Atomic Structure, Mass Spectrometry, Periodic Trends, and Flame Emission Analysis

Subatomic Particles and Fundamental Mass Definitions

• Subatomic Particles Properties and Locations:

  • Proton:

  • Located within the nucleus.

  • Possesses a relative mass of $1$.

  • Carries a relative charge of $+1$.

  • Neutron:

  • Located within the nucleus.

  • Possesses a relative mass of $1$.

  • Carries a relative charge of $0$.

  • Electron:

  • Located in orbitals surrounding the nucleus.

  • Possesses a relative mass of $\frac{1}{1840}$.

  • Carries a relative charge of $-1$.

• Standard Definitions of Relative Masses:

  • Relative Atomic Mass ($A_r$): The average mass of an atom of an element relative to $\frac{1}{12}$ the mass of a carbon-12 atom.

  • Relative Molecular Mass ($M_r$): The average mass of a molecule relative to $\frac{1}{12}$ the mass of a carbon-12 atom. It is determined by summing the relative atomic masses of all individual atoms present in the molecular formula.

  • Relative Isotope Mass: The mass of a single atom of a specific isotope relative to $\frac{1}{12}$ the mass of a carbon-12 atom.

• Isotopes Versus Isomers:

  • Isotopes:

  • Defined as atoms of the same element containing the identical number of protons and identical number of electrons, but possessing different numbers of neutrons.

  • Share the same atomic number but feature different mass numbers.

  • Exhibit virtually identical chemical properties due to having identical electron configurations.

  • Exhibit different physical properties, such as mass and density.

  • Isomers:

  • Chemical species possessing the identical molecular formula but distinct structural formulae.

  • Their distinct structural arrangements confer differing physical and chemical properties.

Mass Spectrometry and Isotopic Analysis

• Applications of Mass Spectrometry:

  • Separating individual atoms and molecules on the basis of their mass.

  • Identifying organic molecules.

  • Determining the relative abundances of isotopes.

  • Identifying ions by determining their mass-to-charge ratio, designated as $m/z$.

• Operating Principles of the Mass Spectrometer:

  • Measures the mass-to-charge ratio ($m/z$) of ions.

  • Because most ions generated carry a single positive charge of $+1$, the resulting $m/z$ value directly corresponds to the isotopic mass of the ion.

• Sequential Stages of Mass Spectrometry:

  • 1. Ionisation: Atoms or molecules are converted into positive ions, typically through bombardment with high-energy electrons that displace and remove electrons from the sample particles.

  • 2. Acceleration: The resulting positive ions are accelerated by an electric field so that all ions attain equal or comparable kinetic energies.

  • 3. Ion Drift or Deflection: Ions are separated based on their distinct mass-to-charge ratios ($m/z$). Lighter ions and ions carrying a greater positive charge experience a greater degree of deflection than heavier or lesser-charged ions.

  • 4. Detection: Positive ions strike a detector, generating an electric current signal. The magnitude of the electrical signal is directly proportional to the relative abundance of the arriving ion.

• Mass Spectrum Characteristics:

  • Displays peaks corresponding to specific mass-to-charge ($m/z$) values.

  • The position of an individual peak specifies the identity of the ion, whereas the peak intensity indicates its relative abundance.

• Isotopic Abundance and Molecular Ion Peaks of Chlorine ($\text{Cl}_2$):

  • Naturally Occurring Isotopes of Chlorine:

  • ${}^{35}\text{Cl}$ accounts for an abundance of $75\%$ ($\frac{3}{4}$).

  • ${}^{37}\text{Cl}$ accounts for an abundance of $25\%$ ($\frac{1}{4}$).

  • Monatomic Ions:

  • Ionisation forms ${}^{35}\text{Cl}^+$ and ${}^{37}\text{Cl}^+$, yielding peaks at $m/z = 35$ and $m/z = 37$.

  • The ratio of peak heights for the atomic ions is $3 : 1$.

