Question

How many unpaired electrons would be found in the ground state of (a) \(\mathrm{Mg}\), (b) \(\mathrm{P}\), and \((\mathbf{c}) \mathrm{V}\) ?

Short answer

There are no unpaired electrons in magnesium (Mg), one unpaired electron in phosphorus (P), and three unpaired electrons in vanadium (V).

Step-by-step solution

Identify Electron Configuration of Magnesium (Mg)

The first step is to determine the ground state electron configuration of magnesium. Magnesium has an atomic number of 12, which means it has 12 electrons. The electron configuration for magnesium is 1s² 2s² 2p⁶ 3s². Since the 3s orbital can hold a maximum of two electrons and they are paired, there are no unpaired electrons for magnesium.

Identify Electron Configuration of Phosphorus (P)

Phosphorus has an atomic number of 15, meaning it has 15 electrons. The electron configuration for phosphorus is 1s² 2s² 2p⁶ 3s² 3p³. The 3p orbital has three electrons, which means there is one pair and one unpaired electron. Therefore, phosphorus has a total of one unpaired electron in its 3p orbital.

Identify Electron Configuration of Vanadium (V)

Vanadium has an atomic number of 23, which means it has 23 electrons. The electron configuration for vanadium is 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d³. The 3d orbital can hold up to 10 electrons. With only 3 electrons in the 3d orbital, all of them are unpaired. Therefore, vanadium has three unpaired electrons in its 3d orbital.

Key concepts

Electron Configuration

Understanding electron configuration is essential for visualizing how electrons are distributed in an atom's orbitals. Electrons occupy orbitals in a manner that minimizes the energy of the atom, which is known as its ground state. The configuration follows a set of principles: the Aufbau principle, which dictates that electrons fill orbitals starting with the lowest energy level; Pauli's exclusion principle, which states that an orbital can hold a maximum of two electrons with opposite spins; and Hund's rule, which directs that electrons will fill an orbital singly before pairing up.

To represent this, a notation system is used where each orbital is written in order of increasing energy alongside a superscript indicating the number of electrons within each orbital. For example, carbon with 6 electrons would be written as 1s² 2s² 2p². The arrangement of these electrons can predict many properties of the element including its reactivity and the types of bonds it will form. In your exercise, identifying unpaired electrons required determining the electron configuration of each element which was the first crucial step.

Ground State

The ground state of an atom is its lowest energy state, wherein the electrons are arranged in the most stable configuration possible according to quantum mechanics. The electrons will naturally organize themselves to minimize the energy of the atom, filling the available orbitals starting from the lowest energy level proceeding to higher levels only when needed.

Understanding the ground state is important because it provides a reference point for predicting the chemical and physical behavior of elements. Unpaired electrons, which are electrons not shared in a pair within an orbital, can make an element more chemically reactive and are crucial in determining magnetic properties. For example, in your exercise, these unpaired electrons allow us to discern that phosphorus has potential for chemical reactions based on its single unpaired electron, while magnesium's lack of unpaired electrons suggests less reactivity.

Atomic Number

Every element on the periodic table is defined by its unique atomic number, which represents the number of protons in the nucleus of an atom. This number also indirectly tells us the number of electrons in a neutral atom since atoms are electrically neutral with an equal number of protons and electrons.

Understanding the atomic number is the starting point for identifying an element and predicting its chemical properties, including its valence electrons and typical bonding behaviors. In the exercise provided, the atomic numbers gave us the necessary information to figure out the electron configurations for magnesium (Mg), phosphorus (P), and vanadium (V). As the atomic number increases, so does the complexity of the electron configuration, which can ultimately affect the number of unpaired electrons and, therefore, an element's chemistry and magnetism.