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 \(] 4 s^{1} 3 d^{10} 4 p^{2} 5 p^{1}\) \((\mathbf{c})[\mathrm{Kr}] 5 s^{2} 4 d^{2} 5 p^{1}\)

Short answer

The ground-state condensed electron configurations for the given excited states are: (a) Fluorine (F): [He] \(2s^2 2p^5\) (b) Germanium (Ge): [Ar] \(4s^2 3d^{10} 4p^2\) (c) Niobium (Nb): [Kr] \(5s^1 4d^4\)

Step-by-step solution

Determine the electron count for each configuration

First, we need to determine the total number of electrons for each given configuration. This will help us figure out the elements corresponding to the configurations. (a) \(1s^2 2s^2 2p^4 3s^1\) The configuration has 2 + 2 + 4 + 1 = 9 electrons. (b) [Ar] \(4s^1 3d^{10} 4p^2 5p^1\) The configuration has 18 (Ar has 18 electrons) + 1 + 10 + 2 + 1 = 32 electrons. (c) [Kr] \(5s^2 4d^2 5p^1\) The configuration has 36 (Kr has 36 electrons) + 2 + 2 + 1 = 41 electrons.

Identify the elements

Now that we know the electron count for each configuration, we can identify the elements according to the number of electrons they have. (a) The element with 9 electrons is Fluorine (F). (b) The element with 32 electrons is Germanium (Ge). (c) The element with 41 electrons is Niobium (Nb).

Write the ground-state electron configuration

To find the ground-state electron configuration, we will arrange the electrons in the available subshells in the increasing order of energy levels. (a) Fluorine (F) - Ground-state configuration is \(1s^2 2s^2 2p^5\) or [He] \(2s^2 2p^5\). (b) Germanium (Ge) - Ground-state configuration is \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^2\) or [Ar] \(4s^2 3d^{10} 4p^2\). (c) Niobium (Nb) - Ground-state configuration is \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^1 4d^4\) or [Kr] \(5s^1 4d^4\). So the ground-state condensed electron configurations are: (a) [He] \(2s^2 2p^5\) (b) [Ar] \(4s^2 3d^{10} 4p^2\) (c) [Kr] \(5s^1 4d^4\)

Key concepts

Excited States

When we talk about excited states of an atom, we refer to the situation where electrons are not in the lowest possible energy levels or configurations. Normally, an electron in an atom occupies the lowest available energy level, known as the ground state. However, when an atom absorbs energy, electrons can jump to higher energy levels, creating what is called an excited state.

For example, if an electron in a hydrogen atom normally occupies the 1s orbital, an influx of energy can promote it to the 2s or even a higher orbital like 2p. This arrangement is not stable, and the electron will eventually release energy and fall back down to a lower energy level. In solutions, recognizing the difference between an atom's ground state and excited state configurations is crucial, especially in exercises involving electron transitions, spectroscopy, or photochemistry.

Ground-State Electron Configuration

The ground-state electron configuration is the arrangement of electrons around the nucleus of an atom in the lowest energy configuration. Electrons fill subshells in an order determined by their energy level, which is elegantly outlined by the Aufbau principle. Essentially, this means electrons prefer the 'cheapest seats' in terms of energy cost, which corresponds to the lowest potential energy.

For instance, the ground-state configuration for Carbon, with six electrons, is expressed as \(1s^2 2s^2 2p^2\). Improving upon our understanding of this concept, it's vital to recognize that while elements in their ground state are in their most stable form, incorrect electron configurations can lead to identifying the wrong element, as seen in some solutions where an electron configuration might represent an excited state rather than the ground state.

Electronic Structure of Atoms

The electronic structure of atoms describes the organization of electrons in an atom's electron shells and subshells based on quantum mechanics. Each electron is described by quantum numbers that dictate its energy level, the shape of the orbital it occupies, and its orientation and spin within that orbital. These parameters guide us in the application of Hund's Rule, Pauli Exclusion Principle, and the Aufbau Principle to correctly populate an atom's orbitals in exercises.

To develop this concept and apply it to homework or real-world problems, visualize it as if constructing a building from the ground up. The foundation (nuclear charge, electron shells) determines how the structure (electron configuration) will rise. Always remember that electrons seek the lowest energy, and understanding this electronic 'architecture' is pivotal in explaining chemical properties and reactivity of elements.