Chem 101 (Week 2 Notes)

Why do wavefunctions sometimes take positive and negative values?

Signs indicate phase. Phases matter for interference and node formation in orbitals.

How does squaring a wavefunction relate to electron location?

Square gives probability density; peaks show likely electron regions; zeros are nodes where electrons aren’t found

Why is probability at the nucleus zero for many orbitals?

Radial probability often vanishes at r=0 due to wavefunction behavior.

What causes radial nodes in atomic orbitals?

Higher energy wavefunctions have additional zero’s (radial nodes) as distance increases. Nodes define regions of zero electron probability

How do 2s and 1s radial distributions compare practically?

2s has an inner small peak plus an outer larger peak with a node between; explains why 2s electrons sometimes penetrate closer to nucleus

Why can a single orbital have multiple regions of high probability?

Wavefunctions oscillate; squaring yields multiple peaks (Shells) indicating likely electron radii within one orbital.

What does the principal quantum number n tell you?

N indicates energy level and general size/distance from nucleus; higher n means higher energy and typically larger orbitals.

How does the angular momentum quantum number L affect orbital shape?

L determines orbital type (0=s, 1=p, 2=d,3=f). Nodal planes and lobes that define 3-d shape of probability regions

Why does L range from 0 to n-1?

Mathematical solution to Schrodinger equation; ensures allowed shapes for a given energy shell and sets orbital variety within n

How does magnetic quantum number relate to orientation?

Gives spatial orientations (-1 …+1); explains why p and d orbitals come in multiple, perpendicular or distinct orientations

Why can each orbital hold 2 electrons opposite ms?

Spin quantum number (+1/2 or -1/2) distinguishes 2 electrons in same spatial orbital, satisfying the Pauli exclusion principle

How does degeneracy apply to hydrogen orbitals?

All orbitals with same n are degenerate (same energy) for one-electron systems; transitions to that n are arbitrary among subshells.

Why does degeneracy break in multi-electron atoms?

Electron-electron interactions and shielding lift degeneracy; subshells split into energy in many-electron atoms.

What is penetration and why does it matter for orbital energy?

Penetration: how close orbital density approaches nucleus. Greater penetration reducing shielding and lowers orbital energy relative to others.

Compare penetration of s, p, d, f orbitals at same n

At given n: s penetrates most, then p, d, f; more penetrations means lower energy and greater attraction to nucleus

How does shielding influence orbital energy ordering?

Inner electrons reduce effective nuclear charge for outer electrons; stronger shielding raises outer orbital energy and alters subshell ordering.

Why can 4s be lower in energy than 3d in many atoms?

4s penetrates sufficiently to feel nucleus more, lowering its energy relative to poorly penetrating 3d; explains electron filling order anomalies.

How do radial distribution plots help predict chemical behavior

They show where electron density resides (inner vs. outer peaks) indicating ease of removal, bonding propensity, and shielding effects.

Hund’s rule

Electrons occupy degenerate orbitals singly with parallel spins to minimize repulsion, lowering total energy (maximize multiplicity)

Pauli Exclusion Principle

No 2 electrons in an atom can have identical sets of quantum numbers; at most two per orbital with opposite spins.

How can the periodic table help predict valence electrons?

Main-group columns give outer s and p electron counts; valence electrons determine bonding and reactivity patterns.

Why are transition-metal valence electrons less obvious from group number?

They involve both outer s and inner d electrons; counting s + d gives valence but d occupancy can shift with oxidation state

Magnetic Quantum Number

Determines spatial orientation. (2L+1)

Integer values from -L to +L

Orbitals with greater penetration feel

Greater nuclear attraction (lower energy)

What is the ordering for penetration within the same principal shell?

s > p > d > f

Atomic Radius

the distance from the nucleus of an atom to the outermost electrons

Periodic Trend for Atomic Radius

Increases down a group; decreases from left to right

Why does atomic radius increase down a group?

Principal quantum number n increases, causing the outer electrons to be farther from nucleus

Why does atomic radius decrease across a row?

Effective nuclear charge Zeff increases

Cations are

Smaller than their neutral atoms

Anions are

Larger than their neutral atoms

Ionization Energy

The energy required to remove an electron from an atom in its gaseous state

Which group of elements has the most negative electron affinities

The halogens (group 7A)

First ionization energy

The energy required to remove the first electron from an atom in the gaseous state

Periodic Trends for First Ionization Energy

Decreases down a column; increases across a row

Why does First IE decrease down a column?

Outermost electrons are further away from nucleus (easier to remove)

Why does First Ionization Energy increase across a row?

Effective nuclear charge increases

Effective Nuclear Charge

The net positive charge experienced by an electron in a multi-electron atom

Zeff is always

Smaller than Z (actual proton number) due to shielding

Zeff increases

Across a period (more protons, similar shielding)

Why does effective nuclear charge not have a vivid trend down a column?

Because the principal quantum number n increases, the electrons are farther, reducing the attraction even if Zeff is larger

Electron Affinity

The energy associated with an element in its gaseous state gaining an electron

First electron affinity is usuallly

Exothermic (energy released in gaining one electron)

Periodic Trend for Electron Affinity

Decreases across a row (more negative)

Why does electron affinity decrease across a row

Effective nuclear charge increases

Periodic Trend for Metallic Character

Increases down a column; Decreases across a row

Why does metallic character increase down a column

Ionization energy decreases

Why does Metallic Character decrease across a row

Ionization energy increases