Question

Which of the following electron configurations correspond to an excited state? Identify the atoms and write the ground-state electron configuration where appropriate. a. 1\(s^{2} 2 s^{2} 3 p^{1}\) b. 1\(s^{2} 2 s^{2} 2 p^{6}\) c. 1\(s^{2} 2 s^{2} 2 p^{4} 3 s^{1}\) d. \([\mathrm{Ar}] 4 s^{2} 3 d^{5} 4 p^{1}\) How many unpaired electrons are present in each of these species?

Short answer

The electron configurations a, c, and d represent excited states. The respective atoms and ground-state configurations are: a) Boron (B) with 1\(s^{2} 2 s^{2} 2 p^{1}\), c) Fluorine (F) with 1\(s^{2} 2 s^{2} 2 p^{5}\), and d) Gallium (Ga) with \([\mathrm{Ar}] 4 s^{2} 3 d^{10} 4 p^{1}\). Configuration b represents a Neon (Ne) atom in the ground state. The number of unpaired electrons in each configuration is: a) 1, b) 0, c) 3, and d) 6.

Step-by-step solution

Ground state rules check:

Remember the three rules: -Aufbau principle: electrons occupy the lowest energy orbitals available -Pauli exclusion principle: no two electrons in the same atom can have the same four quantum numbers -Hund's rule: electrons will occupy orbitals with the same energy (degenerate orbitals) singly before pairing up Verify that the given electron configurations follow the rules above. **Step 2: Identify the atoms represented by each configuration and write the ground-state electron configuration if appropriate**

Identifying atoms:

Use the periodic table and electron configuration patterns to identify which atom corresponds to each given electron configuration. If any of the configurations don't correspond to a ground state, find the correct ground-state electron configuration. **Step 3: Calculate the number of unpaired electrons in each configuration**

Count unpaired electrons:

Count how many electrons remain unpaired (i.e., do not have a partner with an opposite spin) in each configuration. This will give us the number of unpaired electrons for each electron configuration specified. Now let's implement these steps for each given electron configuration: a. 1\(s^{2} 2 s^{2} 3 p^{1}\)

Excited or ground state:

This configuration does not follow the Aufbau principle since it skips the 2\(p\) subshell. It is an excited state.

Atom and ground-state configuration:

The ground-state configuration should be 1\(s^{2} 2 s^{2} 2 p^{1}\), which corresponds to the Boron (B) atom.

Unpaired electrons:

There is one unpaired electron in the 3\(p\) subshell. b. 1\(s^{2} 2 s^{2} 2 p^{6}\)

Excited or ground state:

This configuration follows all rules and is the ground state.

Atom and ground-state configuration:

The configuration corresponds to a Neon (Ne) atom in its ground state.

Unpaired electrons:

There are no unpaired electrons in this configuration. c. 1\(s^{2} 2 s^{2} 2 p^{4} 3 s^{1}\)

Excited or ground state:

This configuration does not follow the Aufbau principle since it skips the 2\(p\) subshell. It is an excited state.

Atom and ground-state configuration:

The ground-state configuration should be 1\(s^{2} 2 s^{2} 2 p^{5}\), which corresponds to the Fluorine (F) atom.

Unpaired electrons:

There are two unpaired electrons in the 2\(p\) subshell and one unpaired electron in the 3\(s\) subshell, making a total of three unpaired electrons. d. \([\mathrm{Ar}] 4 s^{2} 3 d^{5} 4 p^{1}\)

Excited or ground state:

This configuration does not follow the Aufbau principle since it skips the 3\(d^{10}\) subshell. It is an excited state.

Atom and ground-state configuration:

The ground-state configuration should be \([\mathrm{Ar}] 4 s^{2} 3 d^{10} 4 p^{1}\), which corresponds to the Gallium (Ga) atom.

Unpaired electrons:

There are five unpaired electrons in the 3\(d\) subshell and one unpaired electron in the 4\(p\) subshell, making a total of six unpaired electrons.

Key concepts

Aufbau Principle

The Aufbau Principle is essential for understanding electron configurations in atoms. It provides a guideline on the order in which electrons fill the available energy orbitals. According to this principle, electrons enter the lowest available energy levels first before moving to higher ones. This helps predict the ground-state electron configuration of an atom.
The sequence of orbital filling follows a specific order, starting from the 1s orbital, then moving to 2s, 2p, 3s, 3p, 4s, 3d, 4p, and so on. The key to remembering this order is that lower energy orbitals are filled first, following a sequence that sometimes skips in terms of numerical ordering due to energy considerations.
In the exercise problem, configurations a, c, and d showed excited states because they did not adhere to the expected order of filling specified by the Aufbau Principle.

Pauli Exclusion Principle

The Pauli Exclusion Principle plays a crucial role in explaining the structure of electron configurations. It states that no two electrons in the same atom can have identical sets of quantum numbers. In practical terms, this means each orbital can hold a maximum of two electrons with opposite spins.
This principle limits the number of electrons that can occupy a single orbital, emphasizing that each electron must be unique in its set of quantum properties. The uniqueness comes from the combination of four quantum numbers: principal, angular momentum, magnetic, and spin.
In the given problem, adherence to this principle ensures each configuration maintains unique electron placements, preventing incorrect overlaps and ensuring proper electron behavior in orbitals.

Hund's Rule

Hund's Rule is an important guideline when filling degenerate orbitals, or orbitals with the same energy level, such as the three 2p orbitals. According to this rule, electrons will occupy each degenerate orbital singly before pairing up with opposite spins.
By applying Hund's Rule, we can minimize electron-electron repulsion within a subshell, leading to a more stable electron arrangement. This rule is especially important for configurations like 2p^{x}, 3d^{x}, where "x" indicates a number of electrons.
For example, in electron configuration c from the problem, the 2p subshell initially tries to singly occupy each of the available px, py, and pz orbitals before any pairing occurs. This increases stability and predicts the behavior of electrons accurately when they occupy higher energy levels.

Unpaired Electrons

Unpaired electrons are electrons occupying an orbital singly, without a partner electron with opposite spin. Having unpaired electrons can indicate an excited state or the presence of magnetic properties.
In chemistry, the number of unpaired electrons can influence atom reactivity and magnetic properties. For instance, a species with one or more unpaired electrons is often more reactive and can be paramagnetic, while atoms with all electrons paired are typically diamagnetic.
In the exercise, different configurations are analyzed for unpaired electrons. For instance, configuration a has an unpaired electron, demonstrating an excited state, whereas b, being a ground state configuration, has all electrons paired.

Ground State Configuration

Ground state configuration describes the most stable arrangement of electrons around the nucleus of an atom. In this state, electrons fill the lowest available energy levels as described by the Aufbau Principle.
The ground state configuration adheres to all three main rules (Aufbau, Pauli, and Hund's) to find the most stable electron arrangement. This configuration reflects the atomic structure of an element when it has the least energy possible.
For example, configuration b in the problem aligns with the neon atom's ground state. Each electron fills the simplest possible orbital setup, thereby demonstrating how fundamental these rules are in predicting how elements typically exist in nature.