Question

Extend the aufbau sequence through an element that has not yet been identified, but whose atoms would completely fill 7p orbitals. How many electrons such an atom would have? Write its electron configuration using noble-gas notation for the previous noble gas, radon.

Short answer

The unidentified element has 116 electrons, and its electron configuration using noble gas notation is \(\mathrm{[Rn] \: 5f^{14} \: 6d^{10} \: 7p^6}\).

Step-by-step solution

Identify the previous noble gas

The previous noble gas is Radon, with atomic number 86. Its electron configuration is: \[ \mathrm{1s^2 \: 2s^2 \: 2p^6 \: 3s^2 \: 3p^6 \: 4s^2 \: 3d^{10} \: 4p^6 \: 5s^2 \: 4d^{10} \: 5p^6 \: 6s^2 \: 4f^{14} \: 5d^{10} \: 6p^6 \: 7s^2} \]

Add electrons to fill orbitals in accordance to Aufbau principle

We will now add electrons to the orbitals following the Aufbau principle. Remember that s orbitals can hold 2 electrons, p orbitals can hold 6, d orbitals can hold 10, and f orbitals can hold 14. After Radon, the next orbitals to be filled are 5f, 6d, and 7p. In order to fill the 7p orbitals, we have to add electrons as follows: Fill 5f with 14 electrons: \( \mathrm{5f^{14}} \) Fill 6d with 10 electrons: \( \mathrm{6d^{10}} \) Fill 7p with 6 electrons: \( \mathrm{7p^6} \)

Calculate the total number of electrons

To calculate the total number of electrons in this unidentified element, we need to add the electrons from Radon, as well as the additional electrons we added in Step 2. Radon has 86 electrons + 14 electrons in 5f + 10 electrons in 6d + 6 electrons in 7p = 116 electrons in total.

Write the electron configuration using noble gas notation

Finally, we write the electron configuration for this unidentified element using noble gas notation. We will use Radon as a starting point and write down the electron configuration for the rest of the filled orbitals: \[ \mathrm{[Rn] \: 5f^{14} \: 6d^{10} \: 7p^6} \] The unidentified element has 116 electrons, and its electron configuration using noble gas notation is \(\mathrm{[Rn] \: 5f^{14} \: 6d^{10} \: 7p^6}\).

Key concepts

Aufbau Principle

The Aufbau Principle is a fundamental concept in chemistry that dictates how electrons are added to atomic orbitals as the atomic number increases. The term 'aufbau' comes from a German word meaning 'construction' or 'building up'. This principle helps us determine the electron configuration of an atom. According to this rule, electrons are added to the lowest energy orbital first before moving to higher energy orbitals.

• Electrons fill orbitals in a specific order: 1s, 2s, 2p, 3s, 3p, and so on.
• The filling order can be understood by referring to the "building up" diagram or the diagonal rule.
• After filling the 6p orbitals in Radon, the next orbitals to be filled are 5f, then 6d, and finally 7p.

By following the Aufbau Principle, chemists can predict and understand the electron configuration for any element in the periodic table.

Atomic Orbitals

Atomic orbitals are regions around the nucleus where electrons are likely to be found. These orbitals have specific shapes and energy levels that determine how they are populated by electrons. Each type of orbital—s, p, d, and f—has its unique characteristics.
Different orbitals can hold different numbers of electrons.

• s orbitals are spherical and can hold up to 2 electrons.
• p orbitals have a dumbbell shape and can accommodate 6 electrons across three different orientations—p_x, p_y, and p_z.
• d orbitals are more complex in shape and can hold up to 10 electrons distributed among five orientations.
• f orbitals, the most complex, can hold 14 electrons, scattered across seven orientations.

Understanding these orbital types is crucial when writing electron configurations, as they guide where each electron resides within an atom.

Noble Gas Notation

Noble gas notation is a shorthand way of writing electron configurations that emphasizes the filled electron shells of noble gases. It simplifies the process by using the symbol of the previous noble gas as a bracketed reference, followed by the configuration of any additional electrons.
This notation is particularly useful for elements with large numbers of electrons. It helps write out electron configurations without listing every electron individually.

• For example, Radon has an electron configuration that can be expressed as \[ [Rn] \] plus any additional electrons in higher shells.
• In the case of the unidentified element filling the 7p orbitals, the noble gas notation of its electron configuration is\[ [Rn] \5f^{14} \6d^{10} \7p^6 \]

Noble gas notation reduces the complexity of electron configurations and makes it easier to visualize and understand the placement of electrons among different orbital levels.