Quantum Chemistry and Electron Configurations

Comprehensive question-and-answer study flashcards covering quantum chemistry, wave equations, Bohr theory, quantum numbers, electron configurations, and periodic trends.

What is the relationship between wave frequency and energy?

Wave frequency and energy are directly proportional: less frequency means less energy, and more frequency means more energy.

What is the relationship between wavelength and frequency?

Wavelength and frequency have an inverse relationship; as wavelength increases, frequency decreases.

What formula relates wave speed, frequency, and wavelength, and what is the speed of light?

The formula is $\text{speed of wave} = \text{frequency} \times \text{wavelength}$, and the speed of light is $c = 3.00 \times 10^8\,\text{m/s}$.

What is the frequency of light having a wavelength of $681\,\text{nm}$?

$\text{frequency} = \frac{3.00 \times 10^8\,\text{m/s}}{681 \times 10^{-9}\,\text{m}} = 4.41 \times 10^{14}\,\text{s}^{-1}$ (or $\text{Hz}$).

Based on the provided wave diagram, what two wave properties are specifically labeled?

Wavelength (the distance between consecutive wave crests) and amplitude (the displacement from the centerline to a crest or trough).

How are refraction, diffraction, and interference defined for waves?

Refraction is bending when passing between media; diffraction is bending around an edge or through narrow openings; and interference is when wave amplitudes reinforce or cancel each other.

How does the Doppler effect apply to light according to the notes?

The further the object is from light, the longer the wavelength.

What is the formula for the energy of quantum radiation, and what is the value of Planck's constant ($h$)?

$E = h \times \text{frequency} = \frac{hc}{\text{wavelength}}$, where $h = 6.6260755 \times 10^{-34}\,\text{J}\cdot\text{s}$.

What is the work function in the photoelectric effect?

The minimum energy required to release an electron ($\text{e}^-$) from a metal surface, equal to $h \times (\text{threshold frequency})$.

What is the equation for the kinetic energy of an electron in the photoelectric effect?

$KE = h(\text{frequency}) - \text{work function} = E_{\text{photon}} - E_{\text{binding}}$. If $E_{\text{photon}} > E_{\text{binding}}$, the electron will move; a negative value means it will not move.

What is the kinetic energy of an electron emitted from strontium by light with a wavelength of $4.2 \times 10^{-7}\,\text{m}$, given a binding energy of $4.39 \times 10^{-19}\,\text{J}$?

$KE = 3.43 \times 10^{-20}\,\text{J}$, calculated by subtracting $E_{\text{binding}} = 4.39 \times 10^{-19}\,\text{J}$ from $E_{\text{photon}} = \frac{hc}{\lambda} = \frac{(6.626 \times 10^{-34}\,\text{J}\cdot\text{s})(3.00 \times 10^8\,\text{m/s})}{4.2 \times 10^{-7}\,\text{m}} = 4.733 \times 10^{-19}\,\text{J}$.

How do emission and absorption spectra differ?

Emission spectra consist of bright lines at discrete wavelengths, whereas absorption spectra consist of a characteristic series of dark lines.

What do upward and downward arrows indicate on an electronic energy level diagram?

An upward arrow ($\uparrow$) indicates absorption (absorbing a photon to enter an excited state), while a downward arrow ($\downarrow$) indicates emission (electron transition to a lower state, releasing energy).

If an electron transitions such that $E_1 = E_2 + E_3$, and $\lambda_2 = 1200\,\text{nm}$ and $\lambda_3 = 600\,\text{nm}$, what is $\lambda_1$?

$\frac{1}{\lambda_1} = \frac{1}{\lambda_2} + \frac{1}{\lambda_3} = \frac{1}{1200} + \frac{1}{600} = 0.0025$, so $\lambda_1 = \frac{1}{0.0025} = 400\,\text{nm}$.

What is Bohr's formula for the energy levels of a hydrogen atom, and to what systems does it apply?

$E_{\text{electron}} = -\frac{R_H}{n^2}$, where $R_H = 2.178 \times 10^{-18}\,\text{J}$ (or $2.179 \times 10^{-18}\,\text{J}$) and $n = 1, 2, 3\dots$. This formula applies only to hydrogen and hydrogen-like ions.

What wavelength of light is released when an electron in a hydrogen atom drops from $n_i = 6$ to $n_f = 3$?

$\lambda = 1.095 \times 10^{-6}\,\text{m}$, calculated from $\Delta E_{\text{electron}} = -(2.179 \times 10^{-18}\,\text{J})\left(\frac{1}{3^2} - \frac{1}{6^2}\right) = -1.816 \times 10^{-19}\,\text{J}$ and $\lambda = \frac{hc}{|\Delta E|}$.

What is de Broglie's equation and what principle does it establish?

$\lambda = \frac{h}{mv}$, which gives the wavelength of an object with mass $m$ and velocity $v$, treating electrons as having both particle and wave properties.

What does Heisenberg's Uncertainty Principle state, and what is its mathematical expression?

You cannot determine the precise position and momentum of an electron simultaneously; its mathematical formula is $\Delta x \cdot m\Delta v \ge \frac{h}{4\pi}$.

