Question

Without referring to your textbook or a periodic table, write the full electron configuration, the orbital box diagram, and the noble gas shorthand configuration for the elements with the following atomic numbers. a. \(Z=21\) b. \(Z=15\) c. \(Z=36\) d. \(Z=38\) e. \(Z=30\)

Short answer

a. Electron configuration: \(1s^2, 2s^2, 2p^6, 3s^2, 3p^6, 4s^2, 3d^1\). Orbital box diagram: 1s, 2s, 3s, 4s all have [↑↓]; 2p, 3p all have [↑↓] [↑↓] [↑↓]; 3d has [↑ ] [ ] [ ] [ ] [ ]. Noble gas shorthand: \([Ar] 4s^2 3d^1\) b. Electron configuration: \(1s^2, 2s^2, 2p^6, 3s^2, 3p^3\). Orbital box diagram: 1s, 2s, 3s all have [↑↓]; 2p has [↑↓] [↑↓] [↑↓]; 3p has [↑ ] [↑ ] [↑ ]. Noble gas shorthand: \([Ne] 3s^2 3p^3\) c. Electron configuration: \(1s^2, 2s^2, 2p^6, 3s^2, 3p^6, 4s^2, 3d^{10}, 4p^6, 5s^2\). Orbital box diagram: 1s, 2s, 3s, 4s, 5s all have [↑↓]; 2p, 3p, 4p all have [↑↓] [↑↓] [↑↓]; 3d has [↑↓] [↑↓] [↑↓] [↑↓] [↑↓]. Noble gas shorthand: \([Kr]\) d. Electron configuration: \(1s^2, 2s^2, 2p^6, 3s^2, 3p^6, 4s^2, 3d^{10}, 4p^6, 5s^2, 4d^{10}\). Orbital box diagram: 1s, 2s, 3s, 4s, 5s, 6s all have [↑↓]; 2p, 3p, 4p all have [↑↓] [↑↓] [↑↓]; 3d, 4d both have [↑↓] [↑↓] [↑↓] [↑↓] [↑↓]. Noble gas shorthand: \([Kr] 5s^2 4d^{10}\) e. Electron configuration: \(1s^2, 2s^2, 2p^6, 3s^2, 3p^6, 4s^2, 3d^{10}\). Orbital box diagram: 1s, 2s, 3s, 4s, 5s all have [↑↓]; 2p, 3p, 4p all have [↑↓] [↑↓] [↑↓]; 3d has [↑↓] [↑↓] [↑↓] [↑↓] [↑↓]. Noble gas shorthand: \([Ar] 4s^2 3d^{10}\)

Step-by-step solution

Determine Electron Configuration

Follow the Aufbau principle to fill in the orbitals: \(1s^2, 2s^2, 2p^6, 3s^2, 3p^6, 4s^2, 3d^1\).

Create the Orbital Box Diagram

In the orbital diagram, each box represents an orbital, and arrows represent electrons. We draw the orbital diagram according to the electron configuration: s-orbitals (1 box): 1s: [↑↓] 2s: [↑↓] 3s: [↑↓] 4s: [↑↓] p-orbitals (3 boxes): 2p: [↑↓] [↑↓] [↑↓] 3p: [↑↓] [↑↓] [↑↓] d-orbitals (5 boxes): 3d: [↑ ] [ ] [ ] [ ] [ ] Noble gas shorthand configuration: \([Ar] 4s^2 3d^1\) b. \(Z=15\)

Determine Electron Configuration

Follow the Aufbau principle to fill in the orbitals: \(1s^2, 2s^2, 2p^6, 3s^2, 3p^3\).

Create the Orbital Box Diagram

According to the electron configuration, we have the following orbital diagram: s-orbitals: 1s: [↑↓] 2s: [↑↓] 3s: [↑↓] p-orbitals: 2p: [↑↓] [↑↓] [↑↓] 3p: [↑ ] [↑ ] [↑ ] Noble gas shorthand configuration: \([Ne] 3s^2 3p^3\) c. \(Z=36\)

Determine Electron Configuration

Follow the Aufbau principle to fill in the orbitals: \(1s^2, 2s^2, 2p^6, 3s^2, 3p^6, 4s^2, 3d^{10}, 4p^6, 5s^2\).

