Question

Write the full electron configuration \(\left(1 s^{2} 2 s^{2},\right.\) etc. ) for each of the following elements. a. phosphorus, \(Z=15\) b. calcium, \(Z=20\) c. potassium, \(Z=19\) d. boron, \(Z=5\)

Short answer

a. Phosphorus: \(1s^{2}2s^{2}2p^{6}3s^{2}3p^{3}\) b. Calcium: \(1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^{2}\) c. Potassium: \(1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^{1}\) d. Boron: \(1s^{2}2s^{2}2p^{1}\)

Step-by-step solution

a. Phosphorus, \(Z=15\)

To find the electron configuration for Phosphorus, we will follow these steps: 1. Identify the atomic number (Z), which is 15 for phosphorus. 2. Fill the orbitals following the order: \(1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p\). Note that the given exercise only requires us to write the electron configuration up to the given atomic number (Z), in this case, 15. 3. Fill the orbitals with electrons, starting with the lowest energy level (\(1s\)), and following the order given in step 2, until all 15 electrons have been placed. Electron Configuration: \(1s^{2}2s^{2}2p^{6}3s^{2}3p^{3}\)

b. Calcium, \(Z=20\)

To find the electron configuration for Calcium, we will follow the same steps as before: 1. Identify the atomic number (Z), which is 20 for calcium. 2. Fill the orbitals following the order mentioned in step 2 of phosphorus until all 20 electrons have been placed. Electron Configuration: \(1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^{2}\)

c. Potassium, \(Z=19\)

To find the electron configuration for Potassium, we will follow the same steps as before: 1. Identify the atomic number (Z), which is 19 for potassium. 2. Fill the orbitals following the order mentioned in step 2 of phosphorus until all 19 electrons have been placed. Electron Configuration: \(1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^{1}\)

d. Boron, \(Z=5\)

To find the electron configuration for Boron, we will follow the same steps as before: 1. Identify the atomic number (Z), which is 5 for boron. 2. Fill the orbitals following the order mentioned in step 2 of phosphorus until all 5 electrons have been placed. Electron Configuration: \(1s^{2}2s^{2}2p^{1}\)

Key concepts

Atomic Number

The atomic number of an element is a fundamental concept in chemistry. It represents the number of protons in the nucleus of an atom.
It is denoted by the symbol \(Z\). The atomic number also indicates the number of electrons in a neutral atom.
For example, Phosphorus has an atomic number of 15, meaning it has 15 protons and, in a neutral state, 15 electrons.

• Phosphorus: \(Z=15\)
• Calcium: \(Z=20\)
• Potassium: \(Z=19\)
• Boron: \(Z=5\)

This number is pivotal when writing electron configurations, as it tells us how many electrons we need to arrange in orbitals.

Orbitals Filling Order

Electrons in an atom occupy orbitals in a specific order based on increasing energy levels. This order can be remembered using the Aufbau principle, which means "building up."
The general order for filling orbitals is:

• \(1s\)
• \(2s\)
• \(2p\)
• \(3s\)
• \(3p\)
• \(4s\)
• \(3d\)
• \(4p\)
• ...and so on

This order corresponds to the lowest energy levels being filled first. An easy way to determine this order is by using the orbital diagram known as the Aufbau diagram.

Phosphorus Electron Configuration

Phosphorus, identified by its atomic number \(Z=15\), has an electron configuration that can be determined by filling its electrons into the appropriate orbitals.
First, fill the \(1s\) orbital with 2 electrons, then the \(2s\) with 2 more. Continue with the \(2p\), which can hold up to 6 electrons.
Subsequently, the \(3s\) orbital is filled with 2 electrons. The remaining 3 electrons go into the \(3p\) orbital.
Thus, the electron configuration for Phosphorus is: \[1s^2 2s^2 2p^6 3s^2 3p^3\]

Calcium Electron Configuration

For calcium, with an atomic number of \(Z=20\), distribute its electrons starting from lower-energy orbitals.
The \(1s\), \(2s\), and \(2p\) orbitals will be fully occupied by 10 electrons, total.
Next, the \(3s\) and \(3p\) orbitals get filled with 8 more electrons. Finally, the \(4s\) orbital is filled with the last 2 electrons.
Calcium's electron configuration is therefore:\[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2\]

Potassium Electron Configuration

Potassium has an atomic number of \(Z=19\). We determine its electron configuration by placing 19 electrons into the orbitals.
Starting with the \(1s\), \(2s\), and \(2p\) orbitals, these contain the first 10 electrons.
Then, the \(3s\) and \(3p\) orbitals hold the next 8.
The final electron goes into the \(4s\) orbital.

• Potassium concludes with:\[1s^2 2s^2 2p^6 3s^2 3p^6 4s^1\]

This configuration reflects its position as the first element in the 4th period of the periodic table.

Boron Electron Configuration

Boron, with an atomic number \(Z=5\), is smaller in electron count, resulting in a shorter configuration.
The \(1s\) orbital accommodates 2 electrons, and the \(2s\) has 2, leaving 1 more electron to be placed.
This remaining electron occupies the \(2p\) orbital.
Thus, boron's electron configuration is represented as:

• \(1s^2 2s^2 2p^1\)

This reflects its place on the second row of the periodic table, specifically in Group 13.