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. scandium, \(Z=21\) b. yttrium, \(Z=39\) c. lanthanum, \(Z=57\) d. actinium, \(Z=89\)

Short answer

The electron configurations for the given elements using the symbol of the previous noble gas are: a. Scandium (Sc): \([Ar] 3d^1 4s^2\) b. Yttrium (Y): \([Kr] 4d^1 5s^2\) c. Lanthanum (La): \([Xe] 5d^1 6s^2\) d. Actinium (Ac): \([Rn] 6d^1 7s^2\)

Step-by-step solution

Find the Previous Noble Gas

The noble gas preceding scandium is argon (Ar) with an atomic number of 18. We will use this to represent the core electrons.

Determine Remaining Electrons and Write Configuration

Scandium (Z=21) has 3 more electrons than argon (Z=18). Thus, we need to write the electron configuration for the 3 remaining electrons. In order, the orbitals are filled as 3d1 and 4s2. Based on this, the electron configuration for scandium is: \[Sc = [Ar] 3d1 \; 4s^2\] b. Yttrium, Z=39

Find the Previous Noble Gas

The noble gas preceding yttrium is krypton (Kr) with an atomic number of 36. We will use this to represent the core electrons.

Determine Remaining Electrons and Write Configuration

Yttrium (Z=39) has 3 more electrons than krypton (Z=36). Thus, we need to write the electron configuration for the 3 remaining electrons. In order, the orbitals are filled as 4d1 and 5s2. Based on this, the electron configuration for yttrium is: \[Y = [Kr] 4d1 \; 5s^2\] c. Lanthanum, Z=57

Find the Previous Noble Gas

The noble gas preceding lanthanum is xenon (Xe) with an atomic number of 54. We will use this to represent the core electrons.

Determine Remaining Electrons and Write Configuration

Lanthanum (Z=57) has 3 more electrons than xenon (Z=54). Thus, we need to write the electron configuration for the 3 remaining electrons. In order, the orbitals are filled as 5d1 and 6s2. Based on this, the electron configuration for lanthanum is: \[La = [Xe] 5d1 \; 6s^2\] d. Actinium, Z=89

Find the Previous Noble Gas

The noble gas preceding actinium is radon (Rn) with an atomic number of 86. We will use this to represent the core electrons.

Determine Remaining Electrons and Write Configuration

Actinium (Z=89) has 3 more electrons than radon (Z=86). Thus, we need to write the electron configuration for the 3 remaining electrons. In order, the orbitals are filled as 6d1 and 7s2. Based on this, the electron configuration for actinium is: \[Ac = [Rn] 6d1 \; 7s^2\]

Key concepts

Noble Gas Core Notation

When writing out the electron configuration of an element, the noble gas core notation simplifies the process by using the symbol of the closest noble gas that precedes the element in the periodic table. The noble gases are the group of elements that are exceptionally stable and include helium (He), neon (Ne), argon (Ar), krypton (Kr), xenon (Xe), and radon (Rn).

Using the noble gas core notation highlights the valence electrons, which are the electrons in the outermost shell that largely determine an element's chemical properties. For example, when writing the electron configuration for scandium (Sc), instead of listing all 21 electrons, you can start with [Ar], which stands for the last noble gas before scandium with 18 electrons. Then, you only need to account for the additional 3 electrons to determine Sc's electron configuration, resulting in [Ar] 3d1 4s2, a much simpler notation.

Atomic Number

The atomic number, represented by the symbol Z, is a fundamental property of an element that tells you the number of protons in an atom's nucleus. By extension, in a neutral atom, the atomic number also equals the number of electrons orbiting the nucleus. This number is crucial for understanding electron configuration because it determines the element's position in the periodic table and its chemical behavior.

For example, yttrium (Y) has an atomic number of 39, meaning it has 39 protons and, in a neutral state, 39 electrons. Knowing the atomic number helps us follow the correct order when filling in the electron shells, leading us to Y's electron configuration: [Kr] 4d1 5s2.

Orbital Filling Order

Electrons fill orbitals following a specific sequence known as the orbital filling order. This order is based on the increasing energy levels and subshells, typically illustrated by the Aufbau principle and often visualized through a diagram that ranks subshells by their energy levels.

Using the filling order, electrons first occupy lower energy levels before moving on to higher ones. For example, in lanthanum (La), the electron configuration begins with [Xe], followed by the addition of electrons to the next available subshells, which are 5d1 and then 6s2, reflecting the sequence determined by the orbital energy hierarchy. Each subshell is filled to its capacity (2 electrons for s, 6 for p, 10 for d, and 14 for f) before electrons are added to the next subshell.

Periodic Table

The periodic table is a tabular arrangement of all known elements organized by increasing atomic number and grouped by common chemical properties. Columns, known as groups, contain elements with similar outer electron configurations, which translates to comparable chemical behaviors. Rows, or periods, align elements with increasing energy levels.

For instance, actinium (Ac) is found in the actinide series, a block of elements listed below the main body of the periodic table. Actinium's electron configuration uses the previous noble gas, which is radon (Rn), and continues with the additional electrons [Rn] 6d1 7s2. The periodic table aids in predicting the electron configuration and understanding elements' chemical characteristics, positioning Ac among other heavy, typically radioactive elements.