Quantum Mechanics and Atomic Orbitals: Examples, Rules, Exercises, & Solutions

Examples & Further Rules

Orbits

Remarks

  1. The shell with a principal quantum number (n) consists of exactly n subshells. (Example: n = 3 has 3 subshells (s, p, d))
  2. Each subshell consists of a specific number of orbitals, each corresponds to a different allowed value of ml. (Example: p subshell has 3 orbitals with ml values of +1, 0 and -1)
  3. For a given value of l, there are (2l +1) allowed values of ml , ranging from −l to +l.
    Example: l = 2 (d subshell) has 2 × 2 + 1 = 5 orbitals with 5 values of ml +2, +1, 0, − 1, − 2)
  4. The total number of orbitals in a shell that has a principal quantum number (n) is (n2).(Example: n = 3 has 9 orbitals total)

Example

In the third shell: n =3 is the shell number → 3 sub-shells with l values 0, 1, 2 called s, p, d → 3s, sp, sd see illustrated below:
Third Shell

Exercise

Exercise on Finding the Designated Shell

Check your answers here: Solution to the Exercise on Finding the Designated Shell




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Date of last modification: 2024