Question

Use the periodic table to write electron configurations for each element. (a) \(\mathrm{Tl}\) (b) \(\mathrm{Co}\) (c) \(\mathrm{Ba}\) (d) \(\mathrm{Sb}\)

Short answer

The electron configurations are (a) \(\mathrm{Tl}: [Xe] 6s^2 4f^{14} 5d^{10} 6p^1\), (b) \(\mathrm{Co}: [Ar] 4s^2 3d^7\), (c) \(\mathrm{Ba}: [Xe] 6s^2\), and (d) \(\mathrm{Sb}: [Kr] 5s^2 4d^{10} 5p^3\).

Step-by-step solution

Identify the Atomic Number

Find the atomic number of thallium (Tl) from the periodic table, which corresponds to the number of protons and electrons in a neutral atom.

Electron Configuration of Tl

Write down the electron configuration of Tl by filling the orbitals in order of increasing energy, following the Aufbau principle, Hund's rule, and the Pauli exclusion principle until all the electrons are placed.

Identify the Atomic Number of Co

Find the atomic number of cobalt (Co) from the periodic table to determine the number of electrons for its electron configuration.

Electron Configuration of Co

Determine the electron configuration for Co, filling the electrons into orbitals based on the standard order.

Identify the Atomic Number of Ba

Find the atomic number of barium (Ba) from the periodic table.

Electron Configuration of Ba

Write out the electron configuration for Ba by arranging electrons according to energy levels.

Identify the Atomic Number of Sb

Determine the atomic number of antimony (Sb) from the periodic table.

Electron Configuration of Sb

Arrange the electrons in Sb's orbitals according to their energy levels to obtain its electron configuration.

Key concepts

Periodic Table

The periodic table is an essential tool in chemistry that organizes all known elements according to their atomic number, which is the number of protons in the nucleus of an atom. Each element in the table is positioned in a way that reflects its electronic properties. Looking at the periodic table, you can tell a lot about an element's electron configuration—the arrangement of electrons around its nucleus—simply by noting its position.

For instance, elements in the same column, or group, have similar valence electron configurations, which means they exhibit comparable chemical behaviors. The periodic table is divided into blocks that correspond to the outermost electron orbitals, such as the s-block, p-block, d-block, and f-block, which helps in predicting the electron configuration pattern for each element.

Aufbau Principle

The Aufbau principle is a fundamental guideline used to determine the electron configuration of an atom in its ground state. This principle states that electrons occupy orbitals with the lowest energy first before filling higher energy levels. Think of it like filling up seats in a theater from the front rows to the back—it’s a systematic process of building up the electron configuration.

To visualize this process, a diagram or chart known as an 'energy level diagram' can be used, clarifying which orbitals are to be filled first. Following this principle ensures that the electron configuration of any element reflects the most stable, lowest energy arrangement possible.

Hund's Rule

Hund's rule further refines the way electrons are distributed across orbitals within the same subshell. According to this rule, electrons will fill degenerate orbitals—orbitals that have the same energy—singly before any electron pairing occurs. It’s akin to people sitting in a bus; passengers will typically sit in empty rows alone before sharing a row with others.

This rule addresses the electron arrangements within the same energy level, prioritizing maximizing the number of unpaired electrons. This creates the most stable configuration because electrons in the same orbital repel each other due to their negative charge. By occupying separate orbitals, they minimize the electron-electron repulsions.

Pauli Exclusion Principle

The Pauli exclusion principle is a quantum mechanical concept that no two electrons in an atom can have the same set of four quantum numbers. This effectively means that an orbital can hold a maximum of two electrons, and they must have opposite spins. The quantum numbers describe the properties of the orbital and the position of an electron, therefore, enforcing a unique state for each electron.

When two electrons occupy the same orbital, they are represented by arrows pointing in opposite directions. This principle is crucial for accurately assigning electrons to an atom’s orbitals and for predicting how atoms will engage in chemical bonding.

Atomic Number

The atomic number is a fundamental characteristic of an element. It is equal to the number of protons found in the nucleus of an atom, which is also the number of electrons in a neutral atom. This atomic number defines the identity of an element and determines its position on the periodic table.

For instance, if you need to write the electron configuration for a neutral cobalt (Co) atom, you would start by finding its atomic number, which is 27, indicating that cobalt has 27 protons and, in its neutral state, 27 electrons to place in orbitals according to the rules we've discussed.

Orbital Energy Levels

Orbitals are the regions around an atom's nucleus where electrons are most likely to be found. These orbitals have different shapes and energy levels, often described by principal quantum numbers (n=1,2,3,...), and are grouped into types (s, p, d, f). The energy increases with the principal quantum number and other factors like nuclear charge.

Electron configurations are written according to the increasing energy of these orbitals. As a tip for remembering the order in which electrons fill the orbitals, many students use mnemonics or an 'orbital diagram' that outlines the sequence according to the Aufbau principle. This proper arrangement of electrons is what governs the chemical properties and reactivity of elements.