Problem 109 - Chemistry Matter and Change

Question

Write the electron configuration for each atom. (Chapter 5) \(\begin{array}{ll}{\text { a. iodine }} & {\text { d. krypton }} \\ {\text { b. boron }} & {\text { e. calcium }} \\ {\text { c. chromium }} & {\text { f. cadmium }}\end{array}\)

Step-by-Step Solution

Answer

The electron configurations of the given elements are: a. Iodine (I): \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^5\) b. Boron (B): \(1s^2 2s^2 2p^1\) c. Chromium (Cr): \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^1 3d^{5}\) d. Krypton (Kr): \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6\) e. Calcium (Ca): \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2\) f. Cadmium (Cd): \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10}\)

Step 1: Identify the atomic number of each element

Refer to the periodic table to find the atomic number (number of electrons) for each given element: a. Iodine (I): 53 b. Boron (B): 5 c. Chromium (Cr): 24 d. Krypton (Kr): 36 e. Calcium (Ca): 20 f. Cadmium (Cd): 48

Step 2: Write the electron configuration using the fill order rules

Following the fill order 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p, start filling the orbitals with electrons for each element: a. \(Iodine (I): 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^5\) b. \(Boron (B): 1s^2 2s^2 2p^1\) c. \(Chromium (Cr): 1s^2 2s^2 2p^6 3s^2 3p^6 4s^1 3d^{5}\) (Chromium is an exception because it is more stable with a half-filled 3d subshell) d. \(Krypton (Kr): 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6\) e. \(Calcium (Ca): 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2\) f. \(Cadmium (Cd): 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10}\)

Step 3: Present the electron configurations

The electron configurations of the given elements are: a. Iodine (I): \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^5\) b. Boron (B): \(1s^2 2s^2 2p^1\) c. Chromium (Cr): \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^1 3d^{5}\) d. Krypton (Kr): \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6\) e. Calcium (Ca): \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2\) f. Cadmium (Cd): \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10}\)

Key Concepts

Atomic Number

The atomic number is a fundamental property of an element, defined as the number of protons in the nucleus of its atom. Each element's atomic number also equals the number of electrons for a neutral atom, making it crucial for understanding electron configurations. For instance, iodine has an atomic number of 53, meaning it has 53 protons and, in its neutral state, 53 electrons.
Identifying the atomic number allows us to determine the number of electrons to distribute among the subshells when writing electron configurations. The periodic table is an essential tool that organizes elements by their atomic numbers, providing a handy reference to determine this key figure for any element.

Periodic Table

The periodic table arranges all known elements based on their atomic number, electron configuration, and recurring chemical properties. It is divided into rows called periods and columns known as groups, allowing us to detect patterns in element behavior.
Elements within the same group typically share similar properties because they have the same number of electrons in their outermost shell. For example, iodine is placed in group 17, known as the halogens, which all have similar highly reactive properties. By using the periodic table, we quickly locate an element’s position, helping us predict its electron configuration by understanding where electrons start to fill subshells.

• Groups - Vertical columns in the periodic table.
• Periods - Horizontal rows in the periodic table.
• Blocks - Sections of the periodic table where subshells are filled, such as s-block, p-block, d-block, and f-block.

Subshells

Atoms have electron shells which are layers around the atomic nucleus, and each shell contains subshells. These subshells are labeled as s, p, d, and f, where each type can hold a different number of electrons:

• s subshells can hold 2 electrons
• p subshells can hold 6 electrons
• d subshells can hold 10 electrons
• f subshells can hold 14 electrons

The arrangement and capacity of these subshells determine the electron configuration of an atom, guiding how electrons are distributed. For example, boron has a configuration of \(1s^2 2s^2 2p^1\), filling the 1s and 2s completely and beginning to fill the 2p subshell.

Fill Order

Electron configuration is determined by the order in which subshells are filled. This follows the Aufbau principle, indicating that electrons occupy the lowest energy orbitals first. The common sequence is:

• 1s
• 2s
• 2p
• 3s
• 3p
• 4s
• 3d
• 4p
• 5s
• 4d
• 5p
• 6s
• 4f
• 5d
• 6p
• 7s
• 5f
• 6d
• 7p

Using this order, we fill in electrons for each element by starting at the lowest available energy level, moving upward. This sequence helps explain how calcium has the configuration \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2\).

Electron Configuration Exceptions

Though the fill order provides a systematic way to assign electron states, some elements show exceptions due to increased stability in half-filled or filled d and f subshells. Chromium is a classic example. Instead of the expected \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^4\) configuration, it actually has \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^1 3d^5\).
This is because having a half-filled d subshell (\(3d^5\)) offers additional stability, making it a favorable configuration for chromium. Understanding these exceptions is crucial for accurately writing the correct electron configurations for certain elements and can often be spotted on the periodic table by looking for other unusual behaviors shared with elements of similar placement.