Question

Write the condensed electron configurations for the following atoms and indicate how many unpaired electrons each has: (a) Mg, (b) Ge, (c) Br, (d) V, (e) \(\mathrm{Y}\), (f) Lu.

Short answer

The condensed electron configurations and number of unpaired electrons for the given elements are: (a) Mg: [Ne] 3s² (0 unpaired electrons), (b) Ge: [Ar] 4s² 3d¹⁰ 4p² (2 unpaired electrons), (c) Br: [Ar] 4s² 3d¹⁰ 4p⁵ (1 unpaired electron), (d) V: [Ar] 4s² 3d³ (3 unpaired electrons), (e) Y: [Kr] 5s² 4d¹ (1 unpaired electron), (f) Lu: [Xe] 6s² 4f¹⁴ 5d¹ (1 unpaired electron).

Step-by-step solution

Find the electron configurations

To find the electron configuration of each element, we need to know the atomic numbers, which indicate the number of electrons for an atom in its ground state. The electron configuration shows the distribution of electrons in the atom's energy levels and orbitals. (a) Mg (magnesium) - atomic number: 12 Full electron configuration: 1s² 2s² 2p⁶ 3s² (b) Ge (germanium) - atomic number: 32 Full electron configuration: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p² (c) Br (bromine) - atomic number: 35 Full electron configuration: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁵ (d) V (vanadium) - atomic number: 23 Full electron configuration: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d³ (e) Y (yttrium) - atomic number: 39 Full electron configuration: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹ (f) Lu (lutetium) - atomic number: 71 Full electron configuration: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹⁰ 5p⁶ 6s² 4f¹⁴ 5d¹

Condensed electron configurations

To find the condensed electron configuration, we replace the core electron configuration with the symbol of the noble gas that precedes each element in the periodic table. (a) Mg: [Ne] 3s² (b) Ge: [Ar] 4s² 3d¹⁰ 4p² (c) Br: [Ar] 4s² 3d¹⁰ 4p⁵ (d) V: [Ar] 4s² 3d³ (e) Y: [Kr] 5s² 4d¹ (f) Lu: [Xe] 6s² 4f¹⁴ 5d¹

Unpaired electrons

To find the unpaired electrons, we examine the electron configuration for any partially filled orbitals. The number of unpaired electrons in these orbitals is the number of unpaired electrons for the element. (a) Mg: [Ne] 3s² - no unpaired electrons (0 unpaired electrons) (b) Ge: [Ar] 4s² 3d¹⁰ 4p² - two unpaired electrons in the p orbital (2 unpaired electrons) (c) Br: [Ar] 4s² 3d¹⁰ 4p⁵ - one unpaired electron in the p orbital (1 unpaired electron) (d) V: [Ar] 4s² 3d³ - three unpaired electrons in the d orbital (3 unpaired electrons) (e) Y: [Kr] 5s² 4d¹ - one unpaired electron in the d orbital (1 unpaired electron) (f) Lu: [Xe] 6s² 4f¹⁴ 5d¹ - one unpaired electron in the d orbital (1 unpaired electron)

Key concepts

Atomic Number

The atomic number of an element is a fundamental concept in chemistry that identifies the number of protons in the nucleus of an atom. It is represented by the symbol 'Z' and is unique to each element, determining its position on the periodic table.

For example, magnesium (Mg) has an atomic number of 12, meaning it contains 12 protons in its nucleus. Similarly, germanium (Ge) has an atomic number of 32, indicating it has 32 protons. The atomic number also tells us the number of electrons orbiting in the neutral atom, which is essential for determining its electron configuration.

Unpaired Electrons

Unpaired electrons refer to the electrons in an atom that are not part of an electron pair. Electron pairs occur when two electrons occupy the same orbital and have opposite spins, thereby stabilizing the atom.

When orbitals are not fully filled, they can contain unpaired electrons, which are important for understanding the chemical behavior of elements, particularly their magnetic properties and reactivity. For instance, in germanium (Ge), there are two unpaired electrons found in the 4p orbital, while vanadium (V) has three unpaired electrons in the 3d orbitals. These unpaired electrons can participate in chemical bonding or cause paramagnetism in the element.

Orbital Distribution

Orbital distribution explains how electrons are arranged around the nucleus of an atom. Electrons occupy regions called orbitals in a hierarchical order based on increasing energy levels.

Each orbital can hold a maximum of two electrons, and the distribution follows a specific order known as the Aufbau principle, which fills the lower energy levels before moving to higher ones. In elements like bromine (Br), the orbitals fill up in the sequence of s, p, d, and f orbitals. Recognizing the order and the maximum capacity of each orbital is vital for writing correct electron configurations.

Noble Gas Notation

Noble gas notation is a simplified way to write an element's electron configuration. It uses the electron configuration of the nearest noble gas that precedes the element in the periodic table to represent the core electrons, followed by the valence electrons' configuration.

This shorthand notation simplifies the electron configurations, making it easier to identify valence electrons, which are important in chemical reactions. For instance, the noble gas notation for yttrium (Y) is [Kr] 5s² 4d¹, indicating that it shares the same core electron configuration as krypton (Kr) and has additional electrons in the 5s and 4d orbitals.