Question

Write the complete orbital diagram for each of the following elements, using boxes to represent orbitals and arrows to represent electrons. a. scandium, \(Z=21\) b. sulfur, \(Z=16\) c. potassium, \(Z=19\) d. nitrogen, \(Z=7\)

Short answer

The complete orbital diagrams for the given elements are as follows: a. Scandium (Sc), \(Z=21\): 1s: \(\uparrow \downarrow\) , 2s: \(\uparrow \downarrow\), 2p: \(\uparrow \downarrow \uparrow \downarrow \uparrow \downarrow\), 3s: \(\uparrow \downarrow\), 3p: \(\uparrow \downarrow \uparrow \downarrow \uparrow \downarrow\), 4s: \(\uparrow \downarrow\), 3d: \(\uparrow\) b. Sulfur (S), \(Z=16\): 1s: \(\uparrow \downarrow\), 2s: \(\uparrow \downarrow\), 2p: \(\uparrow \downarrow \uparrow \downarrow \uparrow \downarrow\), 3s: \(\uparrow \downarrow\), 3p: \(\uparrow \downarrow \uparrow \downarrow \uparrow \) c. Potassium (K), \(Z=19\): 1s: \(\uparrow \downarrow\), 2s: \(\uparrow \downarrow\), 2p: \(\uparrow \downarrow \uparrow \downarrow \uparrow \downarrow\), 3s: \(\uparrow \downarrow\), 3p: \(\uparrow \downarrow \uparrow \downarrow \uparrow \downarrow\), 4s: \(\uparrow\) d. Nitrogen (N), \(Z=7\): 1s: \(\uparrow \downarrow\), 2s: \(\uparrow \downarrow\), 2p: \(\uparrow \uparrow \uparrow\)

Step-by-step solution

Determine the electron configuration

Since Scandium (Sc) has an atomic number of 21, it has 21 electrons. So, its electron configuration is \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^1\).

Draw the complete orbital diagram

To draw the orbital diagram for Scandium, we follow the electron configuration: 1s: \(\uparrow \downarrow\) (2 electrons) 2s: \(\uparrow \downarrow\) (2 electrons) 2p: \(\uparrow \downarrow \uparrow \downarrow \uparrow \downarrow\) (6 electrons) 3s: \(\uparrow \downarrow\) (2 electrons) 3p: \(\uparrow \downarrow \uparrow \downarrow \uparrow \downarrow\) (6 electrons) 4s: \(\uparrow \downarrow\) (2 electrons) 3d: \(\uparrow \) (1 electron) b. Sulfur, \(Z=16\)

Determine the electron configuration

Since Sulfur (S) has an atomic number of 16, it has 16 electrons. So, its electron configuration is \(1s^2 2s^2 2p^6 3s^2 3p^4\).

Draw the complete orbital diagram

To draw the orbital diagram for Sulfur, we follow the electron configuration: 1s: \(\uparrow \downarrow\) (2 electrons) 2s: \(\uparrow \downarrow\) (2 electrons) 2p: \(\uparrow \downarrow \uparrow \downarrow \uparrow \downarrow\) (6 electrons) 3s: \(\uparrow \downarrow\) (2 electrons) 3p: \(\uparrow \downarrow \uparrow \downarrow \uparrow \) (4 electrons) c. Potassium, \(Z=19\)

Determine the electron configuration

Since Potassium (K) has an atomic number of 19, it has 19 electrons. So, its electron configuration is \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^1\).

Draw the complete orbital diagram

To draw the orbital diagram for Potassium, we follow the electron configuration: 1s: \(\uparrow \downarrow\) (2 electrons) 2s: \(\uparrow \downarrow\) (2 electrons) 2p: \(\uparrow \downarrow \uparrow \downarrow \uparrow \downarrow\) (6 electrons) 3s: \(\uparrow \downarrow\) (2 electrons) 3p: \(\uparrow \downarrow \uparrow \downarrow \uparrow \downarrow\) (6 electrons) 4s: \(\uparrow\) (1 electron) d. Nitrogen, \(Z=7\)

Determine the electron configuration

Since Nitrogen (N) has an atomic number of 7, it has 7 electrons. So, its electron configuration is \(1s^2 2s^2 2p^3\).

Draw the complete orbital diagram

To draw the orbital diagram for Nitrogen, we follow the electron configuration: 1s: \(\uparrow \downarrow\) (2 electrons) 2s: \(\uparrow \downarrow\) (2 electrons) 2p: \(\uparrow \uparrow \uparrow \) (3 electrons)

Key concepts

Electron Configuration

Understanding the electron configuration of an element is crucial to grasping many aspects of chemistry and physics. It describes how electrons are distributed in an atom's orbitals. Electrons are organized in energy levels, or shells, around the nucleus, and within each shell, they're further organized into subshells. These subshells have types s, p, d, or f, each capable of holding a different maximum number of electrons (2, 6, 10, and 14, respectively). For example, sulfur with an atomic number of 16 has an electron configuration of 1s2 2s2 2p6 3s2 3p4, showing how its 16 electrons are spread across various shells and subshells.

The order in which subshells are filled is determined by their energy levels—with electrons generally occupying the lowest available energy level first, following the principle known as Aufbau's principle. Recognizing these patterns aids in predicting how atoms will behave in chemical bonding and reactions.

Atomic Number

The atomic number of an element, symbolized as 'Z,' is a fundamental property that reflects the number of protons in the nucleus of its atoms. More importantly, in a neutral atom, the atomic number also indicates the number of electrons orbiting the nucleus. This is because atoms are electrically neutral, so the number of positively charged protons equals the number of negatively charged electrons. Therefore, when we discuss the atomic number in relation to electron configuration, such as potassium with an atomic number of 19 (Z=19), we're referring to an atom that contains 19 electrons to place in the energy levels and subshells of the atom's electron cloud.

Subshells and Orbitals

Diving deeper into atomic structure, subshells are components of electron shells and contain one or more orbitals. An orbital is a region in an atom where there is a high probability of finding an electron. Each type of subshell contains a set number of orbitals: an 's' subshell has 1 orbital, a 'p' subshell has 3 orbitals, a 'd' has 5, and an 'f' has 7. Each orbital can hold up to 2 electrons.

Let's consider nitrogen (Z=7), which has the electron configuration of 1s2 2s2 2p3. Nitrogen's first two electrons fill the 1s orbital, the next two electrons fill the 2s orbital, and the remaining three are distributed in the 2p orbitals. The way these electrons are placed in the individual p orbitals is governed by Hund's rule.

Hund's Rule

Hund's rule provides a guideline for how electrons fill degenerate (equal energy) orbitals within a subshell. According to this rule, electrons will occupy separate orbitals within the same subshell before pairing up. This helps to minimize electron repulsion and keep atoms in a lower energy state. For instance, the 2p orbitals of nitrogen will be filled with one electron each before any pairing occurs, resulting in an orbital diagram where there are three half-filled 2p orbitals, as shown in the exercise solution.

In practice, when drawing an orbital diagram, we would denote each of these individual electrons as an arrow in a box, with up and down pointing arrows representing the two possible spins for a pair of electrons. Hund's rule is essential for predicting and understanding the magnetic properties of atoms and the way they interact with each other to form chemical bonds.