Electron Configuration: Subshell Notation

Q1 — Sample Band 6 response (8 marks), annotated

Unpaired electrons and paramagnetism: Paramagnetic behaviour arises because electrons have an intrinsic spin — either spin-up (↑) or spin-down (↓). The Pauli exclusion principle requires that two electrons sharing an orbital must have opposite spins, causing their magnetic moments to cancel. An unpaired electron has a net spin magnetic moment that is not cancelled; in an external magnetic field it aligns with the field, creating an attractive force. The greater the number of unpaired electrons, the stronger the paramagnetic attraction [1 mark — mechanism linking Pauli exclusion, spin cancellation, and paramagnetism].

Chromium and 6 unpaired electrons: The abbreviated configuration [Ar]3d⁵4s¹ means the 3d subshell contains 5 electrons (one in each of the 5 d orbitals by Hund’s rule — all singly occupied, all parallel spin) and the 4s subshell contains 1 electron (also unpaired). This gives 5 + 1 = 6 unpaired electrons in total, which is why Cr is more strongly paramagnetic than Mn (which has 5 unpaired 3d electrons but 2 paired 4s electrons = 5 unpaired total). The anomalous promotion of one 4s electron to complete the half-filled 3d subshell both maximises exchange stability and maximises unpaired electron count [1 mark — correct analysis of 5 d + 1 s unpaired electrons with reference to Hund’s rule].

Niobium anomaly: Expected configuration for Nb (Z=41) would be [Kr]4d³5s², but the actual is [Kr]4d⁴5s¹. This occurs because a greater number of d electrons increases exchange energy (the stabilising interaction between electrons with parallel spins). Promoting one 5s electron into the 4d subshell raises the 4d occupancy from 3 to 4; combined with 1 unpaired 5s electron, this gives 5 unpaired electrons total. The energy gained from the additional exchange interactions in 4d⁴ exceeds the energy cost of the promotion, making the anomalous configuration more stable [1 mark — exchange energy and extra d-subshell stability explanation].

Copper prediction: Copper has the anomalous configuration [Ar]3d¹⁰4s¹. The 3d¹⁰ subshell is completely filled: each of the 5 d orbitals contains 2 electrons with opposite spins, so all d electrons are paired (0 unpaired). The single 4s¹ electron is unpaired (1 unpaired electron). Therefore Cu has 1 unpaired electron and is weakly paramagnetic in this configuration [1 mark — correct prediction of 1 unpaired electron and paramagnetic behaviour].

Limitation: One limitation is that unpaired electron count is calculated for isolated atoms in the ground state, but in real metals the electrons occupy delocalised band states, not discrete atomic orbitals. The actual magnetic behaviour of a bulk metal depends on band structure, exchange coupling between neighbouring atoms, and temperature — for example, iron (Fe) is ferromagnetic (permanent magnet), not just paramagnetic, due to cooperative alignment of electron spins across domains, which cannot be predicted from the atomic configuration alone [1 mark — valid limitation referencing difference between atomic and bulk/solid-state behaviour].

Marking criteria summary (8 marks): 1 = explains paramagnetism via unpaired electron spin and Pauli exclusion. 1 = correctly accounts for Cr having 6 unpaired electrons (5 from 3d⁵ by Hund’s + 1 from 4s¹). 1 = explains Nb anomaly using exchange energy / d-subshell stability driving the promotion. 1 = predicts Cu has 1 unpaired electron (paired 3d¹⁰ + unpaired 4s¹) and is paramagnetic. 1 = states a valid limitation of the atomic model for bulk magnetism. 1 = uses precise quantum terminology throughout (Pauli exclusion, Hund’s rule, exchange energy, spin, paramagnetic). 1 = integrates the data table correctly (references at least two elements by configuration). 1 = reaches an explicit evaluative conclusion connecting electron configuration to observable magnetic property.

Q2 — Sample Band 6 response (7 marks), annotated

Hypothesis: If each element has a unique electron configuration, then heating a pure sample will produce a unique set of emission lines corresponding to the specific energy differences between electron subshells in that element. Comparing observed emission wavelengths to a reference database will allow identification of the element and determination of its electron configuration. Independent variable: the identity of the unknown element. Dependent variable: the wavelengths of emission lines observed in the spectrum. [1 mark]

Procedure: (1) Place a small sample of the unknown metal on a platinum wire loop; heat in a hot flame or arc discharge to excite the electrons to higher energy subshells. (2) Pass the emitted light through the spectrometer prism/grating; record all visible emission lines and their wavelengths in nm. (3) Compare the observed wavelengths to the published emission line database for elements Z = 1–36; identify the element by the unique pattern of its characteristic lines. (4) Using the identified element’s Z value, apply the Aufbau principle to construct the ground-state electron configuration — fill subshells 1s, 2s, 2p, 3s… in energy order; apply Hund’s rule within each subshell (fill singly before pairing) and the Pauli exclusion principle (max 2 electrons per orbital with opposite spins). Record full and abbreviated configurations. [1 mark — four steps including a comparison to reference data]

Application of Aufbau and Hund’s rule: The emission spectrum reflects which subshells are occupied in the excited atom because electrons return from specific high-energy subshells to lower ones. To determine the ground-state configuration, the Aufbau principle orders filling from 1s upward in energy; within each subshell, Hund’s rule specifies that all orbitals receive one electron with parallel spins before any is doubly filled. This ensures the maximum number of half-filled orbitals and minimum electron repulsion, consistent with the lowest-energy (ground-state) configuration observed spectroscopically [1 mark].

Falsification: If the emission spectrum of the unknown sample matches no single element in the reference database, or if two different samples produce identical spectra, the hypothesis would be falsified — the spectral pattern does not uniquely map to one electron configuration [1 mark].

Limitations: (1) If the sample contains even trace impurities of another element, additional emission lines will appear and could be misidentified as part of the unknown element’s spectrum, leading to incorrect identification [1 mark]. (2) Elements with similar Z values (e.g. Ni Z=28 and Co Z=27) have closely spaced emission lines; low spectral resolution may fail to distinguish them, producing ambiguous results [1 mark].

Improvement: Use a high-resolution inductively coupled plasma optical emission spectrometer (ICP-OES) which provides sub-nm resolution and can identify trace elements; repeat with a second technique (e.g. X-ray fluorescence) to cross-validate the identification [1 mark].

Marking criteria summary (7 marks): 1 = testable hypothesis linking emission lines to electron configuration; 1 = four clear procedural steps including comparison to reference data; 1 = correct application of Aufbau and Hund’s in configuration writing; 1 = states a valid falsification condition; 1 = first valid limitation; 1 = second valid limitation; 1 = one specific, practical improvement.