How many orbitals are there in the third shell n3?

Understanding Atomic Shells and Orbitals

1. Principal Quantum Number (n)

• The principal quantum number, n, indicates the shell or main energy level of an electron in an atom.
• The value of n can be any positive integer (1, 2, 3, ...).
• n=3 refers to the third shell.

2. Subshells and Quantum Numbers

Each shell is divided into subshells, labeled as s, p, d, f, etc., determined by the azimuthal quantum number (l):

• For a given n, possible values of l range from 0 to n-1.
• For n=3:
  • l = 0 → 3s subshell
  • l = 1 → 3p subshell
  • l = 2 → 3d subshell

3. Orbitals in Each Subshell

Each subshell contains a specific number of orbitals, determined by the magnetic quantum number (ml):

• Number of orbitals in each subshell = 2l + 1

4. Total Number of Orbitals in the n=3 Shell

Add up the orbitals in each subshell:

• 3s: 1 orbital
• 3p: 3 orbitals
• 3d: 5 orbitals

Total orbitals in third shell (n=3):

1 (3s) + 3 (3p) + 5 (3d) = 9 orbitals