General Chemistry Exam Review: Atomic Structure, Bonding, and Periodic Trends

Atomic Structure and Quantum Numbers

Quantum Numbers

Quantum numbers describe the properties of atomic orbitals and the electrons in those orbitals. Each electron in an atom is defined by a unique set of four quantum numbers:

• Principal quantum number (n): Indicates the energy level and size of the orbital. $n = 1, 2, 3, \ldots$

• Angular momentum quantum number (l): Defines the shape of the orbital. $l = 0, 1, \ldots, n-1$

• Magnetic quantum number (m_l): Specifies the orientation of the orbital. $m_l = -l, \ldots, 0, \ldots, +l$

• Spin quantum number (m_s): Describes the spin of the electron. $m_s = +\frac{1}{2}$ or $-\frac{1}{2}$

Only certain combinations of quantum numbers are allowed, following these rules:

• $n$ must be a positive integer.

• $l$ must be an integer from $0$to$n-1$.

• $m_l$ must be an integer from $-l$ to $+l$.

• $m_s$ must be $+\frac{1}{2}$ or $-\frac{1}{2}$.

Example: For $n=3$, $l=2$, $m_l=1$, $m_s=+\frac{1}{2}$ is allowed.

Electron Configuration

Electron configuration describes the arrangement of electrons in an atom's orbitals. The notation uses numbers and letters to indicate energy levels and subshells, with superscripts for the number of electrons.

• Example: [Kr] 5s2 4d8 5p4 is an electron configuration for an element (additional info: This configuration is not standard; likely a typo or meant to represent a specific element's excited state).

Core and Valence Electrons

• Core electrons: Electrons in the inner shells, not involved in bonding.

• Valence electrons: Electrons in the outermost shell, involved in chemical bonding.

• Example: Phosphorus (P) has 10 core electrons (1s2 2s2 2p6).

Atomic and Periodic Properties

Atomic Radius

Atomic radius increases down a group and decreases across a period (left to right) in the periodic table.

• Largest atomic radius in period 3: Sodium (Na) has the largest atomic radius in the third period.

Ionization Energy

Ionization energy is the energy required to remove an electron from an atom. It increases across a period and decreases down a group.

• Highest ionization energy: Oxygen (O) has the highest ionization energy among Li, O, S, PO4.

Electromagnetic Radiation and Photons

Photon Energy and Wavelength

The energy of a photon is inversely proportional to its wavelength:

• $E = \frac{hc}{\lambda}$

• Where $E$ is energy, $h$ is Planck's constant ($6.626 \times 10^{-34}$ J·s), $c$ is the speed of light ($3.00 \times 10^8$ m/s), and $\lambda$ is wavelength.

• Lowest energy photon: Red light ($\lambda = 650$ nm) has the lowest energy among visible colors listed.

• Example calculation: For $\lambda = 405$ nm, $E = \frac{6.626 \times 10^{-34} \times 3.00 \times 10^8}{405 \times 10^{-9}}$

Atomic Emission

When an electron transitions from a higher energy level to a lower one, it emits a photon with energy equal to the difference between the two levels:

• $E = -R_H \left( \frac{1}{n_f^2} - \frac{1}{n_i^2} \right)$

• Where $R_H$ is the Rydberg constant ($2.18 \times 10^{-18}$ J), $n_i$ is the initial level, $n_f$ is the final level.

• Example: Electron drops from $n=5$ to $n=2$ in hydrogen atom.

Chemical Bonding and Molecular Structure

Bond Formation and Energy

• Bond formation: Releases energy.

• Bond breaking: Requires energy.

Covalent Bonds Between Carbon Atoms

• Bond length: Triple bond (C≡C) is shortest and strongest; single bond (C–C) is longest and weakest.

• Example: C≡C bond is the strongest and shortest among carbon-carbon bonds.

Lewis Structures

Lewis structures represent the arrangement of electrons in molecules. The best Lewis structure minimizes formal charges and follows the octet rule.

• XeO2: The best Lewis structure places double bonds between Xe and each O, with lone pairs on O and Xe as needed.

• NC13: Nitrogen atom has 3 bond pairs and 1 lone pair.

Formal Charge

Formal charge is calculated as:

• $\text{Formal charge} = \text{Valence electrons} - \text{Nonbonding electrons} - \frac{1}{2} \times \text{Bonding electrons}$

• Example: In borate ion (BO33–), boron has a formal charge of 0, oxygen atoms have a formal charge of –1 each.

Orbitals and Electron Diagrams

Orbital Shapes

• s-orbital: Spherical shape.

• p-orbital: Dumbbell shape.

• d-orbital: Cloverleaf shape.

Orbital Diagrams

Orbital diagrams use arrows to represent electron spins in each orbital. Noble gas notation can be used to simplify configurations.

• Nickel (Ni): [Ar] 4s2 3d8

• Fe2+ ion: [Ar] 3d6

Subshell Electron Count

• s subshell: 2 electrons

• p subshell: 6 electrons

• d subshell: 10 electrons

• f subshell: 14 electrons

Matching Quantum Terms

Term	Definition
Shell	n
Shape	l
Spatial orientation	ml
Spin	ms

Applications and Experimental Evidence

Flame Test and Element Identification

Passing electricity through a salt (e.g., during a 'pickle' demonstration) excites electrons, which emit light of characteristic wavelengths when they return to lower energy levels. The color of the emitted light can be used to identify the element present.

• Example: Sodium emits a bright yellow color in flame tests.

Summary Table: Subshell Electron Capacity

Subshell	Maximum Electrons
s	2
p	6
d	10
f	14

Additional info: Some questions and configurations in the original file are slightly ambiguous or contain typographical errors. Academic context and standard chemistry knowledge were used to clarify and expand the study notes for completeness.