Problem 87 - General Chemistry: Principles and Modern Applications

Question

The following electron configurations correspond to the ground states of certain elements. Name each element. (a) \([\mathrm{Rn}] 7 s^{2} 6 d^{2} ;\) (b) \([\mathrm{He}] 2 s^{2} 2 p^{2} ;\) (c) \([\mathrm{Ar}] 3 d^{3} 4 s^{2}\) (d) \([\mathrm{Kr}] 4 d^{10} 5 s^{2} 5 p^{4} ;\) (e) \([\mathrm{Xe}] 4 f^{2} 6 s^{2} 6 p^{1}\)

Step-by-Step Solution

Answer

The elements corresponding to these electron configurations are: (a) Thorium (Th); (b) Carbon (C); (c) Vanadium (V); (d) Tellurium (Te); (e) Thulium (Tm).

Step 1: Identity The Noble Gas Core

The electron configurations are given with a noble gas core, represented by the symbol of the noble gas in square brackets. For example, in (a) \([\mathrm{Rn}] 7 s^{2} 6 d^{2}\), Rn stands for Radon, which has 86 electrons. This is the inert gas core for this element.

Step 2: Count the Additional Electrons

Count the number of electrons outside the noble gas core. In the previous example, the number of additional electrons is \(7s^{2}\) or 2 electrons and \(6d^{2}\) or 2 electrons. Adding these to the 86 electrons of the noble gas core gives a total of 90 electrons.

Step 3: Identify the Element

The element is identified by its atomic number, which is equal to the total number of electrons in the neutral atom. An atom with 90 electrons is thorium (Th).

Step 4: Repeat the Process

Repeat the process for each of the electron configurations given in the assignment.

Key Concepts

Atomic Number

The atomic number of an element is a fundamental property. It represents the number of protons in the nucleus, which is also equal to the number of electrons in a neutral atom. When identifying an element based on its electron configuration, noting the atomic number is crucial.
For example, if the electron configuration totals 90 electrons, this matches the atomic number 90, identifying thorium (Th).
Remember, the atomic number not only helps identify the element but also tells us about its position in the periodic table. This number helps us locate elements in the order of increasing complexity, from hydrogen to heavier elements.

Noble Gas Core

Noble gas cores simplify the electron configurations by summarizing the filled electron shells with the notation of the nearest noble gas. For instance, the notation r \([ ext{Rn}]\) denotes a core filled up to the number of electrons in radon.
This core includes all the electrons in complete orbital shells that are equivalent to radon. The noble gases, like helium, neon, and argon, are the key markers, as they have complete outer electron shells.

• Radon, denoted as \([ ext{Rn}]\), accounts for 86 electrons
• Helium, or \([ ext{He}]\), accounts for 2 electrons
• Argon, or \([ ext{Ar}]\), accounts for 18 electrons

This method streamlines electron configurations, making it quicker to write and easier to interpret.

Ground State

The ground state of an atom is its lowest energy state, where the electrons are in the closest possible orbitals to the nucleus. This is the most stable configuration for the atom. The step-by-step solution assumes we are dealing with the configurations in their ground states when identifying elements.
Electrons will always fill orbitals in the order of increasing energy levels, starting with the lowest. This is according to the Aufbau principle, which guides the order in which orbitals are filled. Therefore, when we analyze electron configurations, they usually reflect the atom in this state of lowest energy.

• Octet rule stability
• Minimum energy principle

This fundamental understanding of the ground state helps in predicting chemical reactions and bonding.

Electron Count

Counting electrons is essential to decipher the electron configuration. This count includes both those electrons in the noble gas core and the additional ones indicated in the notation after the core.
For instance, in r \([ ext{Rn}] 7s^2 6d^2\):

• The radon core contributes 86 electrons.
• The additional configuration part \(7s^2\) adds another 2 electrons, and \(6d^2\) adds 2 more.
• This totals to 90 electrons for the element thorium (Th).

Knowing how to count these electrons ensures accuracy in determining elements and their properties. Once you add up the total, the electron count equals the atomic number of the atom.