Question

Niobium \((\mathrm{Nb} ; Z=41)\) has an anomalous ground-state electron configuration for a Group \(5 \mathrm{~B}(5)\) element: \([\mathrm{Kr}] 5 s^{1} 4 d^{4} .\) What is the expected electron configuration for elements in this group? Draw partial orbital diagrams to show how paramagnetic measurements could support niobium's actual configuration.

Short answer

The expected electron configuration is \text{[Kr]} \(5s^2 4d^3\). Niobium's actual configuration \text{[Kr]} \(5s^1 4d^4\) is more stable, confirmed by stronger paramagnetism.

Step-by-step solution

- Identify the expected electron configuration

For Group 5 elements, the expected electron configuration typically follows the pattern of having electrons fill the 's' and 'd' orbitals. Elements in this group generally have the configuration of \text{[Noble Gas]} \(ns^2 (n-1)d^3\). For Niobium (Nb, \(Z=41\)), following this rule, the expected electron configuration would be \text{[Kr]} \(5s^2 4d^3\).

- Note the actual electron configuration of Niobium

The actual electron configuration of Niobium is given as \text{[Kr]} \(5s^1 4d^4\). This is an anomalous configuration, meaning it does not follow the general expected pattern.

- Explain electron configurations and stability

The stability of electron configurations often involves the lower energy coming from half-filled and fully-filled subshells. For Niobium, having one electron in the \(5s\) orbital and four in the \(4d\) orbital may provide greater stability via exchange energy and reduced electron-electron repulsion in the \(d\) orbitals.

- Draw partial orbital diagrams

To show how paramagnetic measurements support Niobium's actual configuration, consider the spin of electrons. The expected configuration \text{[Kr]} \(5s^2 4d^3\) would result in the \(4d\) orbital having three unpaired electrons, showing paramagnetism. However, the actual configuration \text{[Kr]} \(5s^1 4d^4\) results in the \(4d\) orbital having four unpaired electrons, showing stronger paramagnetism.Expected configuration: \(4d\): \( \uparrow\downarrow \uparrow \uparrow \downarrow \)Actual configuration: \(4d\): \( \uparrow\uparrow \uparrow \uparrow \downarrow \)

- Summarize findings

Niobium's actual electron configuration of \text{[Kr]} \(5s^1 4d^4\) is more stable and supported by paramagnetic measurements showing four unpaired electrons. This configuration leads to stronger paramagnetism than the expected configuration.

Key concepts

Paramagnetism

Paramagnetism occurs when a material has unpaired electrons in its atomic or molecular structure. These unpaired electrons have magnetic moments that align with an external magnetic field, causing the material to be attracted to the magnetic field. In the context of Niobium's electron configuration, the actual configuration [Kr] 5s^1 4d^4 leads to four unpaired electrons in comparison to the expected configuration [Kr] 5s^2 4d^3, which has three unpaired electrons. When we measure the paramagnetism of Niobium, the presence of these four unpaired electrons results in a stronger paramagnetic behavior, supporting the stated actual configuration.
This difference in the number of unpaired electrons is crucial for understanding why Niobium's configuration is more strongly paramagnetic than expected. In simpler terms, more unpaired electrons mean a higher magnetic susceptibility.

Electron Configuration Stability

The stability of an element's electron configuration largely depends on the energy levels of the orbitals and the arrangement of electrons within those orbitals. Stability can often be enhanced by achieving half-filled or fully-filled subshells. In the case of Niobium, the actual electron configuration [Kr] 5s^1 4d^4 showcases a higher stability than the expected [Kr] 5s^2 4d^3. This is because having four electrons in the 4d subshell reduces electron-electron repulsion and achieves a more stable energy state through exchange energy. Exchange energy is the stabilization gained when electrons with parallel spins exchange places, leading to less repulsion among them.
Niobium's configuration is an example where the anomaly provides greater stability, despite not following the general filling order predicted by the Aufbau principle. Such exceptions emphasize the intricate balance between various energy considerations in determining the most stable electron configuration for an element.

Orbital Diagrams

Orbital diagrams are visual representations of the electron configuration of an element, showing how electrons occupy different orbitals. Each orbital is represented by a box, and electrons are shown as arrows within these boxes. The arrows represent the spins of the electrons.
For Niobium, the expected configuration [Kr] 5s^2 4d^3 would be illustrated with the 5s orbital containing both electrons paired, and the 4d orbital containing three unpaired electrons. In contrast, Niobium's actual configuration [Kr] 5s^1 4d^4 is shown with one unpaired electron in the 5s orbital and four unpaired electrons in the 4d orbital.
Here’s the partial orbital diagram for both configurations:
Expected:
- 5s: ↑↓
- 4d: ↑ ↓ ↑

Actual:
- 5s: ↑
- 4d: ↑ ↑ ↑ ↑
These diagrams visually underscore why Niobium has more unpaired electrons, corroborating its stronger paramagnetic properties.