What do the first three quantum numbers ($n$, $l$, and $m_l$) describe?

The principal quantum number ($n$) describes the shell and relative size; the angular momentum quantum number ($l$) describes the orbital shape and subshell ($l = 0 \rightarrow n-1$); and the magnetic quantum number ($m_l$) describes the orbital orientation around the nucleus ($m_l = -l \rightarrow +l$).

Which subshell letter notations correspond to the angular momentum quantum numbers $l = 0, 1, 2, 3, 4, 5$?

$l = 0 \rightarrow s$, $l = 1 \rightarrow p$, $l = 2 \rightarrow d$, $l = 3 \rightarrow f$, $l = 4 \rightarrow g$, and $l = 5 \rightarrow h$.

For principal quantum level $n = 5$, what are the subshells, total number of orbitals, and total electron capacity?

The subshells are $5s, 5p, 5d, 5f$, and $5g$; the total number of orbitals is $n^2 = 25$; and the total electron capacity is $2n^2 = 50\,\text{e}^-$.

What are the allowed values for the spin magnetic quantum number ($m_s$), and what does the Pauli exclusion principle state?

$m_s = +\frac{1}{2}$ or $-\frac{1}{2}$. The Pauli exclusion principle states that no two electrons in an atom can have the same set of four quantum numbers.

What are the characteristic shapes of $s$, $p$, and $d$ orbitals based on electron density?

An $s$ orbital is spherical, a $p$ orbital is dumbbell-shaped (two lobes), and a $d$ orbital is cloverleaf-shaped (four lobes).

What is the definition of degenerate orbitals?

Orbitals that have the exact same energy level.

What is the noble gas electron configuration of platinum ($\text{Pt}$)?

$[\text{Xe}] 6s^2 4f^{14} 5d^8$.

From which subshell do transition metals lose electrons first when forming cations?

Transition metals lose valence electrons from the highest principal quantum number ($n$) value first (the outermost $s$ subshell) before losing electrons from the inner $d$ subshell.

What are the electron configurations of neutral iron ($\text{Fe}$), $\text{Fe}^{2+}$, and $\text{Fe}^{3+}$?

$\text{Fe} = [\text{Ar}] 4s^2 3d^6$, $\text{Fe}^{2+} = [\text{Ar}] 3d^6$ (loss of the $4s$ valence electrons), and $\text{Fe}^{3+} = [\text{Ar}] 3d^5$ (further loss of one $3d$ electron to achieve a stable half-filled $d$ subshell).

What are isoelectronic ions?

Ions that have identical electron configurations, such as $\text{Mg}^{2+}$ ($\text{Mg} \rightarrow \text{Mg}^{2+} + 2\text{e}^-$) and $\text{O}^{2-}$ ($\text{O} + 2\text{e}^- \rightarrow \text{O}^{2-}$), both having the $[\text{Ne}]$ configuration.

How do paramagnetic and diamagnetic materials differ in their magnetic properties?

Paramagnetic materials are weakly attracted to a magnetic field because they contain unpaired electrons, whereas diamagnetic materials are not attracted because all of their electrons are paired.

What are the periodic trends for atomic radius across a period and down a group?

Atomic radius increases down a group due to having more shells, and decreases across a period from left to right due to increased nuclear charge pulling electrons closer.

How does ion size compare between cations, anions, and members of an isoelectronic series?

Cations are smaller than their parent atoms due to loss of electrons; anions are larger due to gain of electrons; and within an isoelectronic series, more protons result in a smaller radius (e.g., $\text{Be}^{2+}$ is smaller than $\text{Li}^+$).

What is ionization energy (IE), and what are its general periodic trends?

Ionization energy is the energy required to remove $1\,\text{mol}$ of electrons from gaseous atoms or ions (in $\text{kJ/mol}$). It increases from left to right across a period and increases from bottom to top up a group.

On this table of successive ionization energies, what is signified by the red step-line?

It marks the point of breaking into the core electrons, which requires a massive increase in ionization energy compared to removing valence electrons.

Why is the first ionization energy of boron ($\text{B}$) lower than that of beryllium ($\text{Be}$)?

Boron's outermost electron enters the higher-energy $2p$ subshell ($2s^2 2p^1$), making it easier to remove to leave an empty $2p$ subshell, whereas beryllium has a completely filled $2s^2$ subshell.

Why is the first ionization energy of oxygen ($\text{O}$) lower than that of nitrogen ($\text{N}$)?

Oxygen has a paired electron in its $2p$ subshell ($2p^4$); electron-electron repulsion makes this paired electron easier to remove because doing so results in a stable, half-filled $2p^3$ subshell.

What is electron affinity (EA), and what is its periodic trend?

Electron affinity is the energy released when $1\,\text{mol}$ of gaseous atoms gains electrons to become anions ($\text{Cl} + \text{e}^- \rightarrow \text{Cl}^-$); more energy is released (EA increases) the smaller the atomic radius (up a group and to the right across a period).

Why do Group 2 elements have an electron affinity near zero ($\approx 0$)?

Group 2 elements have a completely filled $s$ subshell ($s^2$); adding an electron requires placing it into a higher-energy, completely empty $p$ subshell.