Question

Use electron-configuration notation to show how electrons are distributed in a ground-state silicon (Si) atom. How many valence electrons does this atom have? Answer: Silicon has atomic number 14, so it has 14 electrons. We start by putting the first two electrons in the 1s subshell, the next two in the 2s subshell, the next six in the \(2 p\) subshell, the next two in the 3s subshell, and the remaining two in the \(3 p\) subshell: \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{2}\) The highest principal quantum number is 3, and summing up the electrons in the two \(n=3\) subshells tells us this atom has four valence electrons.

Short answer

A ground-state silicon atom has an electron configuration of \(1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{2}\) and has 4 valence electrons.

Step-by-step solution

Write the electron configuration of the silicon atom

According to the Aufbau principle, electrons are added one at a time to the lowest energy orbitals. We can write the electron configuration of a silicon atom as: \[1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{2}\]

Determine the highest principal quantum number

The highest principal quantum number (n) represents the outermost energy level of the atom. In our electron configuration, the highest principal quantum number is 3. The subshells in this energy level are 3s and 3p.

Calculate the number of valence electrons

Valence electrons are the electrons in the outermost energy level (n=3) of the atom. In the 3s and 3p subshells, we have: \[3s^{2} 3p^{2}\] Adding up the electrons in these two subshells, we have a total of 2 + 2 = 4 valence electrons. So, a ground-state silicon atom has an electron configuration of \(1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{2}\) and has 4 valence electrons.

Key concepts

Valence Electrons

Valence electrons are the electrons residing in the outermost shell of an atom, which can play a crucial role in chemical reactions and bonding. These electrons determine an atom's capacity to gain, lose, or share electrons, and thus largely dictate the chemical properties of the element.

Taking silicon as an example, by examining its electron configuration (1s^2 2s^2 2p^6 3s^2 3p^2), we observe that the electrons in the highest energy level—here the third shell (n=3)—are the valence electrons. There are 4 valence electrons in the case of silicon, which means it can form four bonds with other atoms. Generally, atoms with a full outer shell are stable and less likely to react chemically, whereas those with fewer valence electrons than the noble gas configuration tend to be more reactive.

Aufbau Principle

The Aufbau principle is a fundamental guideline for determining the electron configuration of atoms. It states that electrons fill atomic orbitals in order of increasing energy levels, with the lowest energy orbitals being filled first. Think of it like filling up seats in a theatre from front to back to ensure a clear view (minimum energy) for everyone.

As per this principle, silicon's electrons will occupy the 1s orbital first, then the 2s, and continue in this pattern until all electrons have been placed. The notation 1s^2 2s^2 2p^6 3s^2 3p^2 shows this orderly fill-up for silicon, where numbers denote the principal quantum number, 's' and 'p' represent the type of subshell, and the superscripts indicate the number of electrons in that subshell. It is crucial to remember, however, that the actual filling order gets more complex with larger atoms, as certain orbitals in higher shells might have lower energy than those in lower shells.

Principal Quantum Number

The principal quantum number, symbolized as 'n', indicates the relative size and energy of atomic orbitals. It is an integer starting from 1, which increases as one moves to outer shells, meaning that higher n values correspond to higher energy levels and larger orbitals. For instance, the principal quantum number for the innermost shell of silicon is 1 (1s), and the highest occupied shell, which holds the valence electrons, is 3 (3s and 3p).

In our example of a silicon atom, the highest principal quantum number is three, which tells us that the valence electrons are in the third shell, giving us a clear indication of the atom's reactivity and how it might form bonds. Just like a ladder where higher steps represent higher energy levels, 'n' helps us to visualize the electrons' arrangement and their potential influence on chemical behavior.