Chem 150: Coulomb's Law, Effective Nuclear Charge, and Periodic Trends

Vocabulary flashcards covering Coulomb's Law, electron pairing/promotion energies, electron configurations of transition metals, effective nuclear charge, electron shielding, and periodic trends in atomic and ionic radii.

Electrostatic potential energy ($PE$)

The potential energy between two charges defined by Coulomb's Law as $PE = \frac{k q_1 q_2}{r}$, which is negative for attractive forces and positive for repulsive forces.

Repulsive force (Coulomb's Law)

An electrostatic interaction resulting from charges of identical signs, indicated by a positive potential energy value (such as $-1 \times -1$ for two interacting electrons).

Attractive force (Coulomb's Law)

An electrostatic interaction resulting from charges of opposite signs, indicated by a negative potential energy value (such as $-1 \times 1$ for an electron and a proton).

Pairing energy cost

The energy required to place two electrons into the same orbital due to mutual electron–electron electrostatic repulsion.

Electron promotion

The process of moving an electron to a higher energy orbital farther from the nucleus, which costs energy because the attractive force from the nucleus decreases as distance increases.

Chromium electron configuration exception

The anomalous ground-state electron configuration $[\text{Ar}] 4s^1 3d^5$, adopted because the energy cost to promote an electron from $4s$ to $3d$ is lower than the energy cost of pairing two electrons in the $4s$ orbital.

Effective nuclear charge ($Z_{\text{eff}}$)

The actual magnitude of positive charge experienced by an electron in an atom, defined generally by the formula $Z_{\text{eff}} = Z - \sigma$.

Electron shielding (screening)

The partial obstruction of the positive nuclear charge experienced by valence electrons, contributed to significantly by inner core electrons.

Core electrons

Electrons located in completed inner electron shells of an atom.

Valence shell

The outermost electron shell of an atom.

Atomic radius

The distance between the nucleus of an atom and its valence shell.

Covalent radius

The atomic radius in nonmetals, defined as half the distance between adjacent, identical nuclei connected by a chemical bond.

Metallic radius

The atomic radius in metals, defined as half the distance between the nuclei of two adjacent, identical metal atoms.

Atomic radius trend across a period

Atomic radius decreases from left to right across a period due to increasing effective nuclear charge ($Z_{\text{eff}}$), which draws the valence shell closer to the nucleus.

Atomic radius trend down a group

Atomic radius increases going down a group due to an increasing principal quantum number ($n$), placing the outermost shell farther from the nucleus.

Determinants of orbital size

The primary factors governing orbital size: orbital type (primarily principal quantum number $n$, with minor effects from $s$, $p$, or $d$), nuclear charge ($Z$), and electron–electron repulsion/screening (combined in $Z_{\text{eff}}$).

Cation

A positively charged ion formed by losing electrons; its radius is smaller than the parent neutral atom due to reduced electron–electron repulsions and possible loss of an entire valence shell.

Anion

A negatively charged ion formed by gaining electrons; its radius is larger than the parent neutral atom due to increased electron–electron repulsions in the valence shell.

Isoelectronic species

Atoms or ions that possess the exact same total number of electrons and identical electron configurations (e.g., $\text{Na}^+$ and $\text{Ne}$, or $\text{Cl}^-$ and $\text{Ar}$).

Ionization rule for d-block elements

The principle that electrons are removed first from the shell with the highest principal quantum number ($n$), meaning $s$ electrons are removed before $d$ electrons (e.g., $\text{Fe}$ forms $\text{Fe}^{2+}$ by losing electrons from $4s$ rather than $3d$).