MCQ Detailed View

In quantum mechanics, the arrangement and properties of electrons are described using four quantum numbers: principal (n), azimuthal (ℓ), magnetic (mℓ), and spin (ms). Each quantum number provides specific information about electrons inside an atom.

The magnetic quantum number (mℓ) is associated with the orientation of orbitals in three-dimensional space. It does not describe the size or shape of the orbital, but rather the direction in which the orbital is aligned around the nucleus.

For a given value of the azimuthal quantum number ℓ, the magnetic quantum number mℓ can have integer values ranging from:

$$m\ell =-\ell ,-(\ell -1),\dots ,0,\dots ,+(\ell -1),+\ell$$

This means:

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  For s-orbital (ℓ = 0): mℓ = 0 → only one orientation

  
  


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  For p-orbital (ℓ = 1): mℓ = -1, 0, +1 → three orientations (px, py, pz)

  
  


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  For d-orbital (ℓ = 2): mℓ = -2, -1, 0, +1, +2 → five orientations

  
  


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  For f-orbital (ℓ = 3): mℓ = -3 to +3 → seven orientations

  
  

Thus, the magnetic quantum number determines how many orbitals are possible in a subshell and how they are oriented relative to each other. For example, p-orbitals are dumbbell-shaped and exist in three orientations along x, y, and z axes. This distinction arises because of different mℓ values.

Historically, the magnetic quantum number was introduced to explain the splitting of spectral lines in a magnetic field, a phenomenon known as the Zeeman effect. This demonstrated that orbitals have directional properties influenced by external magnetic fields.

To summarize:

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  n → size of orbital

  
  


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  ℓ → shape of orbital

  
  


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  mℓ → orientation of orbital

  
  


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  ms → spin of electron

  
  

Therefore, the magnetic quantum number specifies the orientation of orbitals in space, making option C the correct answer