MCQ Detailed View

In atomic structure, quantum numbers are used to describe the position and behavior of an electron within an atom. There are four quantum numbers: principal quantum number (n), azimuthal quantum number (ℓ), magnetic quantum number (mₗ), and spin quantum number (mₛ). Each one provides unique information about the electron’s state.

The azimuthal quantum number (ℓ) is also known as the angular momentum quantum number. It defines the shape of the orbital in which the electron resides and determines the subshells (s, p, d, f) within a principal shell. For example:

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  ℓ = 0 → s-orbital (spherical)

  
  


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  ℓ = 1 → p-orbital (dumbbell-shaped)

  
  


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  ℓ = 2 → d-orbital (clover-shaped)

  
  


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  ℓ = 3 → f-orbital (complex shapes)

  
  

The values of ℓ depend on the principal quantum number (n). For a given n, ℓ can take integer values from 0 to (n − 1).

One of the key roles of ℓ is its relationship with orbital angular momentum of an electron. The magnitude of orbital angular momentum (L) is given by:

L=ℓ(ℓ+1)ℏL = \sqrt{\ell(\ell + 1)} \hbarL=ℓ(ℓ+1)ℏ

where ℏ=h2π\hbar = \frac{h}{2\pi}ℏ=2πh is the reduced Planck’s constant.

This means that the azimuthal quantum number directly defines the electron’s angular momentum, which is a fundamental property in quantum mechanics and determines how electrons move around the nucleus.

It is important to note that the azimuthal quantum number does not define spin (that’s the spin quantum number), nor does it define magnetic momentum (that’s related to the magnetic quantum number mₗ). Similarly, it has nothing to do with the e/m ratio, which was discovered in cathode ray experiments.

Thus, the correct answer is that the azimuthal quantum number defines the angular momentum of an electron.