  • Diatomic Molecular Ions ($\text{Cl}_2^+$):

  • ${}^{35}\text{Cl}-{}^{35}\text{Cl}^+$, generating a molecular-ion peak at $m/z = 70$.

    • Relative intensity: $\frac{3}{4} \times \frac{3}{4} = \frac{9}{16}$

  • ${}^{35}\text{Cl}-{}^{37}\text{Cl}^+$ or ${}^{37}\text{Cl}-{}^{35}\text{Cl}^+$, generating a molecular-ion peak at $m/z = 72$.

    • Relative intensity: $2 \times \frac{3}{4} \times \frac{1}{4} = \frac{6}{16}$

  • ${}^{37}\text{Cl}-{}^{37}\text{Cl}^+$, generating a molecular-ion peak at $m/z = 74$.

    • Relative intensity: $\frac{1}{4} \times \frac{1}{4} = \frac{1}{16}$

  • Produces three molecular-ion peaks at $m/z = 70$, $72$, and $74$ in an intensity ratio of $9 : 6 : 1$.

Ionisation Energy and Periodic Trends

• Ionisation Energy Definitions and Equations:

  • First Ionisation Energy: The energy required to remove one mole of electrons from one mole of gaseous atoms to form one mole of gaseous $1+$ ions.     $X(g) \rightarrow X^+(g) + e^-$

  • Second Ionisation Energy: The energy required to remove one mole of electrons from one mole of gaseous $1+$ ions to form one mole of gaseous $2+$ ions.     $X^+(g) \rightarrow X^{2+}(g) + e^-$

  • Comparison Between Successive Ionisation Energies: The second ionisation energy is invariably higher than the first ionisation energy because the electron is removed from an already positively charged ion, causing the remaining electrons to experience a significantly stronger electrostatic attraction toward the nucleus.

• Ionisation Energy Trend Down a Group:

  • Ionisation energy exhibits an overall decrease descending any group in the periodic table.

  • While the absolute nuclear charge increases due to additional protons, this effect is outweighed by:

  • Increasing Atomic Radius: Valence electrons are located in shells progressively farther from the nucleus.

  • Increasing Electron Shielding: Additional inner electron shells repel the outermost valence electrons, diminishing the net nuclear pull.

  • Consequently, the outermost electron requires less energy to remove.

• Ionisation Energy Trend Across a Period:

  • Ionisation energy exhibits a general increase traversing left to right across a period due to:

  • Increasing nuclear charge resulting from the addition of protons to the nucleus.

  • Electrons occupying the same principal energy level, which keeps electron shielding relatively constant.

  • Decreasing atomic radius, pulling valence electrons closer to the nucleus.

  • Substantially stronger electrostatic attraction between the nucleus and the valence electron.

  • Discontinuities and Exceptions Across a Period:

  • Small decreases occur when an electron enters a subshell of higher energy (such as transitioning from an $s$ to a $p$ subshell).

  • Small decreases occur where two electrons must pair up within the same orbital; the resulting electron–electron repulsion destabilizes the pair and makes one electron easier to remove.

Atomic and Ionic Radii and Periodic Table Organization

• Atomic Radius Trends:

  • Down a Group: Atomic radius increases because additional principal electron shells are added to the atom.

  • Across a Period: Atomic radius decreases because the increasing positive nuclear charge exerts a stronger inward pull on electrons within the same shell.

• Ionic Radii Comparisons:

  • Positive Ions (Cations): Consistently smaller than their parent neutral atoms because the loss of one or more outer electrons reduces electron repulsion and can result in the complete shedding of the outermost principal shell.

  • Negative Ions (Anions): Consistently larger than their parent neutral atoms because the acquisition of extra electrons intensifies electron–electron repulsion, causing the electron cloud to expand outward.

• Periodic Table Blocks and Structure:

  • The periodic table is organized into blocks based on the identity of the subshell containing the highest-energy valence electrons:

  • $s$-block: Encompasses Group 1 and Group 2 elements.

