Question

Using the symbol of the previous noble gas to indicate the core electrons, write the electron configuration for each of the following elements. a. zirconium, \(Z=40\) b. vanadium, \(Z=23\) c. bromine, \(Z=35\) d. silicon, \(Z=14\)

Short answer

The electron configurations for the elements are as follows: a. Zirconium (Z=40): \([\text{Kr}] \ 4d^2 \ 5s^2\) b. Vanadium (Z=23): \([\text{Ar}] \ 3d^3 \ 4s^2\) c. Bromine (Z=35): \([\text{Ar}] \ 3d^{10} \ 4s^2 \ 4p^5\) d. Silicon (Z=14): \([\text{Ne}] \ 3s^2 \ 3p^2\)

Step-by-step solution

Identify the previous noble gas

The previous noble gas to zirconium is krypton (Kr), which has an atomic number of 36.

Determine the electron configuration

Starting from the previous noble gas, we fill the corresponding orbitals using the aufbau principle. The electron configuration for zirconium (\(Z = 40\)) is \([\text{Kr}] \ 4d^2 \ 5s^2\). #b. Vanadium (Z=23)#

Identify the previous noble gas

The previous noble gas to vanadium is argon (Ar), which has an atomic number of 18.

Determine the electron configuration

The electron configuration for vanadium (\(Z = 23\)) is \([\text{Ar}] \ 3d^3 \ 4s^2\). #c. Bromine (Z=35)#

Identify the previous noble gas

The previous noble gas to bromine is argon (Ar), which has an atomic number of 18.

Determine the electron configuration

The electron configuration for bromine (\(Z = 35\)) is \([\text{Ar}] \ 3d^{10} \ 4s^2 \ 4p^5\). #d. Silicon (Z=14)#

Identify the previous noble gas

The previous noble gas to silicon is neon (Ne), which has an atomic number of 10.

Determine the electron configuration

The electron configuration for silicon (\(Z = 14\)) is \([\text{Ne}] \ 3s^2 \ 3p^2\).

Key concepts

Noble Gas Core

In chemical notation, the noble gas core refers to the shorthand method of representing electron configurations by using the preceding noble gas from the periodic table. Noble gases are elements characterized by their full outer electron shells, which make them extremely stable.
These gases, such as helium (He), neon (Ne), argon (Ar), and krypton (Kr), are used as core references because they conveniently represent filled electron shells.

• The noble gas core reduces the complexity of electron configuration notation by allowing chemists to focus on the valence electrons—the electrons in the outer shell.
• For example, using the noble gas core simplifies zirconium's electron configuration from its full form to electrons after krypton are expressed as \[\text{Kr}]\ 4d^2\ 5s^2\].

This method not only saves time but also highlights the electrons most involved in chemical reactions.

Aufbau Principle

The Aufbau principle is a fundamental guideline in chemistry for determining the electron configuration of an atom. It states that electrons fill atomic orbitals in an order of increasing energy levels. This principle is key in predicting and understanding the structure of atoms in terms of electron distribution.
The general order of filling is from the lowest to the highest energy orbital:

• The lowest energy levels fill first, starting with the 1s orbital, then 2s, 2p, 3s, and so on.
• However, due to overlapping energy levels, the 4s orbital fills before the 3d orbitals.

This 3d-4s energy overlap can sometimes lead to confusion, but following the Aufbau principle mitigates this by providing a logical sequence for the filling of orbitals.
Applying this principle enables us to write accurate electron configurations by using it in conjunction with the Pauli Exclusion Principle and Hund’s Rule to ensure stability and predict the chemical behavior of elements.

Chemical Elements

Chemical elements are substances consisting entirely of one type of atom, characterized by a specific number of protons in their nuclei. They are the basic building blocks of matter and appear on the periodic table.
Each element has a unique set of properties and specific atomic structure determined by its place in the periodic table:

• For instance, silicon is a chemical element with atomic number 14, meaning it has 14 protons.
• Understanding elements includes recognizing how they bond chemically: zirconium, for example, often bonds with oxygen to form zirconia.

Studying these elements helps us comprehend the diversity and complexity of matter in science.
In relation to electron configurations, such as for silicon \[\text{Ne}]\ 3s^2\ 3p^2\], we can predict how elements will interact and react chemically, based on the distribution and energy levels of their electrons.

Periodic Table

The periodic table is a systematic arrangement of chemical elements, organized based on their atomic number, electron configurations, and recurring chemical properties. Its tabular layout classifies elements into periods (rows) and groups (columns), reflecting trends in chemical behavior.
Several features of the periodic table help when determining electron configurations:

• Elements are arranged in order of increasing atomic number, revealing patterns that are fundamental to understanding material properties.
• The structure of the periodic table reflects the Aufbau principle, positioning elements according to similar properties.
• It also separates the elements into blocks: s-block, p-block, d-block, and f-block, based on their electron configuration.

Thus, the periodic table not only serves as a tool for predicting chemical behavior but also for categorizing elements according to electron filling patterns and energy levels.

Quantum Numbers

Quantum numbers are sets of numerical values that describe specific properties of electrons within an atom. They are vital to understanding electron configurations and the placement of electrons in various energy levels.
Each electron has four quantum numbers that together define its unique quantum state:

• Principal quantum number (\[n\]) indicates the energy level and distance from the nucleus.
• Angular momentum quantum number (\[l\]) correlates to the shape of the orbital.
• Magnetic quantum number (\[m_l\]) specifies the orientation of the orbital.
• Spin quantum number (\[m_s\]) defines the direction of the electron spin.

By using these numbers, we can precisely map out where electrons reside and predict their contribution to an element's chemical properties. They play a crucial role in applying the Aufbau principle to fill orbitals sequentially and appropriately.