Question

Draw atomic orbital diagrams representing the ground-state electron configuration for each of the following elements. a. \(\mathrm{Na}\) b. \(\mathrm{Co}\) c. \(\mathrm{Kr}\) How many unpaired electrons are present in each element?

Short answer

The ground-state electronic configurations for the given elements are as follows: a. Sodium (Na) has 1 unpaired electron in its 3s orbital. b. Cobalt (Co) has 3 unpaired electrons in its 3d orbitals. c. Krypton (Kr) has no unpaired electrons in its ground state.

Step-by-step solution

Determine the number of electrons for each element

Using the periodic table, we can find the atomic number of each element, which also represents the number of electrons in its neutral state. The atomic numbers are: a. Na: 11 b. Co: 27 c. Kr: 36

Determine the electron filling order using aufbau principle

Following the aufbau principle, determine the order in which the electrons will fill the orbitals. We can use the standard electron filling notation: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p... We will fill the electrons according to the elements we have (Na = 11, Co = 27, Kr = 36).

Construct the orbital diagrams

Using Hund's rule, construct the orbital diagrams for Na, Co, and Kr, filling electrons from lowest energy to highest. a. Sodium (Na: 11 electrons) 1s: ↑↓ 2s: ↑↓ 2p: ↑↓ ↑↓ ↑↓ 3s: ↑ b. Cobalt (Co: 27 electrons) 1s: ↑↓ 2s: ↑↓ 2p: ↑↓ ↑↓ ↑↓ 3s: ↑↓ 3p: ↑↓ ↑↓ ↑↓ 4s: ↑↓ 3d: ↑ ↑ ↑ ↑ ↑ ↑↓ ↑↓ c. Krypton (Kr: 36 electrons) 1s: ↑↓ 2s: ↑↓ 2p: ↑↓ ↑↓ ↑↓ 3s: ↑↓ 3p: ↑↓ ↑↓ ↑↓ 4s: ↑↓ 3d: ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ ↑↓ 4p: ↑↓ ↑↓ ↑↓

Count unpaired electrons

Now, count the unpaired electrons for each element: a. Sodium (Na): 1 unpaired electron b. Cobalt (Co): 3 unpaired electrons c. Krypton (Kr): 0 unpaired electrons The ground-state electronic configurations for these elements are as follows: a. Sodium (Na) has 1 unpaired electron in its ground state. b. Cobalt (Co) has 3 unpaired electrons in its ground state. c. Krypton (Kr) has no unpaired electrons in its ground state.

Key concepts

Aufbau Principle

The Aufbau Principle is a key concept in determining the electron configuration of an atom. It helps us understand the sequence in which electrons fill the atomic orbitals. The word "aufbau" is German for "building up", and that is just what this principle describes.

Electrons fill orbitals starting with the lowest energy levels before moving on to those with higher energy. The order does not always follow the numerical order of energy levels, so it's important to learn this sequence. Here's a quick guide to remember the order: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, and so on.

You can use this sequence to add electrons to orbitals one by one. For instance, Sodium (Na) has 11 electrons, filling up to the 3s orbital, while Cobalt (Co) with 27 electrons starts filling the 3d orbitals, and Krypton (Kr) with 36 electrons reaches into the 4p orbitals.

Hund's Rule

When placing electrons into orbitals, Hund's Rule becomes important. This rule is super helpful! It tells us that every orbital in a given subshell gets one electron first before any of them can hold a second electron.

This approach minimizes the repulsion between electrons since they prefer to remain unpaired in separate orbitals. For example, when filling the 3d subshell of Cobalt, you add one electron to each of the five available 3d orbitals before any of them gets a second electron.

This is why we find Cobalt has unpaired electrons. Hund's Rule ensures that the spins of the electrons remain as unpaired as possible across orbitals which helps in determining the magnetic properties of an element.

Atomic Orbitals

Atomic orbitals are regions around the nucleus where electrons are most likely to be found. Each orbital can hold up to two electrons, and orbitals come in different shapes and sizes, like s, p, d, and f types.

The most basic and lowest energy orbital, the s orbital, is a sphere shape. The p orbitals are more like dumbbells, while d and f orbitals have more complex shapes.

When we're mapping out an element's electron configuration, we arrange electrons in these orbitals following the Aufbau Principle and Hund's Rule. For example, in Krypton (Kr), once all s and p orbitals are filled, the electron configuration ends with a full set of p orbitals, making Krypton very stable.

Unpaired Electrons

Unpaired electrons are single electrons found in an atomic orbital. They are significant because they affect the chemical and magnetic properties of an atom.

For chemistry, these unpaired electrons often result in an atom's reactivity, while in terms of magnetism, the unpaired electrons contribute to the paramagnetic properties of an atom. Let's look at our elements: Sodium (Na) has one unpaired electron in the 3s orbital, which plays a significant role in its reactivity.

• Na - 1 unpaired electron
• Co - 3 unpaired electrons, found in the 3d orbitals
• Kr - No unpaired electrons, which adds to its inert nature

Understanding the number of unpaired electrons is crucial when analyzing how an element will interact and bond with others.