CHM 101 Exam 2

Relationship between wavelength and frequency

Inversely proportional: as wavelength ($\lambda$) increases, frequency ($\nu$) decreases ($c = \lambda \nu$).

Relationship between photon energy and frequency

Directly proportional: higher frequency corresponds to higher energy ($E = h\nu$).

Relationship between photon energy and wavelength

Inversely proportional: shorter wavelength corresponds to higher energy ($E = \frac{hc}{\lambda}$).

Quantum jump resulting in photon emission

Occurs when an electron transitions from a higher energy level to a lower energy level, releasing excess energy as light.

Quantum jump resulting in photon absorption

Occurs when an electron absorbs energy and transitions from a lower energy level to a higher energy level.

Effect of a larger energy gap in an electronic transition

Emits or absorbs a photon with higher energy, higher frequency, and a shorter wavelength.

Bohr model

An atomic model postulating that electrons travel in discrete, fixed circular orbits around the nucleus at specific quantized energy levels.

Scientific significance of the Bohr model

Introduced the concept of quantized energy states in atoms and mathematically explained the emission line spectrum of hydrogen.

Ground state

The lowest possible electronic energy state of an atom.

Excited state

An energetic state reached when an electron absorbs energy and transitions to an orbital of higher energy.

Limitations of the Bohr model

Only successfully predicts spectra for single-electron systems ($H$, $He^+$); fails for multi-electron atoms and incorrectly treats electrons as orbiting on fixed planar tracks.

Atomic orbital

A three-dimensional mathematical probability region where an electron is most likely to be found (typically around $90\%$ probability).

Maximum electron capacity of an individual orbital

$2$ electrons, which must have opposite spin states.

Shape and angular momentum quantum number ($l$) of an $s$ orbital

Spherical; $l = 0$.

Shape and angular momentum quantum number ($l$) of a $p$ orbital

Dumbbell-shaped; $l = 1$.

Shape and angular momentum quantum number ($l$) of a $d$ orbital

Cloverleaf-shaped (or dumbbell with a donut); $l = 2$.

Shape and angular momentum quantum number ($l$) of an $f$ orbital

Complex/multi-lobed; $l = 3$.

Number of orbitals and maximum electron capacity in an $s$ sublevel

$1$ orbital; holds a maximum of $2$ electrons.

Number of orbitals and maximum electron capacity in a $p$ sublevel

$3$ orbitals; holds a maximum of $6$ electrons.

Number of orbitals and maximum electron capacity in a $d$ sublevel

$5$ orbitals; holds a maximum of $10$ electrons.

Number of orbitals and maximum electron capacity in an $f$ sublevel

$7$ orbitals; holds a maximum of $14$ electrons.

Principal quantum number ($n$)

Identifies the main shell or principal energy level; takes positive integer values ($n = 1, 2, 3, \dots$).

Angular momentum quantum number ($l$)

Identifies the shape of the orbital or subshell; takes integer values from $0$ to $n - 1$.

Magnetic quantum number ($m_l$)

Specifies the spatial orientation of an orbital in space; takes integer values ranging from $-l$ to $+l$.

Spin quantum number ($m_s$)

Specifies the intrinsic angular momentum (spin) of an electron; takes values of $+\frac{1}{2}$ or $-\frac{1}{2}$.

Number of quantum numbers required to specify an orbital vs. an electron

An orbital requires three quantum numbers ($n, l, m_l$); an individual electron requires four ($n, l, m_l, m_s$).

Aufbau principle

Electrons fill available atomic orbitals of lowest energy before occupying higher energy levels.

Hund's rule

Every orbital in a subshell is singly occupied with parallel spins before any orbital is doubly occupied.

Pauli exclusion principle

No two electrons in an atom can have the exact same set of all four quantum numbers; an orbital holds at most two electrons with opposite spins.

Quantum rule violated if $2p$ orbitals pair before each orbital has one electron

Hund's rule.

Core electrons

Electrons residing in inner, filled principal energy levels (noble gas core) that do not participate in chemical bonding.

