GENERAL CHEMISTRY · ELECTRONIC STRUCTURE

Relate the energy.
Check the state.

Connect Quantum Theory, Orbital Types, and Electron Configuration, then retrieve all nine study objectives with twelve randomized five-choice questions.

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3guided lessons

12practice questions

9study objectives

5choices per item

A repeatable electronic routine

Relate. Permit. Fill. Remove.

01Relate
Use c = λν and E = hν without losing the inverse relationship.
02Permit
Reject impossible subshells and quantum-number sets before filling.
03Fill
Apply Aufbau, Pauli, and Hund as three separate constraints.
04Remove
For cations, remove from the highest principal shell first.

Three prerequisite-linked lessons

Energy before occupancy.

Each ledger answers a different question: how energy relates, whether a state is allowed, and how electrons occupy or leave that state.

LESSON 1 · 16 MIN

Study + retrieve

Quantum relationships from wavelength to evidence

Relate wavelength, frequency, and photon energy; interpret line-spectrum transitions; and distinguish an orbital probability model from a fixed path.

ESSENTIAL QUESTIONWhich relationship or energy difference governs the observation?

Photon and transition ledger

Direction of wavelength, frequency, and photon-energy relationships
Change	Frequency	Photon energy	Invariant
Wavelength increases	Decreases	Decreases	c = λν
Frequency increases	Increases	Increases	E = hν
Amplitude increases	Unchanged	Unchanged per photon	Intensity changes

Electronic transition evidence
Direction	Energy exchange	Photon relationship
Lower → higher level	Absorption	Ephoton = Ehigh − Elow
Higher → lower level	Emission	Ephoton = Ehigh − Elow

500 nm audit5.00 × 10⁻⁷ m → 5.996 × 10¹⁴ Hz → 6.00 × 10¹⁴ Hz

STUDY TABLE · CAPTION INCLUDED

Preserve the inverse pair

For electromagnetic radiation, c = λν. Increasing wavelength lowers frequency because their product remains the speed of light in a vacuum.

λ ↑ means ν ↓
Convert nanometers to meters

Connect frequency to photon energy

A photon carries E = hν, so energy and frequency increase together while energy and wavelength vary inversely.

ν ↑ means E ↑
Amplitude changes intensity—not photon energy

Read transitions as energy differences

Absorption moves an electron upward by taking in a matching photon; emission moves downward and releases a photon whose energy equals the level difference.

Downward transition emits
Largest |ΔE| gives highest-energy photon

Worked example

Light has wavelength 500 nm. Using c = 2.998 × 10⁸ m/s, find its frequency.

1
Convert 500 nm to 5.00 × 10⁻⁷ m.
2
Use ν = c/λ.
3
Divide 2.998 × 10⁸ by 5.00 × 10⁻⁷ to obtain 5.996 × 10¹⁴ s⁻¹.

ConclusionTo three significant figures, the frequency is 6.00 × 10¹⁴ Hz.

Close the notes first

Retrieve the model.

01If wavelength doubles, what happens to frequency?

Frequency is halved.

Their product c remains constant.

02Which transition emits: n = 2 to n = 4, or n = 4 to n = 2?

n = 4 to n = 2.

A downward energy change releases a photon.

03Is an orbital an exact electron route?

No. It represents a quantum state and spatial probability distribution.

The modern model does not assign a classical trajectory.

LESSON 2 · 15 MIN

Study + retrieve

Orbitals as allowed states and capacities

Identify qualitative orbital types, calculate subshell and shell capacities, and reject forbidden quantum-number combinations.

ESSENTIAL QUESTIONIs the proposed state allowed before any electron is placed into it?

Orbital capacity and permission ledger

Subshell angular momentum, orbital count, and electron capacity
Subshell	l	Orbitals, 2l + 1	Maximum electrons
s	0	1	2
p	1	3	6
d	2	5	10
f	3	7	14

Allowed values for the four electron quantum numbers
Number	Allowed values	Meaning
n	1, 2, 3, …	Principal shell
l	0 through n − 1	Subshell type
mₗ	−l through +l	Orbital orientation
mₛ	+1/2 or −1/2	Electron spin state

n = 4 audit1 + 3 + 5 + 7 = 16 orbitals · maximum 32 electrons

STUDY TABLE · CAPTION INCLUDED

Separate a lobe from an orbital

An s orbital is spherically symmetric; a p orbital has two lobes separated by a nodal plane. Two p lobes are regions of one orbital, not two orbitals.

s: spherical
p: two lobes, one orbital

Count states before electrons

s, p, d, and f subshells contain 1, 3, 5, and 7 orbitals. Pauli permits at most two opposite-spin electrons in each orbital.

