Question

Give the electron configurations of (a) \(S,\) (b) \(K\), (c) \(\mathrm{Ti}\) and (d) Sn. (c) \(\mathrm{Ni}\)

Short answer

The electron configurations are (a) S: \(1s^2 2s^2 2p^6 3s^2 3p^4\), (b) K: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^1\), (c) Ti: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^2\), (d) Sn: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^2\), and (c) Ni: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^8\).

Step-by-step solution

Determine the Atomic Numbers

To write the electron configurations, first determine the atomic numbers of the elements. The atomic number corresponds to the number of protons and, in a neutral atom, also the number of electrons. Look up each element on the periodic table to find its atomic number: Sulfur (S) has an atomic number of 16, Potassium (K) is 19, Titanium (Ti) is 22, Tin (Sn) is 50, and Nickel (Ni) is 28.

Write the Electron Configuration for Sulfur (S)

Sulfur has 16 electrons. The electron configuration for Sulfur is obtained by filling the orbitals from lowest to highest energy according to the Aufbau principle, the Pauli exclusion principle, and Hund's rule. The resulting electron configuration for Sulfur (S) is: \( 1s^2 2s^2 2p^6 3s^2 3p^4 \).

Write the Electron Configuration for Potassium (K)

Potassium has 19 electrons. After filling the 1s, 2s, 2p, 3s, and 3p orbitals, the 19th electron occupies the next lowest energy level, which is the 4s orbital. The electron configuration for Potassium (K) is: \( 1s^2 2s^2 2p^6 3s^2 3p^6 4s^1 \).

Write the Electron Configuration for Titanium (Ti)

Titanium has 22 electrons. The electrons fill the 3d orbital after the 4s orbital, following the Aufbau principle. The electron configuration for Titanium (Ti) is written as: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^2\), with two electrons in the 3d orbital.

Write the Electron Configuration for Tin (Sn)

Tin has 50 electrons. To write its electron configuration, follow the order in which energy levels and orbitals are filled. The electron configuration for Tin (Sn) is: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} 5p^2\).

Write the Electron Configuration for Nickel (Ni)

Nickel has 28 electrons. Following the order of filling, the electron configuration for Nickel (Ni) is \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^8\), with eight electrons in the 3d subshell.

Key concepts

Aufbau Principle

The Aufbau principle is a fundamental guideline used in determining the electron configuration of an atom. It instructs us to fill electron orbitals starting with the lowest energy level first before moving to higher energy levels. The word 'Aufbau' is German for 'building up,' and that’s exactly how you should think about this principle—like constructing a building from the ground up.

Imagine each electron as a resident in a vast hotel with multiple floors representing energy levels and various rooms representing orbitals. According to the Aufbau principle, we start populating the hotel from the lower floors before moving up. Electrons fill the 1s orbital first, because it’s the room on the lowest floor, before moving on to 2s, 2p, and so on. This pattern follows a specific sequence known as the Madelung rule, which is often depicted as a diagonal arrow chart.

Let’s take sulfur (S) as an example. Sulfur has an atomic number of 16. Following the Aufbau principle, you begin filling in from the 1s orbital upwards. The configuration for Sulfur becomes: 1s2 2s2 2p6 3s2 3p4. Each subshell is filled according to the increasing energy order: first the 1s, followed by 2s, then 2p, and so on.

Pauli Exclusion Principle

The Pauli Exclusion Principle is another key concept that helps us understand how electrons are distributed in an atom’s orbitals. This principle, proposed by Wolfgang Pauli in 1925, states that no two electrons in an atom can have the same set of four quantum numbers. To put it simply, each room in our electron hotel can only accommodate two residents, and they must be sleeping in different beds—these beds are referred to as an electron’s spin.

An electron's spin can either be up (+1/2) or down (-1/2), and in each orbital room (such as 1s, 2s, or 2p), you can only have one electron with up spin and one with down spin. Going back to our sulfur example, after filling the lower energy orbitals, you would place two electrons with opposite spins in the 3p orbital until you reach 16 electrons for sulfur: 1s2 2s2 2p6 3s2 3p4. You can see the principle in action here, as the electrons are paired up in orbitals with opposite spins.

Hund's Rule

Hund's rule addresses how electrons are distributed among orbitals of the same energy—called degenerate orbitals. It’s the equivalent of deciding how to most comfortably seat passengers when there are multiple empty rows on a bus. Hund's rule states that electrons will fill an empty orbital before they pair up with another electron in the same orbital.

The goal is to maximize the total spin of electrons, which reduces the repulsion between them as they maintain their own space as much as possible. In the case of sulfur, the 3p level contains three degenerate orbitals and, as dictated by Hund's rule, two of these are singly occupied before the third begins to fill: 3p4 means we have three 3p orbitals with one electron each, and one of them will receive the second electron to pair up after the others are half-filled.

This concept is crucial for predicting the ground state electron configurations of atoms, as it affects the electrons’ arrangement within an orbital set, and thus the overall stability and chemical properties of the atom.