MCQ Detailed View

Quantum numbers define the properties of electrons in an atom according to quantum mechanics. There are four quantum numbers: the principal quantum number (n), the azimuthal quantum number (l), the magnetic quantum number (mₗ), and the spin quantum number (mₛ).

The principal quantum number n determines the energy level of an electron and can take positive integer values: 1, 2, 3, and so on. The azimuthal quantum number l determines the shape of the orbital and can take values from 0 to (n-1). The magnetic quantum number mₗ defines the orientation of the orbital and ranges from –l to +l. The spin quantum number mₛ represents the spin of the electron and can be either +½ or –½.

Examining the options:

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  Option A: n = 2, l = 1, mₗ = 0, mₛ = +½ is valid.

  
  


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  Option B: n = 2, l = 1, mₗ = -1, mₛ = +½ is valid.

  
  


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  Option C: n = 2, l = 0, mₗ = 0, mₛ = -½ is valid.

  
  


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  Option D: n = 2, l = 2, mₗ = 1, mₛ = -½ is not allowed, because l cannot be equal to or greater than n. For n = 2, the maximum value of l is 1.

  
  

This rule ensures that the quantum numbers correctly describe the allowed energy levels and orbital shapes of electrons. Understanding which combinations of quantum numbers are allowed is essential in atomic structure, electron configuration, and predicting chemical properties of elements. This question focuses on applying the Pauli exclusion principle and quantum number restrictions to identify impossible electron states.