Question

What is the maximum number of electrons that can occupy the \(n=3\) quantum shell?

Short answer

The maximum number of electrons that can occupy the \(n=3\) quantum shell is 18.

Step-by-step solution

Understanding the Quantum Shell

The principal quantum number, denoted by 'n', determines the energy level or shell of an electron within an atom. Each shell can contain a certain number of subshells, equal to 'n'.

Calculating the Number of Orbitals

The number of orbitals in a given shell is given by the formula \(n^2\). For the third shell where \(n=3\), the number of orbitals is \(3^2=9\).

Determining Maximum Electrons in Orbitals

Each orbital can hold a maximum of 2 electrons. To find the total number of electrons in the \(n=3\) shell, multiply the number of orbitals by 2: \((9 * 2 = 18)\) electrons.

Key concepts

Quantum Shell

Imagine an atom as a tiny, bustling city with electrons whizzing around its nucleus like cars on multiple highways - these highways are what we call quantum shells. A quantum shell represents an electron's orbit around the nucleus at a certain energy level. These shells are like the different floors of a building, each further away from the ground floor, or nucleus, with increasing energy.

The principal quantum number, denoted as 'n', serves as the address for each shell, telling us the floor number. For example, when we speak of the 'n=3' quantum shell, we're talking about the third floor of our atomic building. It's important to note that these shells aren't just simple paths; they're complex regions of space where an electron is most likely to be found.

Knowing the quantum shell is crucial for understanding the architecture of atoms and the arrangement of electrons which is fundamental to the field of chemistry and physics as it influences chemical bonding and the physical properties of materials.

Electron Configuration

Now that we understand highways for electrons or quantum shells, we can talk about traffic patterns or 'electron configuration'. This is essentially the distribution of electrons across different shells and subshells within an atom. Remember that the address system doesn't stop at the quantum shell; it also includes other details like subdivisions of the floors, called subshells, designated by the letters 's', 'p', 'd', and 'f'.

Each type of subshell has a distinct shape and can hold a specific number of electron cars - s holds 2, p holds 6, d holds 10, and f holds 14. By following rules like the Pauli exclusion principle and Hund's rule, we fill up electron spaces in a way that minimizes repulsion and maximizes stability, kind of like finding the optimal parking spots in a crowded lot.

For instance, in the 'n=3' shell, we can have the 3s, 3p, and 3d subshells, each with its characteristic distribution of electrons. The full electron configuration of an atom is like the complete list of how the electrons are arranged across all the occupied shells and subshells, providing a map of how electrons are spread out in their atomic city.

Atomic Orbitals

Diving deeper into the atomic structure, the concept of 'atomic orbitals' further refines our understanding of where electrons live in their quantum shells. Orbitals are the designated parking spaces within subshells we mentioned earlier, where each parking spot fits exactly two electrons. These aren't circular orbits, but rather complex, three-dimensional shapes where electrons are likely to be found, such as spherical for s orbitals and dumbbell-shaped for p orbitals.

The principal quantum number 'n' is also linked to the number of atomic orbitals in a shell; it follows the formula n^2. When we apply this to our n=3 shell, the calculation 3^2 tells us there are nine orbitals within this highway, and if we do the math, multiplying this by the 2-electron limit for each orbital, we get 18. That's how many electron cars can be parked in the third shell safely - a full capacity of 18. Understanding atomic orbitals is not just an exercise in counting; it's about appreciating the fascinating world of quantum mechanics that dictate the behaviors and interactions of the tiniest particles in the universe.