Draw orbital-filling diagrams for atoms with the following atomic numbers. Show each electron as an up or down arrow, and use the abbreviation of the preceding noble gas to represent inner-shell electrons. (a) Z = 25 (b) Z = 56 (c) Z = 28 (d) Z = 47

Verified step by step guidance

1. Identify the preceding noble gas for Z = 56, which is Barium (Ba). The preceding noble gas is Xenon (Xe), with an atomic number of 54. This means the electron configuration starts with [Xe].
2. Determine the number of electrons beyond the noble gas configuration. Since Z = 56 for Barium, there are 56 - 54 = 2 electrons to place beyond the [Xe] configuration.
3. Refer to the periodic table and note that Barium is in the 6th period and the 2nd group, which is the s-block. This indicates that the two electrons will be in the 6s orbital.
4. Draw the orbital filling diagram starting with the [Xe] core represented. Then add the 6s orbital, and place one up arrow (\(\uparrow\)) and one down arrow (\(\downarrow\)) in the 6s orbital to represent the two electrons.
5. Ensure that the arrows are paired correctly (one up and one down in the same orbital) to follow Hund's rule and the Pauli Exclusion Principle, which state that electrons in the same orbital must have opposite spins.

Key Concepts

Electron Configuration

Electron configuration describes the distribution of electrons in an atom's orbitals. It follows the Aufbau principle, which states that electrons fill the lowest energy orbitals first, and is often represented using the notation of noble gas core followed by the valence electrons. For example, the electron configuration for Z = 56 (Barium) is [Xe] 6s², indicating that it has two electrons in the 6s orbital after the xenon core.

Orbital Filling Diagrams

Orbital filling diagrams visually represent how electrons occupy atomic orbitals. Each orbital can hold a maximum of two electrons, which are depicted as arrows pointing up (↑) and down (↓) to indicate their spin. The Pauli exclusion principle states that no two electrons in an atom can have the same set of quantum numbers, which is why the arrows must be paired with opposite spins in each orbital.

Noble Gas Core

The noble gas core is a shorthand notation used in electron configurations to simplify the representation of inner-shell electrons. By using the symbol of the nearest noble gas preceding the element, we can focus on the valence electrons that are involved in chemical bonding. For instance, in the case of Z = 56, the noble gas xenon (Xe) is used to represent the filled inner orbitals, allowing for a more concise electron configuration.