Quantum Numbers and Atomic Orbitals

Vocabulary practice flashcards covering quantum numbers, orbital shapes and capacities, atomic models, and electron energy level transitions.

Heisenberg Uncertainty Principle

The quantum mechanical principle stating that one can never simultaneously know both the exact position and velocity (or energy) of an electron.

Orbital

A probability distribution map that represents the best guess of both the position and energy of an electron, indicating where it is most likely to be found.

Principal Quantum Number ($n$)

The quantum number that designates the principal energy level (PEL), describing the overall size and energy of any given orbital.

Angular Momentum Quantum Number ($l$)

The quantum number that describes the shape of an orbital, with allowed integer values ranging from $0$ up to $n - 1$.

Magnetic Quantum Number ($m_l$)

The quantum number specifying the 3D spatial orientation of an orbital, with integer values ranging from $-l$ to $+l$, including $0$.

Spin Quantum Number ($m_s$)

A fundamental property of an electron designating its magnetic spin state, which can strictly take the value of either $+\frac{1}{2}$ (spin up) or $-\frac{1}{2}$ (spin down).

Stern-Gerlach Experiment

A classic experiment that demonstrated the discrete magnetic spin of electrons by firing them between magnetic poles and observing deflection exclusively to the top ($+\frac{1}{2}$) or bottom ($-\frac{1}{2}$) with nothing in between.

$s$ Orbital

A largely spherical orbital defined by $l = 0$, having only $1$ spatial orientation ($m_l = 0$) and accommodating a maximum of $2$ electrons.

$p$ Orbital

A dumbbell-shaped orbital defined by $l = 1$, possessing $3$ distinct orientations ($p_x$, $p_y$, and $p_z$) and capable of holding up to $6$ electrons.

$d$ Orbital

A largely four-leaf clover-shaped orbital defined by $l = 2$, possessing $5$ distinct spatial orientations and capable of holding up to $10$ electrons.

$f$ Orbital

A multi-lobed orbital defined by $l = 3$, possessing $7$ distinct orientations and capable of accommodating up to $14$ electrons (represented by the lanthanide and actinide blocks).

PEL

An acronym used in lecture referring to the Principal Energy Level, directly designated by the quantum number $n$.

Electron Mass

A physical constant and property of an electron, given as $9.11 \times 10^{-31}\,\text{kg}$.

Rydberg's Constant (in Atomic Transitions)

The proportionality constant given as $-2.18 \times 10^{-18}\,\text{J}$, used to calculate energy changes during atomic electron transitions via $\Delta E = -2.18 \times 10^{-18}\,\text{J} \left(\frac{1}{n_f^2} - \frac{1}{n_i^2}\right)$.

Photon Energy Equation

The relationship used to calculate the energy of an emitted photon from its wavelength: $E = \frac{h c}{\lambda}$, where energy gained by the photon equals the energy lost by the relaxing atom.

Hydrogen Emission Line ($n = 3 \rightarrow n = 2$)

The electronic transition in hydrogen where an electron falls from the third to the second principal energy level, emitting a photon with a wavelength of $656\,\text{nm}$.