Valence electrons

Electrons located in the outermost principal shell ($n$) that participate in chemical bonding and chemical reactions.

Outer electrons

Electrons in the highest principal energy level; for main-group elements, this is identical to the number of valence electrons.

Octet rule

The tendency of main-group atoms to gain, lose, or share electrons until they achieve an outer shell of eight valence electrons.

Isoelectronic species

Atoms and ions that possess the same total number of electrons and identical ground-state electron configurations (e.g., $O^{2-}$, $F^-$, $Ne$, $Na^+$, $Mg^{2+}$).

Electron loss sequence for transition metals forming cations

Electrons are removed from the outermost $ns$ subshell before any electrons are removed from the $(n-1)d$ subshell (e.g., $Fe$ forms $Fe^{2+}$ by losing $4s$ electrons to become $[Ar]3d^6$).

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

Increases across a period from left to right due to increased proton count with minimal additional shielding; remains relatively constant down a group.

Electron shielding

The phenomenon where inner-shell core electrons partially cancel the electrostatic attraction between the positive nucleus and outer valence electrons.

Atomic radius periodic trend

Increases down a group (due to additional electron shells) and increases from right to left across a period (due to lower $Z_{\text{eff}}$, making the atoms largest at the bottom-left).

Cation radius vs. neutral parent atom

Cations are smaller than their parent atoms because electron loss reduces electron-electron repulsion and often vacates the outermost shell.

Anion radius vs. neutral parent atom

Anions are larger than their parent atoms because added electrons increase electrostatic repulsion, causing the electron cloud to expand.

First ionization energy

The minimum energy required to remove the outermost electron from one mole of gaseous neutral atoms in their ground state.

Successive ionization energies

The sequential energies required to remove consecutive electrons ($IE_1 < IE_2 < IE_3$), showing a massive jump once all valence electrons are removed and a core electron is pulled.

Method for identifying an element's group using ionization energies

The location of the dramatic jump in successive ionization energies indicates the removal of core electrons; the number of moderate values prior to the jump matches the number of valence electrons.

Ionization energy periodic trend

Increases from left to right across a period (greater $Z_{\text{eff}}$) and increases from bottom to top up a group (electrons closer to the nucleus).

Lewis dot symbol

A visual notation showing the chemical symbol of an element surrounded by dots representing its valence electrons.

Cation

A positively charged ion formed when a neutral atom loses one or more electrons.

Anion

A negatively charged ion formed when a neutral atom gains one or more electrons.

Naming rule for monatomic anions

Use the root name of the nonmetal element and append the suffix "-ide" (e.g., chloride, oxide, phosphide).

Naming rule for monatomic cations

Use the element name followed by the word "ion" (e.g., sodium ion, magnesium ion).

Coulomb's law applied to ionic bonding

Lattice energy and ionic bond strength increase with greater ion charges ($q_1, q_2$) and smaller ionic radii (shorter internuclear distance $r$).

Criss-cross method for ionic formulas

Setting the numerical charge of each ion as the subscript of the opposite ion to ensure overall electrical neutrality, reducing to the empirical ratio.

Nomenclature for hydrated ionic compounds

State the standard name of the ionic compound followed by a Greek numerical prefix attached to the word "hydrate" (e.g., $CuSO_4 \cdot 5H_2O$ is copper(II) sulfate pentahydrate).

The seven homonuclear diatomic elements

$H_2$, $N_2$, $O_2$, $F_2$, $Cl_2$, $Br_2$, and $I_2$.

Nomenclature rules for binary covalent compounds

Name the first element with a Greek prefix (omitting mono-), then name the second element with a Greek prefix and the suffix "-ide".

Distinction between naming ionic vs. covalent compounds

Covalent compounds require Greek prefixes to specify atom numbers; ionic compounds do not use prefixes because the subscripts are fixed by charge neutrality.

In isoelectronic ions, what determines ionic radius?

the number of protons; the higher the atomic number, the smaller the ion

According to Coulomb’ Law: As size increases, attractive forces ______

decrease