What Is A Quantum Number

A quantum number is a value that is used when describing the energy levels available to atoms and molecules.

It defines the exact position of electron in atom.

photo owner: Universiteit Leiden

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Quantum Numbers for Atoms

chem.libretexts.org

Quantum Numbers

There is four quantum numbers that are used to describe completely the movement and trajectories of each electron within an atom.

  1. Principal
  2. Azimuthal
  3. Magnetic
  4. Spin

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Principal Quantum Numbers (n)

describe the energy of an electron and the most probable distance of the electron from the nucleus.

To know the maximum amount of electron that an energy level can handle, Use this formula 2n² (does not include O , P , Q).

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Azimuthal Quantum Numbers (ℓ)

The azimuthal quantum number is a quantum number for an atomic orbital that determines its orbital angular momentum and describes the shape of the orbital.

Every azimuthal number has his own capacity of electrons

  • S(v=0) ==> 1 orb ==> 2 electrons
  • P(v=1) ==> 3 orbs ==> 6 electrons
  • D(v=2) ==> 5 orbs ==> 10 electrons
  • F(v=3) ==> 10 orbs ==>12 electrons

Ps:open the photo to see the whole image. ((v = value))

photo owner: Byju's

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Magnetic quantum Numbers (mℓ)

Specifie the orientation in space of an orbital of a given energy (n) and shape (l). This number divides the subshell into individual orbitals which hold the electrons; there are 2l+1 orbitals in each subshell.

Every orbital capacity is 2 electrons

Magnetic values are {-3,-2,-1,0,1,2,3}

  • S ==> 1 orb ==> 0
  • P ==> 3 orbs ==> -1,0,1
  • D ==> 5 orbs ==> -2,-1,0,1,2
  • F ==> 7 orbs ==> -3,-2,-1,0,1,2,3

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Spin Quantum Numbers (ms)

describe the angular momentum of an electron. An electron spins around an axis and has both angular momentum and orbital angular momentum. Because angular momentum is a vector, the Spin Quantum Number (s) has both a magnitude (½) and direction (+ or -)

(+½) ===> in the direction of clock

(-½) ===> against the direction of clock

The electrons take place in orbs in a specific way.

Imagine the orbs like beds and electrons like persons. Every person tend to sleep alone in bed (+½) unless there is no bed left so the other person have to sleep upside down (-½).

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Practice

We have to define the exact place of the last electron for the element Neon¹⁰

  1. We have to configure the electrons 1s²,2s²,2p⁶
  2. Now we focus on the last number 2p⁶

• n (the number before the letter) = 2

• ℓ ( = P ) = 1

3. We define P's orbitals

2p⁶ ==> 3 orbs ==> 6 electrons

Every orb contains 2 electrons

4. We have to define spin

|(+½)¹ (-½)⁴|.|(+½)² (-½)⁵ |.|(+½)³ (-½)⁶|.

-----[-1]------. -----[0]------. -----[1]------

The order of spin is marked on top of the electron¹

• mℓ (last electron place) = 1

• ms = -½

Hope you enjoy the explanation :)

See you in the next post 👋.

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