Unit 1: CH01 Syllabus Node

Atomic Structure & TOF Mass Spectrometry

Subatomic particles, TOF mass spectrometry mechanics, electron configurations (Cr/Cu anomalies), and Period 3 ionisation energy trends.

1. Fundamental Subatomic Particles

Every atom consists of a dense central nucleus surrounded by an electron cloud. Three fundamental particles define atomic architecture:

Subatomic Particle Relative Charge Relative Mass Physical Location
Proton (\(p\)) +1 1 Nucleus
Neutron (\(n\)) 0 1 Nucleus
Electron (\(e^-\)) -1 1 / 1840 (0.00054) Orbitals outside nucleus

Atomic Number (\(Z\))

The number of protons in the nucleus of an atom. This quantity defines the chemical identity of the element.

Mass Number (\(A\))

The total number of nucleons (protons plus neutrons) in the nucleus: \[ A = Z + N \]

Isotopes

Atoms of the same element having the same number of protons (same atomic number \(Z\)), but different numbers of neutrons (different mass number \(A\)). Isotopes exhibit identical chemical properties because they have identical electron configurations, but possess slightly differing physical properties (such as density and rate of diffusion).

2. Time of Flight (TOF) Mass Spectrometry

Time of Flight mass spectrometry determines the mass-to-charge ratio (\(m/z\)) and abundance of isotopes and molecules. The operation proceeds through four distinct stages:

Time of Flight (TOF) Mass Spectrometer Schematic Stage 1: Ionisation EI: Knock out e- ESI: Add H+ proton Forms X+ / XH+ Stage 2: Accel Grid (-V) Constant KE = 1/2 m v^2 Stage 3: Drift Region (Flight Tube) Length d (Vacuum, no electric field) t = d * sqrt(m / 2KE) Lighter ions travel faster (arrive first) Light Ion Heavy Ion Stage 4: Detector Ions gain e- Current = count

Stage 1: Ionisation

The sample must be converted into positive ions. OxfordAQA specifies two techniques:

  • Electron Impact (EI): The vaporised sample is bombarded by high-energy electrons fired from an electron gun. A high-energy electron knocks out an outer shell electron: \[ \text{X}(g) \rightarrow \text{X}^+(g) + e^- \] This technique creates molecular ions with high internal energy, causing extensive fragmentation. It is used for elements and low-mass organic molecules.
  • Electrospray Ionisation (ESI): The sample is dissolved in a volatile solvent (such as methanol or water) and forced through a fine hypodermic needle connected to a high positive voltage supply (+3 kV). As droplets enter the vacuum, solvent evaporates and the molecule gains a proton (\(\text{H}^+\)): \[ \text{X}(g) + \text{H}^+(aq) \rightarrow \text{XH}^+(g) \] ESI is a soft ionisation technique that produces minimal fragmentation. The molecular mass of the parent compound is obtained by subtracting 1 from the observed peak: \(M_r = (m/z) - 1\).

Stage 2: Acceleration

Positive ions are accelerated towards a negatively charged electric plate. All ions acquire the same kinetic energy (\(\text{KE}\)):

\[ \text{KE} = \frac{1}{2} m v^2 \]

Stage 3: Ion Drift

Ions pass through a flight tube of length \(d\) under high vacuum with no electric field. Their velocity is inversely proportional to the square root of their mass:

\[ v = \sqrt{\frac{2\text{KE}}{m}} \quad \implies \quad t = \frac{d}{v} = d \sqrt{\frac{m}{2\text{KE}}} \]

Because kinetic energy and tube length are constant, lighter ions travel at higher velocities and arrive at the detector in a shorter flight time.

Stage 4: Detection

Positive ions strike the negatively charged detector plate. Each ion accepts one or more electrons from the plate, neutralizing its charge. This electron flow produces a tiny electric current. The size of the current is directly proportional to the abundance of that ion.

Worked Example: TOF Flight Time Calculation
In a TOF mass spectrometer with a 1.50 m flight tube, an ion of mass 1.16 x 10^-25 kg arrives at the detector in 2.80 x 10^-5 s. Calculate the kinetic energy of the ion, and determine the flight time of an ion of mass 1.45 x 10^-25 kg under identical acceleration.

