General Chemistry Study Guide: Atomic Structure, Electron Configuration, Periodic Trends, and Isotopes

Atomic Orbitals

Types, Properties, and Representation of Atomic Orbitals

Atomic orbitals are regions in an atom where electrons are most likely to be found. Each orbital is characterized by its size, shape, and orientation in space, which are determined by quantum numbers.

• Type of Orbital: Orbitals are classified by their shapes (s, p, d, f). For example, the image shows a p orbital, which has a dumbbell shape and is oriented along a specific axis (x, y, or z).

• Number of Orbitals: Each type of orbital has a specific number of orientations. For p orbitals, there are three (px, py, pz) per energy level starting from n=2.

• Electron Occupancy: Each orbital can hold a maximum of 2 electrons, according to the Pauli Exclusion Principle.

• Shape and Orientation: Orbitals of the same type differ only in their orientation in space (e.g., px, py, pz).

Example: The fourth shell (n=4) contains 4s, 4p, 4d, and 4f orbitals. Each p orbital in this shell is oriented along a different axis.

Electron Configuration and the Periodic Table

Valence Electrons and Electron Configurations

Electron configuration describes the arrangement of electrons in an atom's orbitals. The periodic table helps determine the number of valence electrons, which are electrons in the outermost shell and are crucial for chemical reactivity.

• Valence Electrons: Elements in the same group (column) have the same number of valence electrons. For example, Se, Te, Po, O, and S all have six valence electrons.

• Electron Configuration Notation: The electron configuration of an atom is written using the format: $1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6$.

• Ground State vs. Excited State: The ground state is the lowest energy arrangement of electrons. Excited states occur when electrons occupy higher energy orbitals than normal.

• Noble Gas Notation: Electron configurations can be abbreviated using the previous noble gas. For example, Mo (molybdenum) ground state: $[Kr] 5s^1 4d^5$.

Example: For the configuration $1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6$, the atom is krypton (Kr).

Periodic Trends

Atomic Radius, Ionization Energy, and Effective Nuclear Charge

Periodic trends describe how certain properties of elements change across the periodic table.

• Atomic Radius: The atomic radius increases down a group and decreases across a period. For example, among K+, Ca2+, Al3+, S2−, S−, S, S+, S6+, the largest radius is S2− and the smallest is S6+.

• Effective Nuclear Charge (Zeff): Zeff increases across a period, leading to stronger attraction between nucleus and electrons. For example, O has a higher Zeff than S.

• Ionization Energy: The energy required to remove an electron from an atom. It increases across a period and decreases down a group. For example, F has a higher first ionization energy than Br.

Example: K+ has a smaller radius than S2− due to higher nuclear charge and fewer electrons.

Wavelength, Frequency, and Energy of Photons

Relationships and Calculations

Electromagnetic radiation is characterized by its wavelength ($\lambda$), frequency ($\nu$), and energy ($E$). These quantities are related by fundamental equations.

• Speed of Light: $c = \lambda \nu$

• Energy of a Photon: $E = h \nu$

• Planck's Constant: $h = 6.626 \times 10^{-34} \text{ J} \cdot \text{s}$

• Calculating Wavelength: For a frequency of 15.42 MHz ($1 \text{ MHz} = 1 \times 10^6 \text{ Hz}$), $\lambda = \frac{c}{\nu}$

• Calculating Energy per Mole: $E_{\text{mole}} = E_{\text{photon}} \times N_A$ where $N_A = 6.022 \times 10^{23} \text{ mol}^{-1}$

Example: For $\nu = 15.42 \times 10^6 \text{ Hz}$, $\lambda = \frac{2.998 \times 10^8}{15.42 \times 10^6} \text{ m}$.

Isotopes and Atomic Mass

Isotope Abundance, Mass, and Calculations

Isotopes are atoms of the same element with different numbers of neutrons. The atomic mass of an element is a weighted average based on isotope abundance.

• Isotope Table:

Isotope	Abundance (%)	Isotope Mass (amu)
hydrogen-1	99.98	1.007825
hydrogen-2	0.01	2.014102
hydrogen-3	0.01	3.016049
sulfur-32	94.96	31.972071
sulfur-33	0.76	32.971458
sulfur-34	4.29	33.967867
sulfur-36	0.00	35.967081

• Atomic Number: Number of protons in the nucleus.

• Mass Number: Sum of protons and neutrons.

• Nuclear Charge: Determined by the number of protons.

• Calculating Average Atomic Mass: $\text{Average mass} = \sum (\text{fractional abundance} \times \text{isotope mass})$

Example: For H2S, the most abundant molecule contains hydrogen-1 and sulfur-32.

Mass Spectrometry and Isotope Distribution

Interpreting Mass Spectra

Mass spectrometry is used to determine the isotopic composition of molecules. Peaks in the spectrum correspond to different isotopic combinations.

• Relative Intensity: Indicates the abundance of each isotopic species.

• m/z (mass-to-charge ratio): Used to identify isotopic variants.

• Calculating Formula Weight: The formula weight of a molecule is the sum of the atomic masses of its constituent atoms.

Example: The most abundant H2S molecule contains two hydrogen-1 atoms and one sulfur-32 atom, with a mass of approximately 34.027 amu.

Orbital Box Diagrams and Electron Pairing

Ground and Excited State Configurations

Orbital box diagrams visually represent electron configurations, showing how electrons fill available orbitals according to the Aufbau principle, Pauli Exclusion Principle, and Hund's Rule.

• Occupied Orbitals: The number of orbitals containing electrons in a given configuration.

• Neutral Atom Identification: The electron configuration corresponds to a specific neutral atom (e.g., Kr for $1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6$).

• Excited State: Electrons may occupy higher energy orbitals, resulting in unpaired electrons.

• Electron Pairing: In the ground state, electrons fill orbitals to maximize pairing and minimize energy.

Example: In the ground state, all electrons in the fourth shell experience the weakest attractions to the nucleus.

Classification Statements

Accuracy of Electron Configuration Statements

Statements about electron configurations can be classified as accurate or inaccurate based on quantum mechanical principles.

• Diamagnetic vs. Paramagnetic: Diamagnetic atoms have all electrons paired; paramagnetic atoms have unpaired electrons.

• Quantum Numbers: The highest value of the angular momentum quantum number ($l$) for a given shell is $n-1$.

• Electron Attraction: Electrons in higher shells experience weaker attraction to the nucleus.

• Subshell Occupancy: The highest energy subshell in a configuration is determined by the Aufbau principle.

Example: In any configuration, the highest energy subshell that exists for an atom with $n=4$ is 4f ($l=3$).

Additional info: Some context and examples have been inferred to ensure completeness and clarity for exam preparation.