Question

What is the maximum number of electrons that can fill the first principal energy level?

Short answer

The maximum number of electrons that can fill the first principal energy level is 2.

Step-by-step solution

Understanding principal energy level

There are shells or energy levels in an atom that can hold electrons. These energy levels are known as principal energy levels and are designated by the quantum number n. The first energy layer is n=1.

Application of 2n^2 Rule

The maximum number of electrons that an energy level can hold is given by the formula 2n^2. Here, n represents the number of the energy level. For the first principal energy level (n=1), the maximum number of electrons can therefore be calculated as 2*(1)^2.

Calculation of maximum electrons

By applying the formula 2n^2, where n=1, it results in 2*(1)² = 2. So, the first principal energy level can hold a maximum of 2 electrons.

Key concepts

Quantum Number

Quantum numbers are like unique addresses that pinpoint the location of an electron within an atom. They give us important information about an electron's energy and position. For principal energy levels, the principal quantum number, noted as \( n \), plays a critical role in determining the size and energy of these shells. On the periodic table, each element resides in a principal energy level defined by its \( n \) value.

• The principal quantum number \( n \) can take on positive integer values (e.g., \( n=1 \), \( n=2 \), \( n=3 \), etc.).
• As \( n \) increases, both the energy and size of the principal energy level increase, providing more space for electrons.
• For example, with \( n=1 \), we deal with the very first, and often the closest, energy level to the nucleus.

Understanding quantum numbers is fundamental to grasping how electrons fill different energy levels in atoms, forming the bedrock of electron configurations.

Electron Configuration

Electron configuration is like the seating plan of electrons in an atom. It describes the distribution of electrons among the various principal energy levels and orbitals. Electrons fill these levels in a specific order, following the rules dictated by the quantum numbers.

• Electrons are arranged in a way that minimizes the energy of the atom, starting from the lowest available energy level.
• When electrons fill energy levels, they typically fill the lowest energy state available, which is closest to the nucleus.
• For instance, in the case of the first principal energy level (\( n=1 \)), it can accommodate a maximum of 2 electrons, as dictated by its electron configuration.

This arrangement influences an atom's chemical properties and how it interacts with other atoms. Mastering electron configuration allows us to predict these interactions.

2n^2 Rule

The \( 2n^2 \) rule offers a simple way to calculate the maximum number of electrons that can occupy a principal energy level. Here, \( n \) denotes the principal quantum number, which indicates the energy level of interest.

• To apply the \( 2n^2 \) rule, you multiply the square of the principal quantum number \( n \) by 2.
• For example, in the first principal energy level where \( n=1 \), the maximum number of electrons that can be held is calculated as \( 2 \times (1)^2 = 2 \).
• Higher energy levels, such as \( n=2 \) or \( n=3 \), can host more electrons—specifically, 8 and 18 electrons, respectively—because of the increased space and energy available.

Using the \( 2n^2 \) rule allows us to comprehend how electrons distribute themselves across different energy levels, and ultimately, helps in visualizing the architecture of an atom's electron cloud.