Question

Write the full electron configuration \(\left(1 s^{2} 2 s^{2}, \text { etc. }\right)\) for each of the following elements. a. potassium, \(Z=19\) b. chlorine, \(Z=17\) c. magnesium, \(Z=12\) d. carbon, \(Z=6\)

Short answer

a. Potassium (Z=19): \(1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^{1}\) b. Chlorine (Z=17): \(1s^{2}2s^{2}2p^{6}3s^{2}3p^{5}\) c. Magnesium (Z=12): \(1s^{2}2s^{2}2p^{6}3s^{2}\) d. Carbon (Z=6): \(1s^{2}2s^{2}2p^{2}\)

Step-by-step solution

Potassium (Z=19)

As potassium has an atomic number (Z) of 19, it has 19 electrons. We fill the orbitals referring to the periodic table: 1. 1s orbital can hold 2 electrons, so it is filled first as 1s². 2. Then, 2s orbital is filled, which can hold 2 electrons. The configuration now is 1s²2s². 3. After that, the 2p orbital is filled, which can hold 6 electrons. The configuration becomes 1s²2s²2p⁶. 4. Next, the 3s orbital is filled with 2 electrons, and the configuration is now 1s²2s²2p⁶3s². 5. The 3p orbital is filled with 6 electrons. The configuration becomes 1s²2s²2p⁶3s²3p⁶. 6. Finally, we fill the 4s orbital with 1 electron, as we have only one electron left. The overall electron configuration for potassium (Z=19) is \(1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^{1}\).

Chlorine (Z=17)

For chlorine with an atomic number (Z) of 17, there are 17 electrons. Following the Aufbau principle and filling the orbitals: 1. 1s² 2. 1s²2s² 3. 1s²2s²2p⁶ 4. 1s²2s²2p⁶3s² 5. 1s²2s²2p⁶3s²3p⁵ (last 5 electrons are filled in the 3p orbital) So, the electron configuration for chlorine (Z=17) is \(1s^{2}2s^{2}2p^{6}3s^{2}3p^{5}\).

Magnesium (Z=12)

Magnesium has an atomic number (Z) of 12, with 12 electrons. Filling the orbitals: 1. 1s² 2. 1s²2s² 3. 1s²2s²2p⁶ 4. 1s²2s²2p⁶3s² (last two electrons are filled in the 3s orbital) The electron configuration for magnesium (Z=12) is \(1s^{2}2s^{2}2p^{6}3s^{2}\).

Carbon (Z=6)

Carbon has an atomic number (Z) of 6, with 6 electrons. Filling the orbitals: 1. 1s² 2. 1s²2s² 3. 1s²2s²2p² (last two electrons are filled in the 2p orbital) The electron configuration for carbon (Z=6) is \(1s^{2}2s^{2}2p^{2}\).

Key concepts

Aufbau Principle

Understanding the Aufbau principle is essential when determining the electron configuration of an element. This principle, which means 'building up' in German, refers to the sequence in which electrons populate atomic orbitals. Electrons are not simply scattered around the atom; they follow a specific filling order that minimizes the energy of the atom.

According to the Aufbau principle, electrons fill the lowest energy levels first before moving to higher levels. For instance, the 1s orbital, being the closest to the nucleus, has the lowest energy and is filled first, followed by 2s, 2p, 3s, and so on. This pattern of filling is crucial for predicting and explaining the chemical properties of elements. It helps us understand why elements in the same column of the periodic table have similar chemical characteristics—they have the same valence electron configuration.

Atomic Number

The atomic number, symbolized as 'Z', is a fundamental property of an element that tells us the number of protons found in the nucleus of an atom. This number also equals the number of electrons in a neutral atom, as the positive charge of the protons is balanced by the negative charge of the electrons. Consequently, the atomic number dictates the chemical behavior of the element.

For example, carbon with an atomic number of 6 has six electrons to place in orbitals according to the Aufbau principle. Potassium, on the other hand, with an atomic number of 19, has 19 electrons to distribute. The atomic number thus directly influences the electron configuration which, in turn, affects how an element will interact with other atoms and form compounds.

Orbital Filling Order

Orbital filling order is the sequence followed by electrons when they are arranged into orbitals. This sequence is determined by the relative energies of the orbitals, and it can be remembered through various mnemonics and diagrams, such as the often-used 'aufbau diagram'. Following the Aufbau principle, the sequence in which orbitals are filled is usually: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, and so on.

Within each type of orbital (s, p, d, f), there are a set number of orbital spaces that can be filled with up to two electrons each. The s orbitals can hold 2 electrons, p orbitals can hold 6, d orbitals can hold 10, and f orbitals can hold 14. The order of filling is crucial in predicting the electron configurations for elements and plays a significant role in chemical reactions and bonding.