Create the Orbital Box Diagram

According to the electron configuration, we have the following orbital diagram: s-orbitals: 1s: [↑↓] 2s: [↑↓] 3s: [↑↓] 4s: [↑↓] 5s: [↑↓] p-orbitals: 2p: [↑↓] [↑↓] [↑↓] 3p: [↑↓] [↑↓] [↑↓] 4p: [↑↓] [↑↓] [↑↓] d-orbitals: 3d: [↑↓] [↑↓] [↑↓] [↑↓] [↑↓] Noble gas shorthand configuration: \([Kr]\) d. \(Z=38\)

Determine Electron Configuration

Follow the Aufbau principle to fill in the orbitals: \(1s^2, 2s^2, 2p^6, 3s^2, 3p^6, 4s^2, 3d^{10}, 4p^6, 5s^2, 4d^{10}, 5p^6, 6s^2\)

Create the Orbital Box Diagram

According to the electron configuration, we have the following orbital diagram: s-orbitals: 1s: [↑↓] 2s: [↑↓] 3s: [↑↓] 4s: [↑↓] 5s: [↑↓] 6s: [↑↓] p-orbitals: 2p: [↑↓] [↑↓] [↑↓] 3p: [↑↓] [↑↓] [↑↓] 4p: [↑↓] [↑↓] [↑↓] d-orbitals: 3d: [↑↓] [↑↓] [↑↓] [↑↓] [↑↓] 4d: [↑↓] [↑↓] [↑↓] [↑↓] [↑↓] Noble gas shorthand configuration: \([Kr] 5s^2 4d^{10}\) e. \(Z=30\)

Determine Electron Configuration

Follow the Aufbau principle to fill in the orbitals: \(1s^2, 2s^2, 2p^6, 3s^2, 3p^6, 4s^2, 3d^{10}, 4p^6, 5s^2\).

Create the Orbital Box Diagram

According to the electron configuration, we have the following orbital diagram: s-orbitals: 1s: [↑↓] 2s: [↑↓] 3s: [↑↓] 4s: [↑↓] 5s: [↑↓] p-orbitals: 2p: [↑↓] [↑↓] [↑↓] 3p: [↑↓] [↑↓] [↑↓] 4p: [↑↓] [↑↓] [↑↓] d-orbitals: 3d: [↑↓] [↑↓] [↑↓] [↑↓] [↑↓] Noble gas shorthand configuration: \([Ar] 4s^2 3d^{10}\)

Key concepts

Aufbau Principle

The Aufbau principle, which translates to 'building up', is a fundamental concept in quantum chemistry for determining the electron configuration of elements. According to this principle, electrons fill atomic orbitals in order of increasing energy levels. Electrons first occupy the lowest energy orbital available before moving to higher energy levels.

An easy way to remember the order of fill is to use a mnemonic or the diagonal rule, which proceeds through orbitals in the order: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, and so on. This sequence reflects the relative energies of the orbitals; for instance, even though the 4s orbital is part of the fourth shell, it is filled before the 3d orbital because it has a lower energy.

To ensure that your configuration follows the Aufbau principle, start by filling the 1s orbital with two electrons, then move to 2s, and proceed accordingly with the principle in mind. Remember, each orbital can hold a maximum of two electrons, and Hund’s rule states that electrons will fill an orbital singly before pairing up.

The importance of the Aufbau principle cannot be overstated, as it not only allows us to write electron configurations but is also essential for understanding the chemical properties of elements since the configuration affects an atom’s reactivity and bonding.

Orbital Box Diagram

An orbital box diagram is a visual representation used to illustrate the electron configuration of an atom or molecule. The diagram features boxes or lines that each stand for an orbital, and arrows within the boxes signify electrons.

To draw an accurate box diagram, follow these steps:

• Determine the total number of electrons the element has, based on its atomic number.
• Use the Aufbau principle to decide the order in which to fill the orbitals
• Represent each orbital by a box and fill the orbitals following Hund's rule, which states that every orbital in a sublevel is singly occupied before any orbital is doubly occupied.

The unpaired and paired arrow directions within boxes typically represent the electron spin, with opposite spins for paired electrons.

An orbital box diagram aids in visualizing the arrangement of electrons in their orbitals and can be particularly helpful when dealing with electron configurations involving valence electrons. Moreover, this visual tool is handy when predicting magnetic properties of atoms and the types of bonds they may form.

Noble Gas Shorthand Notation

The noble gas shorthand notation is a simplified way of writing the electron configuration of an element. Instead of listing all the occupied orbitals from the 1s up, the notation uses the electron configuration of the nearest noble gas that precedes the element in question, encapsulated in square brackets, followed by the remainder of the electron configuration.

To use this method, locate the closest noble gas with fewer electrons than the element you're examining. Then, write out the noble gas in brackets as a starting point. From there, include the additional orbitals that are filled after the noble gas up to the element's actual position in the periodic table.

For instance, all electron configurations that go beyond neon start with \[Ne\] and then continue with the orbitals filled after neon. This shorthand is beneficial because it helps avoid repetition and emphasizes the valence electrons, which are the most chemically significant. It's the valence electrons that largely determine an element's chemical properties and its reactivity. If you understand the noble gas shorthand notation, writing and interpreting electron configurations becomes much more manageable.