Question:medium

Given, (A) n=5, m___l = -1; (B) n=3, l=2, m___l = -1, m___s = +1/2. The maximum number of electron(s) in an atom that can have the quantum numbers as given in (A) and (B) respectively are :

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If all four quantum numbers are specified, the answer is always 1 electron. If only three are specified ($n, l, m_l$), the answer is 2 electrons.
Updated On: Feb 24, 2026
  • 8 and 1
  • 26 and 1
  • 2 and 4
  • 4 and 1
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The Correct Option is A

Solution and Explanation

To determine the maximum number of electrons that can have the specified quantum numbers in parts (A) and (B) of the question, we need to understand the roles of each quantum number:

  • Principal quantum number (n): Determines the energy level or shell of an electron.
  • Azimuthal quantum number (l): Determines the subshell and shapes of the atomic orbitals. It can take values from 0 to (n-1).
  • Magnetic quantum number (ml): Determines the orientation of the orbital within a subshell. It ranges from -l to +l.
  • Spin quantum number (ms): Specifies the direction of the electron's spin. It can be +1/2 or -1/2.

Let's solve for both (A) and (B):

  • Part (A):
    • Given: n = 5, ml = -1.
    • Here, there are no restrictions provided for l (azimuthal quantum number), only a specific ml.
    • For n=5, permissible values of l are 0, 1, 2, 3, and 4.
    • The value of ml = -1 is allowed in subshells where l ≥ 1 (i.e., p, d, f, and g). In these, ml can take values from -l to +l.
    • We consider each valid subshell that contains ml = -1:
      • For l=1 (p-subshell): ml values = {-1, 0, +1}
      • For l=2 (d-subshell): ml values = {-2, -1, 0, +1, +2}
      • For l=3 (f-subshell): ml values = {-3, -2, -1, 0, +1, +2, +3}
      • For l=4 (g-subshell): ml values = {-4, -3, -2, -1, 0, +1, +2, +3, +4}
    • Each specific ml can contain 2 electrons (one for each ms = +1/2 and -1/2).
    • Thus, the total electrons = 2 per valid shell having ml = -1 for l = 1, 2, 3, or 4: 
      \(2 \times 4 = 8\) electrons.
  • Part (B):
    • Given: n=3, l=2, ml = -1, ms = +1/2.
    • The values specify a d-orbital (l=2) in the 3rd shell.
    • The values for ml in a d-subshell (l=2) include -2, -1, 0, +1, +2.
    • Only one electron can have the specific ms = +1/2 with given n, l, and ml values.
    • Hence, only 1 electron can have these complete set of quantum numbers.

Conclusion: Therefore, the maximum number of electrons that can fit the given conditions are 8 in Part (A) and 1 in Part (B). Thus, the correct option is:

8 and 1

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