Question

For the element gallium, Ga, are the \(3 d\) electrons classified as valence electrons or core electrons? Explain.

Short answer

For gallium, '3d' electrons are classified as core electrons. They are in a lower energy level than the outermost shell, and hence not involved in chemical bonding.

Step-by-step solution

Aufbau Principle

The Aufbau Principle states that electrons are filled in orbitals, sublevels, and levels in order of increasing energy. The order is as follows: \(1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p\), and so on. The ordering of these levels can also be determined from the periodic table.

Pauli Exclusion Principle

According to Pauli Exclusion Principle, each orbital can hold two electrons with opposite spins. Using this principle, we fill in the electrons for gallium. It is \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^1\). Gallium has 1 electron in the 4p orbital, 10 in the 3d orbitals, 2 in the 4s orbitals, 6 in the 3p and 3s orbitals, 6 in the 2p orbitals, 2 in the 2s orbitals, and 2 in the 1s orbital.

Classifying the Electrons

Now, we determine which electrons are valence electrons and which are core electrons. Valence electrons are electrons on an atom's highest energy level. Gallium's outermost energy level is 'n = 4', thus its valence electrons are found in the 4s and 4p orbitals. As the 3d electrons are in a lower energy level (n = 3), these are considered core electrons.

Key concepts

Aufbau Principle

The Aufbau Principle is a fundamental concept in chemistry for determining the order in which electrons occupy atomic orbitals. Imagine electrons spreading out as they fill energy levels, starting from the lowest to the highest.

According to this principle, electrons fill orbitals in a sequence of increasing energy, starting with the 1s orbital, followed by 2s, 2p, 3s, 3p, 4s, 3d, 4p, and so forth. Each orbital is filled with electrons before the next highest energy level begins to fill. This is crucial for understanding the electron configuration of elements.

• The concept aids in predicting where each electron in an atom resides.
• It ensures that electrons fill the lowest available energy states first, leading to the most stable electron configuration.
• For gallium, Ga, this principle guides us to fill up to the 4p orbital in a specific sequence.

By observing this sequence, it becomes easier to figure out which electrons are classified as core or valence, a necessary undertaking for understanding chemical properties.

Pauli Exclusion Principle

The Pauli Exclusion Principle is key in discussing electron arrangements within atoms. Unlike the Aufbau Principle which talks about the order of filling, this principle sets rules on how electrons are distributed within those orbitals. It states that within any given orbital, there can only be two electrons and they must have opposite spins.

This means: 

• Electronic orbitals can hold a maximum of two electrons.
• These electrons must spin in opposite directions to coexist in the same space.

Using the Pauli Exclusion Principle, we can arrange electrons even more specifically. For gallium, its configuration is spread across multiple energy levels and orbitals – from 1s all the way up to 4p. Each orbital follows the rule of having a pair or less to ensure stable and defined arrangements.

This principle is pivotal in predicting the chemical behavior of atoms, ensuring no duplicate electrons fall within the same quantum state. Therefore, following Pauli’s guideline allows us to correctly pinpoint the location of each electron around an atomic nucleus.

Electron Configuration

Discovering the electron configuration of an element is akin to exploring a blueprint of its atomic composition. It delineates the arrangement of electrons around the nucleus. This not only establishes an understanding of the structure but also illuminates the element's chemical properties and reactivity.

For gallium, the electron configuration is expressed as follows: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^1\). This string of numbers and letters indicates the distribution of electrons across different energy levels and sublevels. Here’s what it reveals:

• The superscript numbers symbolize the total electrons in a given orbital.
• The letters correspond to different types of orbitals, like s, p, d.
• Numbers before the letter indicate the principal energy levels.

Understanding the electron configuration helps categorize electrons into core and valence electrons. For example, in gallium, electrons in the 3d orbitals are deemed core electrons because they are not in the outermost shell. On the contrary, the 4s and 4p electrons are in the highest energy level, making them valence electrons.

Such configuration insights are instrumental for predicting how an element like gallium will bond or react with other elements, ultimately influencing its role in chemical reactions.