What is the total number of orbitals in the third shell? The fourth shell?

Verified step by step guidance

1. Understand that the number of orbitals in a shell is determined by the formula: \( n^2 \), where \( n \) is the principal quantum number representing the shell.
2. For the third shell, set \( n = 3 \). Calculate the number of orbitals using the formula \( n^2 \).
3. For the fourth shell, set \( n = 4 \). Calculate the number of orbitals using the formula \( n^2 \).
4. Recognize that each orbital can hold a maximum of 2 electrons, which is useful for understanding electron capacity but not directly needed for this problem.
5. Summarize the results: The third shell has \( 3^2 \) orbitals, and the fourth shell has \( 4^2 \) orbitals.

Key Concepts

Electron Shells

Electron shells are defined energy levels around an atom's nucleus where electrons reside. Each shell is designated by a principal quantum number (n), which indicates its distance from the nucleus. The third shell corresponds to n=3, while the fourth shell corresponds to n=4, with each shell having a specific capacity for electrons.

Orbitals

Orbitals are regions within an electron shell where there is a high probability of finding an electron. Each shell contains a set number of orbitals, which can be s, p, d, or f types, each with different shapes and capacities. The total number of orbitals in a shell can be calculated using the formula n^2, where n is the principal quantum number.

Calculating Orbitals in Shells

To determine the total number of orbitals in a given shell, the formula n^2 is applied. For the third shell (n=3), the total number of orbitals is 3^2 = 9. For the fourth shell (n=4), the total number of orbitals is 4^2 = 16. This calculation is essential for understanding electron configurations and the distribution of electrons in an atom.