Step 1: Calculate velocity of the first ion:

\[ v_1 = \frac{d}{t_1} = \frac{1.50}{2.80 \times 10^{-5}} = 53571.4\text{ m s}^{-1} \]

Step 2: Calculate kinetic energy:

\[ \text{KE} = \frac{1}{2} m_1 v_1^2 = 0.5 \times (1.16 \times 10^{-25}) \times (53571.4)^2 = 1.6645 \times 10^{-16}\text{ J} \]

Step 3: Calculate flight time for the second ion:

Since both ions possess identical kinetic energy:

\[ \frac{t_2}{t_1} = \sqrt{\frac{m_2}{m_1}} = \sqrt{\frac{1.45 \times 10^{-25}}{1.16 \times 10^{-25}}} = \sqrt{1.25} = 1.11803 \]

\[ t_2 = 2.80 \times 10^{-5} \times 1.11803 = \mathbf{3.13 \times 10^{-5}\text{ s}} \]

3. Electronic Configuration

Electrons reside in principal energy levels (\(n = 1, 2, 3, 4\)) divided into subshells (\(s, p, d, f\)):

  • \(s\)-subshell: 1 orbital (holds maximum 2 electrons).
  • \(p\)-subshell: 3 degenerate orbitals (holds maximum 6 electrons).
  • \(d\)-subshell: 5 degenerate orbitals (holds maximum 10 electrons).
  • \(f\)-subshell: 7 degenerate orbitals (holds maximum 14 electrons).

Transition Metal Anomalies

Chromium (\(Z = 24\)) and Copper (\(Z = 29\))

Chromium and copper do not follow the standard Aufbau filling sequence due to the extra stability of half-filled and fully-filled \(3d\) subshells:

  • Chromium (Cr): \(1s^2 2s^2 2p^6 3s^2 3p^6 3d^5 4s^1\) (or \([\text{Ar}] 3d^5 4s^1\)), NOT \(3d^4 4s^2\).
  • Copper (Cu): \(1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^1\) (or \([\text{Ar}] 3d^{10} 4s^1\)), NOT \(3d^9 4s^2\).

Ion Formation Rule: When transition metals form positive ions, electrons are lost from the \(4s\) orbital before the \(3d\) orbitals. For example, \(\text{Fe}^{2+}\) is \([\text{Ar}] 3d^6\), having lost both \(4s\) electrons.

4. First Ionisation Energy Trends

First Ionisation Energy

The enthalpy change required to remove one mole of electrons from one mole of gaseous atoms to form one mole of gaseous 1+ ions under standard conditions: \[ \text{X}(g) \rightarrow \text{X}^+(g) + e^- \]

First Ionisation Energy Trend Across Period 3 Period 3 Elements First IE (kJ / mol) 0 500 1000 1500 Na Mg Al Si P S Cl Ar Al Dip: 3p1 electron shielded by 3s2 S Dip: 3p4 spin-pairing orbital repulsion

Period 3 General Increase & Anomalies

Across Period 3 (Na to Ar), first ionisation energy exhibits a general increase because nuclear charge increases (more protons) while electrons are added to the same energy shell with similar shielding, drawing valence electrons closer.

Anomaly 1: Aluminium Dip (\(3p^1\))

Aluminium (\(578\text{ kJ mol}^{-1}\)) has a lower first ionisation energy than Magnesium (\(738\text{ kJ mol}^{-1}\)).

Reason: In Mg, the electron is removed from the \(3s\) subshell. In Al, the electron is removed from the higher energy \(3p\) subshell, which is shielded by the inner \(3s^2\) electrons.

Anomaly 2: Sulfur Dip (\(3p^4\))

Sulfur (\(1000\text{ kJ mol}^{-1}\)) has a lower first ionisation energy than Phosphorus (\(1012\text{ kJ mol}^{-1}\)).

Reason: In P, all three \(3p\) orbitals contain a single electron (\(3p_x^1 3p_y^1 3p_z^1\)). In S, one \(3p\) orbital contains a paired set of electrons (\(3p_x^2 3p_y^1 3p_z^1\)). Spin-pair repulsion between the two electrons in the same orbital makes that electron easier to remove.

Trend Down Group 2

First ionisation energy decreases down Group 2 (Be to Ba). Although nuclear charge increases down the group, atomic radius increases significantly and there are more intervening electron shells. The increased distance and electron shielding weaken electrostatic attraction to the nucleus.

5. Practice Questions

Practice Problem (3 Marks)
State and explain the general trend in first ionisation energy across Period 3 from sodium to argon, and write an equation including state symbols for the first ionisation energy of sodium.

Equation: \(\text{Na}(g) \rightarrow \text{Na}^+(g) + e^-\) (1 mark)

Trend & Explanation:

  • General increase across the period. (1 mark)
  • Nuclear charge increases (more protons) while electron shielding remains approximately constant because electrons enter the same third quantum shell. The stronger attraction pulls valence electrons closer, requiring more energy to remove an electron. (1 mark)