Question

Use the periodic table to write electron configurations for each element. (a) \(\mathrm{Al}\) (b) \(\mathrm{Be}\) (c) In (d) \(\mathrm{Zr}\)

Short answer

The electron configurations are: (a) Al: 1s^2 2s^2 2p^6 3s^2 3p^1, (b) Be: 1s^2 2s^2, (c) In: 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^10 4p^6 5s^2 4d^10 5p^1, (d) Zr: 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^10 4p^6 5s^2 4d^2.

Step-by-step solution

Identify the Atomic Numbers

Find the atomic numbers of Al, Be, In, and Zr on the periodic table. The atomic number of an element corresponds to the number of protons and, for a neutral atom, also the number of electrons. Aluminum (Al) has atomic number 13, Beryllium (Be) has atomic number 4, Indium (In) has atomic number 49, and Zirconium (Zr) has atomic number 40.

Write Electron Configurations

Use the atomic numbers to determine the number of electrons for each element and write their electron configurations based on the order of filling the orbital blocks (s, p, d, f). The order follows the Aufbau principle, starting from the lowest to highest energy orbital. Al (13 electrons) follows the pattern 1s, 2s, 2p, 3s, 3p; Be (4 electrons) follows 1s, 2s; In (49 electrons) follows 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p; and Zr (40 electrons) follows 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d.

Complete the Electron Configurations

Allocate the electrons into each identified orbital, keeping in mind the Pauli Exclusion Principle and Hund's Rule. For Al (13 electrons), the configuration is: 1s^2 2s^2 2p^6 3s^2 3p^1. For Be (4 electrons), the configuration is: 1s^2 2s^2. For In (49 electrons), the configuration is: 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^10 4p^6 5s^2 4d^10 5p^1. For Zr (40 electrons), the configuration is: 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^10 4p^6 5s^2 4d^2.

Key concepts

Periodic Table

The periodic table is a tabular arrangement of elements ordered by increasing atomic number. Each element is represented by its chemical symbol and contains details like atomic mass and possibly a color-coded categorization. It's designed to showcase periodic trends in the elements' properties, such as electronegativity, atomic radius, and ionization energy. Elements are arranged into periods (rows) and groups (columns). Understanding the structure of the periodic table helps when writing electron configurations, as it reflects the order in which energy levels and sublevels fill with electrons.

• Periods correspond to the number of electron shells.
• Groups contain elements with similar properties and typically the same number of electrons in their outermost shell.
• Transition metals, lanthanides, and actinides occupy unique positions that affect their electron configurations.

Aufbau Principle

The Aufbau principle is a fundamental guideline used to determine the electron configuration of an atom in its ground state. According to this principle, electrons fill atomic orbitals in order of increasing energy levels, starting with the lowest energy orbital. 'Aufbau' is German for 'building up', and this principle visualizes the build-up of electrons in an atom as a step-by-step process.

Electrons fill the '1s' orbital first, followed by '2s', '2p', and so on. The pattern generally follows the sequence:

• 1s
• 2s
• 2p
• 3s
• 3p

and continues through the energy sublevels with a more complex pattern, especially after the 3p sublevel, to accommodate the proper orbital filling sequence for transition metals and inner transition metals. However, it should be noted that electron configurations can be predicted using the periodic table structure, which reflects this energetic order perfectly.

Pauli Exclusion Principle

The Pauli Exclusion Principle is a rule in quantum mechanics, proposed by Wolfgang Pauli, stating that no two electrons in an atom can have the same set of four quantum numbers. Essentially, this ruling restricts an atomic orbital to a maximum of two electrons, and these electrons must have opposite spins.

When writing electron configurations, this principle reminds us that after one electron fills an orbital, the next electron that enters the same orbital must have an opposite spin. This is denoted using arrows in orbital diagrams, or by the superscript notation in electron configurations, such as '1s^2' indicating that two electrons with opposite spins fill the 1s orbital.

Hund's Rule

Hund's Rule addresses how electrons distribute themselves among orbitals of the same sublevel (like the '2p' orbitals). According to this rule, electrons will fill each degenerate orbital singly first, before doubling up with paired spins. This behavior is because electrons repel each other due to their negative charge, and occupying separate orbitals with parallel spins minimizes their repulsion.

This concept is crucial when allocating electrons in p, d, or f sublevels with more than one orbital. For instance, if we have three 2p orbitals and three electrons to place, Hund's Rule tells us that each electron will go into a separate orbital before any pairing occurs. These rules of electron filling (Aufbau principle, Pauli Exclusion Principle, and Hund's Rule) tie together cohesively to guide students in writing accurate electron configurations for elements.

Atomic Number

The atomic number of an element is perhaps its most defining characteristic. It's equal to the number of protons in the nucleus of an atom and gives the element its identity. In a neutral atom, the atomic number also equals the number of electrons orbiting the nucleus. For example, carbon has an atomic number of 6, which means every carbon atom has 6 protons and, when neutral, 6 electrons.

The importance of the atomic number becomes evident in electron configurations, as it directly determines the number of electrons to be distributed according to the principles previously discussed. Hence, the atomic number is the starting point for writing electron configurations, as shown in the exercise. The periodic table lists elements in ascending order of atomic number, enabling a straightforward method to deduce the number of electrons in an atom and thereby its ground state electron configuration.