  • $p$-block: Encompasses Groups 3 through 8 in modern numbering, excluding transition metals.

  • $d$-block: Encompasses the transition metals.

  • The principal period number corresponds directly to the highest occupied principal energy level.

Orbitals, Subshells, and Electronic Configuration

• Atomic Orbital Characteristics:

  • An atomic orbital represents a specific region of three-dimensional space surrounding the nucleus where there is a high probability of locating an electron, rather than a fixed physical orbit or path.

  • A single orbital can accommodate a maximum capacity of two electrons, which must possess opposite spins.

  • Electron shells are divided into subshells, which in turn consist of orbitals.

• Subshell Specifications:

  • $s$ Subshell:

  • Possesses a spherical geometry.

  • Contains $1$ orbital.

  • Accommodates a maximum of $2$ electrons.

  • $p$ Subshell:

  • Possesses a dumbbell geometry.

  • Contains $3$ orbitals.

  • Accommodates a maximum of $6$ electrons.

  • $d$ Subshell:

  • Possesses a more complex geometry.

  • Contains $5$ orbitals.

  • Accommodates a maximum of $10$ electrons.

• Aufbau Principle and Subshell Filling Hierarchy:

  • Electrons occupy available subshells in order of increasing energy:     $1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p$

  • The $4s$ subshell fills prior to the $3d$ subshell because it initially resides at a lower energy level.

• Transition Metal Anomalies in Electron Configuration:

  • While subshells typically fill progressively according to their capacities ($s = 2$, $p = 6$, $d = 10$), chromium and copper represent distinct exceptions to the expected Aufbau progression.

  • These elements promote an electron from the $4s$ subshell into the $3d$ subshell to achieve enhanced energetic stability associated with half-filled or fully filled $d$ subshells.

  • Chromium ($\text{Cr}$):     $\text{Cr}: 1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,3d^5\,4s^1$

  • Achieves stability via a precisely half-filled $3d^5$ subshell with a single $4s^1$ electron.

  • Copper ($\text{Cu}$):     $\text{Cu}: 1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,3d^{10}\,4s^1$

  • Achieves stability via a completely filled $3d^{10}$ subshell with a single $4s^1$ electron.

Flame Tests and Atomic Emission Spectroscopy

• Analytical Purpose and Procedure:

  • Flame tests serve as qualitative analytical procedures to identify the presence of specific metal ions.

  • A sample of the compound is introduced into a flame, typically supported on a clean metal wire.

• Physical Mechanism of Flame Color Production:

  • Excitation: Thermal energy from the flame is absorbed by the atom or ion, causing an electron to transition from its ground-state energy level to an unstable, higher energy level.

  • Relaxation and Emission: Because the excited state is inherently unstable, the electron spontaneously drops back down to a lower energy level.

  • Photon Release: The exact energy difference between the higher and lower energy levels is emitted as a photon of electromagnetic radiation.

  • Spectral Uniqueness: Every element possesses a unique arrangement of quantized electron energy levels, meaning the resulting energy differences, photon wavelengths, and perceived flame colors are uniquely characteristic of that specific element.

• Characteristic Cation Flame Colors:

  • Lithium ($\text{Li}^+$): Produces a crimson flame.

  • Sodium ($\text{Na}^+$): Produces a yellow flame.

  • Potassium ($\text{K}^+$): Produces a lilac flame.

  • Calcium ($\text{Ca}^{2+}$): Produces a red-orange flame.

  • Copper ($\text{Cu}^{2+}$): Produces a green flame.

• Analytical Limitations and Exceptions:

  • Flame tests are not universally definitive because specific colors can be challenging to differentiate visually.

  • Mixtures containing multiple distinct metal ions can mask individual emissions or interfere with observation.

  • Magnesium ($\text{Mg}$): Does not yield a characteristic visible flame color because the photons emitted during electron relaxation have wavelengths that fall outside the visible light spectrum.