Problem 72 - Chemistry Matter and Change

Question

How many electrons can be contained in all the orbitals related to an argon atom’s third energy level?

Step-by-Step Solution

Answer

A maximum of 18 electrons can be contained in all the orbitals related to an argon atom's third energy level, as calculated using the formula \(2n^2\) with n=3.

Step 1: Identify the energy level

We are given the element Argon (Ar) and asked to find the number of electrons contained in its third energy level. The energy level is represented by the integer value n, and n=3 for this problem.

Step 2: Find the maximum number of electrons in the energy level

Using the formula for the maximum number of electrons in an energy level, which is \(2n^2\), we can determine the number of electrons that can be contained in the third energy level of Argon. Substitute n=3 into the formula: Maximum electrons = \(2(3)^2\)

Step 3: Calculate the number of electrons

Now, we need to perform the calculation: Maximum electrons = \(2(9) = 18\)

Step 4: Provide the answer

Thus, a maximum of 18 electrons can be contained in all the orbitals related to an argon atom's third energy level.

Key Concepts

Energy Levels in Atoms

Understanding the energy levels in atoms is crucial for getting to grips with the structure and behavior of electrons within an atom. An atom consists of a nucleus surrounded by electrons that occupy specific areas called energy levels or shells. These levels are often imagined as the rungs of a ladder, with each rung representing a different level of energy. Electrons naturally occupy the lowest available energy level, adhering to what we call the 'Aufbau principle'.

As electrons absorb energy, they can 'jump' to higher energy levels, but they will 'fall' back to lower levels when releasing energy - a process evident in phenomena such as atomic emission spectra. The energy levels are denoted by the principal quantum number, 'n', which increases with distance from the nucleus. Therefore, the third energy level (n=3), which was highlighted in the exercise about argon, is further away from the nucleus than the first and second levels, and it possesses a higher energy capacity.

Electron Capacity of Orbitals

Orbitals are specific regions within energy levels where electrons are most likely to be found. Each orbital can hold a maximum of two electrons, which must have opposite spins due to the Pauli exclusion principle. Orbitals come in different shapes and are categorized as s, p, d, and f.

Within a given energy level, the electron capacity increases because there are more types of orbitals available. For instance, the first energy level has only one s orbital, while the second energy level contains one s and three p orbitals. To calculate the maximum number of electrons that an energy level can hold, you can use the formula mentioned in the problem: \(2n^2\). This takes into account the number of orbitals and multiplies it by two (for the two electrons per orbital). So in the context of our exercise, for Argon's third energy level (n=3), the formula gives us 18 as the maximum electron capacity. This figure incorporates one s orbital, three p orbitals, and five d orbitals that become available for electron occupation at this level.

Quantum Numbers

Quantum numbers are vital for a nuanced understanding of the arrangement of electrons within an atom. They are essentially the addresses for electrons, specifying their position and spin within the atom's orbitals. There are four quantum numbers: the principal quantum number (n), the azimuthal quantum number (l), the magnetic quantum number (ml), and the spin quantum number (ms).

The principal quantum number, as mentioned before, defines the energy level of the electron. The azimuthal quantum number relates to the shape of the orbital, ranging from 0 to n-1, which for an electron in the third energy level could be 0 (s orbital), 1 (p orbital), or 2 (d orbital). The magnetic quantum number discerns the orientation of the orbital in space, and the spin quantum number indicates the direction of the electron's spin. Each electron in an atom has a unique set of quantum numbers, which helps avoid electron confusion and supports the exclusion principle for a well-structured electron configuration within the atom.