Question

The following electron configurations represent excited states. Identify the element and write its ground-state condensed electron configuration. (a) \(1 s^{2} 2 s^{2} 2 p^{4} 3 s^{1}\), (b) \([\) Ar \(] 4 s^{1} 3 d^{10} 4 p^{2} 5 p^{1}\), (c) \([\mathrm{Kr}] 5 s^{2} 4 d^{2} 5 p^{1}\)

Short answer

(a) Fluorine (F): \(1s^{2} 2s^{2} 2p^{5}\) (b) Germanium (Ge): \([\text{Ar}] 4s^2 3d^{10} 4p^2\) (c) Niobium (Nb): \([\text{Kr}] 5s^1 4d^4\)

Step-by-step solution

(a) Identify the number of electrons and element

To identify the element, we first determine how many electrons are included in the given excited configuration: \(1s^2 2s^2 2p^4 3s^1\). The superscripts show the number of electrons in each energy level and subshell: 2 (1s) + 2 (2s) + 4 (2p) + 1 (3s) = 9 electrons So the element has atomic number of 9, making it Fluorine (F).

(a) Write the ground-state condensed electron configuration

In the ground state, all the electron shells will be filled in order of increasing energy levels using the Aufbau principle. The ground-state configuration for Fluorine is: \[ 1s^{2} 2s^{2} 2p^{5} \]

(b) Identify the number of electrons and element

Starting with the electron configuration \([ \text{Ar} ]4s^1 3d^{10} 4p^{2} 5p^1\), let's identify the element by counting the number of electrons. The "[Ar]" notation means the configuration is the same as the noble gas Argon up to its last filled electron shell. Argon has 18 electrons, and we add the electrons from the given configuration: 18 ([\(\text{Ar}\)]) + 1 (4s) + 10 (3d) + 2 (4p) + 1 (5p) = 32 electrons So the element is Germanium (Ge) with atomic number 32.

(b) Write the ground-state condensed electron configuration

Using the Aufbau principle, we can write the ground-state condensed electron configuration for Germanium: \[ [\text{Ar}] 4s^2 3d^{10} 4p^2\]

(c) Identify the number of electrons and element

We have the electron configuration \([\text{Kr}]5s^2 4d^2 5p^1\). Determine the element by counting the total number of electrons: Kr has 36 electrons, and we count the given electrons: 36 ([\(\text{Kr}\)]) + 2 (5s) + 2 (4d) + 1 (5p) = 41 electrons So the element is Niobium (Nb) with atomic number 41.

(c) Write the ground-state condensed electron configuration

Finally, we write the ground-state condensed electron configuration for Niobium using the Aufbau principle: \[ [\text{Kr}] 5s^1 4d^4 \] So, the correct ground-state condensed electron configurations are: (a) Fluorine (F): \(1s^{2} 2s^{2} 2p^{5}\) (b) Germanium (Ge): \([\text{Ar}] 4s^2 3d^{10} 4p^2\) (c) Niobium (Nb): \([\text{Kr}] 5s^1 4d^4\)

Key concepts

Excited State

Electrons can be thought of as having a specific amount of energy, which dictates their position in an atom. When an electron gains extra energy, for instance, from absorbing light or other electromagnetic radiation, it may move to a higher energy level or "orbital." In this case, the atom is said to be in an "excited state." This doesn't happen naturally without an energy input and is usually a temporary situation.
In an excited state, one or more electrons occupy higher energy levels than they would in the most stable state. For example, in the original exercise:

• Configuration \(1s^2 2s^2 2p^4 3s^1\) for Fluorine (F) shows p electrons jumping to the next s level due to higher energy.
• Similarly, in \([\text{Ar}] 4s^1 3d^{10} 4p^2 5p^1\), the electrons that would typically fill lower energy levels are instead present in higher levels, indicating excitement.

In these examples, extra energy disturbs the order and stability of the ground-state configuration, forming an excited state until the electron returns to its lower, more stable level.

Ground-State

In contrast to the excited state, the ground-state electron configuration is the lowest energy configuration, where electrons fill orbitals in a manner following specific rules. This is where electrons reside by default, due to the principles of quantum mechanics, and embody the most stable arrangement of the atomic electrons.
As seen in the exercise examples:

• Fluorine with 9 electrons has a ground-state configuration of \(1s^2 2s^2 2p^5\), meaning all electrons settle in the lowest available orbitals first.
• Germanium's ground-state involves following this principle, filling the lowest available subshells, leading to \([\text{Ar}] 4s^2 3d^{10} 4p^2\).
• Niobium in ground-state \([\text{Kr}] 5s^1 4d^4 \) indicates electrons returning to the lowest potential energy positions from their excited placements.

Correctly identifying the ground-state electron configurations involves understanding and applying the Aufbau principle effectively to avoid confusion with excited states.

Aufbau Principle

The Aufbau principle is a key rule followed when determining the ground-state electron configuration of atoms. "Aufbau" is a German word meaning "building up," which precisely describes the process of filling up an atom's electron orbitals in a specific order.
According to this principle, orbitals are filled starting at the lowest available energy levels before moving to higher ones. The order can be remembered using the "diagonal rule," where one fills out shells like this:

• 1s
• 2s 2p
• 3s 3p 4s
• 3d 4p 5s... and so on.

For example:

• When finding the ground-state for Germanium, one follows this principle until hitting the noble gas core \([\text{Ar}]\), then continues filling \(4s, 3d\), and \(4p\).
• In Niobium, applying the Aufbau principle ensures we're placing electrons in \([\text{Kr}]\) and subsequent \(5s\) and \(4d\) orbitals correctly.

Understanding this rule helps prevent errors in predicting the electron configuration of any given element.

Atomic Number

Atomic number is a fundamental property of an element that corresponds to the number of protons in the nucleus of an atom, and by extension, also the number of electrons in a neutral atom. It is central to identifying elements and writing their electron configurations.
Knowing the atomic number is crucial for placing electrons correctly across orbitals:

• For Fluorine, the atomic number 9 means it has 9 electrons to position according to energy levels and subshells.
• The atomic number for Germanium is 32, leading us to arrange 32 electrons starting from the Argon core onwards.
• Niobium has an atomic number of 41, these electrons are configured using its noble gas shorthand notation \([\text{Kr}]\).

Atomic numbers allow chemists to trace elements easily on the periodic table, link them with their properties, and predict their reactions. It serves as a guide, ensuring every electron in an element is accounted for during configuration process.