Orbitals = 2l + 1
Capacity = 2(2l + 1)

Audit all four quantum numbers

n begins at 1; l runs from 0 to n − 1; mₗ runs from −l to +l; and mₛ is +1/2 or −1/2.

l < n
|mₗ| ≤ l

Worked example

How many orbitals and electrons can the n = 4 shell contain?

1
For n = 4, l = 0, 1, 2, and 3, corresponding to s, p, d, and f.
2
Add orbital counts: 1 + 3 + 5 + 7 = 16 orbitals.
3
Multiply by two electrons per orbital: 16 × 2 = 32 electrons.

ConclusionThe n = 4 shell contains 16 orbitals and can hold at most 32 electrons.

Close the notes first

Retrieve the model.

01How many orbitals are in a d subshell?

Five.

For d, l = 2 and 2l + 1 = 5.

02Can n = 2 have l = 2?

No.

l must range from 0 through n − 1, so n = 2 permits only 0 and 1.

03How many electrons can one orbital hold?

At most two with opposite spins.

This follows from the Pauli exclusion principle.

LESSON 3 · 17 MIN

Study + retrieve

Electron configurations without shortcut errors

Assemble ground-state configurations, form common ions in the correct removal order, and infer unpaired electrons and magnetic behavior.

ESSENTIAL QUESTIONWhich subshell fills—or empties—next, and how many electrons remain unpaired?

Configuration and ion ledger

Separate roles of the three ground-state occupancy rules
Rule	Question answered	Failure cue
Aufbau	Which available subshell fills next?	A higher-energy subshell fills too early
Pauli	How many electrons fit in one orbital?	More than two or same-spin pair
Hund	How do degenerate orbitals fill?	Pairing before single occupancy

Common neutral-to-ion configuration changes
Species	Starting configuration	Electron change	Result
Mg²⁺	[Ne] 3s²	Remove two 3s electrons	[Ne]
Fe²⁺	[Ar] 4s² 3d⁶	Remove two 4s electrons	[Ar] 3d⁶
Cl⁻	[Ne] 3s² 3p⁵	Add one 3p electron	[Ar]

Magnetism auditAt least one unpaired electron → paramagnetic · all paired → diamagnetic

STUDY TABLE · CAPTION INCLUDED

Apply three rules separately

Aufbau supplies the usual energy order, Pauli limits an orbital to two opposite spins, and Hund places one electron in each degenerate orbital before pairing.

Energy order first
Singly occupy before pairing

Remove by outer shell

For cations, remove electrons from the highest principal shell first. Transition metals therefore lose ns electrons before electrons from the lower-n d subshell.

Charge changes electron count
Fe loses 4s before 3d

Count unpaired electrons

A subshell fills its equal-energy orbitals singly before pairing. Any unpaired electron makes the atom or ion paramagnetic; a fully paired configuration is diamagnetic.

Unpaired → paramagnetic
All paired → diamagnetic

Worked example

Write the abbreviated configuration for Fe²⁺ when neutral Fe is [Ar] 4s² 3d⁶.

1
A 2+ charge means remove two electrons.
2
Remove from the highest principal shell, 4s, before 3d.
3
Removing both 4s electrons leaves [Ar] 3d⁶.

ConclusionFe²⁺ is [Ar] 3d⁶; do not remove two 3d electrons while retaining 4s².

Close the notes first

Retrieve the model.

01What is the maximum occupancy of one orbital?

Two electrons with opposite spins.

Pauli forbids identical four-quantum-number sets.

02Which electrons leave first when Fe forms Fe²⁺?

The two 4s electrons.

Cation formation removes the highest-n occupied shell first.

03What magnetic behavior follows from three unpaired electrons?

Paramagnetic behavior.

Unpaired electron magnetic moments interact with an external field.

All twelve Electronic Structure problems

Choose the governing constraint.

Question order and all five answer options shuffle each time. Reports automatically identify the exact question if you find a problem.

12 PRACTICE QUESTIONS

Retrieve before you review.

Question order and all five answer options are shuffled when you begin. The correct answer stays attached to the same underlying choice.

Continue the sequence

Carry electron structure into molecular structure.

Next, use valence electrons and orbital overlap to build Lewis structures, classify bonds, predict geometry, and evaluate polarity.

Use raw accuracy to choose what to review next—not as an official DAT score prediction.

Continue to Molecular Structure →