Question

One reason spectroscopists study excited states is to gain information about the energies of orbitals that are unoccupied in an atom's ground state. Each of the following electron configurations represents an atom in an excited state. Identify the element, and write its condensed ground-state configuration: (a) \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{1} 3 p^{1}\) (b) \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{4} 4 s^{1}\) (c) \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2} 3 d^{4} 4 p^{1}\) (d) \(1 s^{2} 2 s^{2} 2 p^{5} 3 s^{1}\)

Short answer

a: Mg - \[1s^{2} 2s^{2} 2p^{6} 3s^{2}\], b: Cl - \[1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{5}\], c: Cr - \[1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 4s^{1} 3d^{5}\], d: Ne - \[1s^{2} 2s^{2} 2p^{6}\]

Step-by-step solution

- Identify the Total Number of Electrons

Count the total number of electrons in each electron configuration given. This sum will help to identify the element.

- Deduce the Element from the Electron Count

Use the periodic table to find the element that corresponds to the total number of electrons calculated in the previous step.

- Write the Condensed Ground-State Configuration

For each element identified in the earlier steps, write down the ground-state electron configuration by following the Aufbau principle.

Solution for (a)

Total electrons: 12. The element with 12 electrons is Magnesium (Mg). Ground-state configuration: \[1s^{2} 2s^{2} 2p^{6} 3s^{2}\].

Solution for (b)

Total electrons: 17. The element with 17 electrons is Chlorine (Cl). Ground-state configuration: \[1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{5}\].

Solution for (c)

Total electrons: 24. The element with 24 electrons is Chromium (Cr). Ground-state configuration: \[1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 4s^{1} 3d^{5}\].

Solution for (d)

Total electrons: 10. The element with 10 electrons is Neon (Ne). Ground-state configuration: \[1s^{2} 2s^{2} 2p^{6}\].

Key concepts

excited states

When an atom absorbs energy, its electrons can jump to higher energy levels or orbitals. This state is called an **excited state**. In this state, the atom is not at its lowest possible energy level. This is important in spectroscopy because studying excited states can reveal the structure and energy of orbitals that are normally unoccupied.
For example, in the configuration \(1s^{2} 2s^{2} 2p^{6} 3s^{1} 3p^{1}\), one of the electrons that would normally be in the 3s orbital has moved to the 3p orbital. By studying the energies of these transitions, scientists can understand more about how electrons are arranged in atoms.

ground-state configurations

When an atom is in its lowest energy state, it is said to be in its **ground state**. This state follows a specific arrangement where electrons occupy the lowest available energy levels first. The ground-state configuration of an atom can be determined using the periodic table and the Aufbau principle.
For example, the ground-state electron configuration of Neon (Ne) with 10 electrons is \(1s^{2} 2s^{2} 2p^{6}\). This means that all the electrons are in the lowest energy orbitals available, filling up the 1s and 2s orbitals before moving on to the 2p orbital.

Aufbau principle

The **Aufbau principle** is a guideline for filling up the electron orbitals of an atom. It states that electrons fill orbitals starting from the lowest energy level to the highest. 'Aufbau' is German for 'building up', which is precisely what electrons do when they fill up an atom's available orbitals.
According to the Aufbau principle, electrons will first fill the 1s orbital, then the 2s orbital, followed by the 2p orbitals, and so on. This principle helps us write the ground-state electron configurations. For instance, when writing the ground-state configuration of Magnesium (Mg) with 12 electrons, you start by filling up the 1s, 2s, 2p, and finally the 3s orbitals: \(1s^{2} 2s^{2} 2p^{6} 3s^{2}\).

periodic table

The **periodic table** is an essential tool in chemistry for understanding the properties of elements. It organizes elements based on their atomic number, electron configurations, and recurring chemical properties. Elements in the same column, or group, share similar chemical properties because they have the same number of valence electrons.
By examining the periodic table, we can determine an element's electron configuration easily. For example, for Chlorine (Cl) which has 17 electrons, its ground-state configuration is \(1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{5}\). The table helps us to place each electron in the correct orbital.