Question

What are two things that happen to an electron in an atom as the \(n\) value of the electron increases?

Short answer

As the principal quantum number (n) increases, two significant changes happen to an electron in an atom: 1. The electron's energy increases, causing it to occupy higher energy levels within the atom and be found at a greater average distance from the nucleus due to larger, more extensive orbitals. 2. The number of available orbitals increases, resulting in more possibilities for different subshells and orbital shapes, as well as higher angular momentum for electrons in higher energy levels.

Step-by-step solution

1. Increase in Energy and Distance from Nucleus

As the principal quantum number (n) increases, the energy of the electron increases as well. This means that the electron will occupy higher energy levels within the atom. With this increase in energy, the electron is also found at a greater average distance from the nucleus, since the electrons in the higher energy levels have larger, more extensive orbitals.

2. Increase in Orbitals and Angular Momentum

As the principal quantum number (n) increases, the number of available orbitals for electrons also increases. For each value of n, there are n² orbitals. This means that as n increases, the electrons have more possibilities for different subshells (s, p, d, f) and orbital shapes to occupy. Additionally, the electrons in higher energy levels generally have higher angular momentum, as each subsequent subshell has electrons with a greater angular momentum quantum number (l).

Key concepts

Principal Quantum Number

The principal quantum number, represented by the letter \( n \), is a crucial concept in quantum mechanics. It determines the overall size and energy level of an electron's orbital in an atom. As \( n \) increases, electrons are found in higher energy levels. This means they are farther from the nucleus and possess greater energy.

The value of \( n \) can be any positive integer (1, 2, 3,...). It essentially defines which shell the electron occupies:

• \( n = 1 \) indicates the first energy level (closest to the nucleus).
• \( n = 2 \) means the second energy level, and so on.

This system helps to predict where electrons might reside and their corresponding energy level within an atom.

Electron Energy Levels

Electron energy levels reflect how electrons are distributed around an atom. Each level is associated with a principal quantum number, \( n \). The higher the \( n \), the higher the energy of the electron at that level.

Energy levels are quantized, meaning electrons can only possess certain discrete energy values. This is different from classical physics where energy levels can be continuous. In quantum mechanics, electrons jump between these levels by absorbing or emitting specific amounts of energy, often in the form of photons.

Atomic Orbitals

Atomic orbitals are regions within an atom where there is a high probability of finding electrons. Each orbital is characterized by its shape, size, and orientation in space, determined by the quantum numbers, including the principal quantum number \( n \).

For a given \( n \), there can be \( n^2 \) different orbitals, which differ by their angular momentum quantum number \( l \) and magnetic quantum number \( m \). These orbitals include subshells designated as s, p, d, and f, among others. For instance, at \( n = 1 \), there is only one s orbital; at \( n = 2 \), there are both s and p orbitals.

Angular Momentum

Angular momentum in atomic physics is tied to the movement and position of electrons in their orbitals. It is quantified by the angular momentum quantum number \( l \), which can take on integer values from 0 to \( n-1 \) for any principal quantum number \( n \).

The value of \( l \) determines the shape of the orbital, with each integer value corresponding to different subshells:

• \( l = 0 \) is an s subshell (spherical shape),
• \( l = 1 \) is a p subshell (dumbbell shape),
• \( l = 2 \) is a d subshell, and so forth.

Higher \( n \) values provide more possible \( l \) values, leading to a larger variety of orbital shapes and angular momentum values for electrons.