between electron configurations and observable properties (spectra, reactivity).

  • Be comfortable: (a) identifying energy level structure (n, sublevels s/p/d/f), (b) determining orbital capacities, (c) constructing orbital diagrams, (d) writing complete and abbreviated electron configurations, and (e) applying sublevel-block reasoning on the periodic table to predict electron distribution.

  • Practice problems emphasize applying Hund’s rule, Pauli exclusion, and order of sublevel filling, including Cr and Cu exceptions and the 4s vs 3d ordering in Period 4 and beyond.


Summary connections

  • Atomic spectra reveal discrete energy transitions linked to electron energy levels and sublevels.

  • Sublevels (s, p, d, f) organize electrons within energy levels; their capacities and shapes drive orbital diagrams and configurations.

  • Electron configurations describe real electronic structure; the periodic table is a practical roadmap to build these configurations via sublevel blocks.

  • Periodic trends arise from systematic changes in valence electron count and orbital energy spacings, explained by electron configurations and sublevel filling order.


Quick reference formulas and constants

  • Maximum electrons in energy level n: 2n22n^2

  • Sublevel capacities:

    • s2s\rightarrow 2 electrons

    • p6p\rightarrow 6 electrons

    • d10d\rightarrow 10 electrons

    • f14f\rightarrow 14 electrons

  • Energy of a photon: E=hν=hcλE = h\nu = \frac{hc}{\lambda}

  • Quantized energy levels: allowed energies are discrete; no intermediate values between levels.

  • Order within a given energy level: s < p < d < f


Key terms to review

  • Photon, spectrum, atomic spectrum, continuous spectrum, line spectrum

  • Principal quantum number, energy level, sublevel, orbital

  • s, p, d, f orbitals; shapes and numbers of orbitals

  • Pauli exclusion principle; Hund’s rule

  • Orbital diagram; electron configuration; abbreviated configuration; noble gas core

  • Sublevel blocks on the periodic table; blocks: s, p, d, f

  • Cr and Cu exceptions in electron configurations

  • Trends: atomic size, ionization energy, metallic character, valence electrons