Quantum Numbers, Subshells, and Electrons

Subshells and Orbitals

• Subshell Identification

  • Each subshell corresponds to a specific angular momentum quantum number, denoted by l.
  • Common subshells:
  • When $l = 0$, the subshell is s.
  • When $l = 1$, the subshell is p.
  • When $l = 2$, the subshell is d.

• Examples:

  • For n = 3:
  • If $l = 0$, subshell is 3s.
  • If $l = 1$, subshell is 3p.
  • If $l = 2$, subshell is 3d.

Magnetic Quantum Number (m)

• The values of magnetic quantum number, m, range from $-l$ to $+l$:
  • If $l = 0$, then $m = 0$.
  • If $l = 1$, then $m = -1, 0, 1$ (3 values).
  • If $l = 2$, then $m = -2, -1, 0, 1, 2$ (5 values).

Calculation of Orbitals and Electrons

• Counting Orbitals:

  • 3s: 1 orbital.
  • 3p: 3 orbitals (
  • m values: -1, 0, 1).
  • 3d: 5 orbitals (
  • m values: -2, -1, 0, 1, 2).

• Total Orbitals:

  • Calculated by summing orbitals:
  • $1 (3s) + 3 (3p) + 5 (3d) = 9\ \text{ total orbitals}$.

• Calculating Total Electrons:

  • Each orbital holds a maximum of 2 electrons:
  • 3s: 1 orbital x 2 electrons = 2 electrons.
  • 3p: 3 orbitals x 2 electrons = 6 electrons.
  • 3d: 5 orbitals x 2 electrons = 10 electrons.
  • Total electrons:
  • Adding up electrons:
  • $2 (3s) + 6 (3p) + 10 (3d) = 18\ \text{ total electrons}$.

Formula for Number of Electrons in a Shell

• General Formula:
  • The number of electrons that can fit in a shell is given by the formula:
  • $2n^2$, where n is the principal quantum number.
  • This formula can be utilized to confirm electron counts for any given shell.