chem lecture 8/28

Shells, Subshells, and Orbitals

• Shell: principal energy level, numbered n = 1, 2, 3, …; think of shells as broad “cities” where electrons reside. Each shell can hold a certain number of electrons, and is the outer boundary for where electrons are found at a given energy level.
• Subshell: within a shell, electrons occupy subshells labeled s, p, d, f, etc. Subshell shapes indicate where electrons are likely to be found:
• s subshell: spherical
• p subshell: dumbbell-shaped (contains 3 orbitals)
• d subshell: clover-like (more complex shapes)
• f subshell: more complex shapes
• Orbital: the exact region within a subshell where a particular electron resides (a specific quantum state). Example: the 2p subshell contains 3 orbitals, each can hold up to 2 electrons, for a total of 6 in the 2p subshell.
• Capacities of subshells (maximum electrons):
• s\text{ subshell} \rightarrow 2
• p\text{ subshell} \rightarrow 6
• d\text{ subshell} \rightarrow 10
• f\text{ subshell} \rightarrow 14
• General rule for a subshell with angular momentum quantum number l: the maximum number of electrons is N = 2(2l+1); orbitals in a subshell are 2l+1 in number, each orbital can hold 2 electrons.
• Orientation and number of p orbitals: the p subshell has 3 orbitals aligned along axes (commonly described along x, y, z); thus there are 3 p orbitals contributing to the total capacity of 6 electrons in the p subshell.
• Orbital shapes in a simple visualization:
• s\text{ (l=0)}:\; \text{sphere}
• p\text{ (l=1)}:\; \text{dumbbell}
• d\text{ (l=2)}:\; \text{clover/other shapes}
• Shell, subshell, and orbital hierarchy (addressing where electrons “live”):
• Shell = city
• Subshell = environment within the city (s, p, d, f)
• Orbital = exact apartment within the environment
• How these factors determine configurations: the total number of electrons determines how many subshells are needed and how many electrons go into each subshell.
• Example address notation for a single electron configuration component: for a given atom, a configuration part can be written as (shell)(subshell)(electrons in that subshell). Example: 1s^2 means 2 electrons in the first shell, in the s subshell.

Radius, Shielding, and Periodicity

• Radius is determined by the space occupied by electrons (and the number of shells). As you go down a group, you add more electron shells, increasing the overall radius.
• Across a period (left to right), the number of shells remains the same, but the increasing nuclear charge (more protons) pulls electrons closer to the nucleus.
• Shielding effect: inner electron shells shield outer electrons from the full positive charge of the nucleus; but across a period, the shielding effect stays roughly the same while the nuclear charge increases, causing a contraction of the atomic radius.
• Summary: down a group → radius increases due to more shells; across a period → radius decreases due to stronger effective nuclear charge with similar shielding.

Building electron configurations ( Aufbau principle and order of filling)

• Electrons fill subshells in a specific sequence (Aufbau order). A commonly used filling sequence is:
• 1s \rightarrow 2s \rightarrow 2p \rightarrow 3s \rightarrow 3p \rightarrow 4s \rightarrow 3d \rightarrow 4p \rightarrow 5s \rightarrow 4d \rightarrow 5p \rightarrow 6s \rightarrow 4f \rightarrow 5d \rightarrow 6p \rightarrow 7s \rightarrow 5f \rightarrow 6d \rightarrow 7p
• The order is often remembered with the diagonal rule, which guides how electrons populate the available subshells as energy levels rise.
• Practical guidance from the transcript: start filling from the lowest-energy shell and proceed in the designated order; when two subshells are available at a similar energy, follow the established filling rule (not skipping directly to a higher shell if a lower-energy subshell in a lower shell is not full).
• Example reasoning for filling: to fill Boron (5 electrons), start with 1s^2 (two electrons), then fill 2s^2 (two more), leaving one electron to place in the next available subshell 2p, giving 1s^2 2s^2 2p^1.

Worked examples from the transcript

• Boron (atomic number 5, electrons = 5):
• Fill order: 1s^2 \; 2s^2 \; 2p^1
• Final configuration: 1s^2\; 2s^2\; 2p^1
• Chlorine (atomic number 17, electrons = 17):
• Fill order leads to: 1s^2 \; 2s^2 \; 2p^6 \; 3s^2 \; 3p^5
• Final configuration: 1s^2\; 2s^2\; 2p^6\; 3s^2\; 3p^5
• Magnesium (atomic number 12, electrons = 12):
• Fill order: 1s^2 \; 2s^2 \; 2p^6 \; 3s^2
• Final configuration: 1s^2\; 2s^2\; 2p^6\; 3s^2
• Sodium (atomic number 11, electrons = 11):
• Fill order: 1s^2 \; 2s^2 \; 2p^6 \; 3s^1
• Final configuration: 1s^2\; 2s^2\; 2p^6\; 3s^1
• Hydrogen (atomic number 1, electrons = 1):
• Fill order: 1s^1
• Final configuration: 1s^1
• Note on energy levels and orbitals: the lower energy levels fill first, and electrons occupy the lowest available subshell consistent with the Aufbau principle.

Outermost electrons and valence concepts

• The electrons in the outermost energy level (highest principal quantum number n with electrons present) are called the valence electrons.
• Valence electrons determine much of an element’s chemical properties (bonding, reactivity, etc.).
• The outermost shell is often referred to as the valence shell; the electrons there are responsible for forming bonds and participating in chemical reactions.

Connections to broader concepts and real-world relevance

• Periodic trends in atomic radius and shielding explain why atoms get smaller across a period and larger down a group.
• The Aufbau filling order underpins the periodic table’s structure and the placement of elements by electron configuration.
• The shapes and numbers of orbitals relate to chemical behavior, magnetism, and spectroscopy.
• The concept of valence electrons links to oxidation states, bonding patterns, and reactivity in real-world chemistry.

Quick recap of key takeaways

• Shells, subshells, and orbitals organize where electrons reside: shell (n), subshell (s, p, d, f), orbitals (specific states).
• Capacities: s\rightarrow 2, p\rightarrow 6, d\rightarrow 10, f\rightarrow 14; general capacity formula N = 2(2l+1).
• Across a period, radius decreases due to increasing nuclear charge with similar shielding; down a group, radius increases with more shells.
• Electron configurations follow the Aufbau order; examples include \text{B}: 1s^2 2s^2 2p^1, \text{Cl}: 1s^2 2s^2 2p^6 3s^2 3p^5, \text{Mg}: 1s^2 2s^2 2p^6 3s^2, \text{Na}: 1s^2 2s^2 2p^6 3s^1, \text{H}: 1s^1.
• Outer electrons are the valence electrons and largely determine chemical properties.