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:
Energy difference for a transition:
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 .
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:
Sublevel capacities:
electrons
electrons
electrons
electrons
Energy of a photon:
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