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15 January, 18:12

For each of the following, give the sublevel designation, the allowable ml values, and the number of orbitals:

(a) n = 2, l = 0

(b) n = 3, l = 2

(c) n = 5, l = 1

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Answers (1)
  1. 15 January, 20:41
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    (a) n = 2, l = 0 ⇒ sublevel s, ⇒ ml = 0, number of orbitals = 1

    (b) n = 3, l = 2 ⇒ sublevel d, ⇒ ml = 0, ±1, ±2, number of orbitals = 5

    (c) n = 5, l = 1 ⇒ sublevel p, ⇒ ml = 0, ±1, number of orbitals = 3

    Explanation:

    The rules for electron quantum numbers are:

    1. Shell number, 1 ≤ n,

    2. Subshell number, 0 ≤ l ≤ n - 1, from s, p, d, f, g, h ...

    3. Orbital energy shift, - l ≤ ml ≤ l

    4. Spin, either - 1/2 or + 1/2

    In our case

    (a) n = 2, l = 0 ⇒ sublevel s

    -l ≤ ml ≤ l ⇒ ml = 0, number of orbitals = 1

    (b) n = 3, l = 2 ⇒ sublevel d

    -l ≤ ml ≤ l ⇒ ml = 0, ±1, ±2, number of orbitals = 5

    (c) n = 5, l = 1 ⇒ sublevel p

    -l ≤ ml ≤ l ⇒ ml = 0, ±1, number of orbitals = 3
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