Principal Quantum Number (n)
It indicates the main energy level or shell in
which an electron is located.
* The principal quantum number is denoted by the
symbol n. n can have positive integer values: 1, 2, 3, 4, ...
Shells are often labeled with letters:
n = 1 → K
n = 2 → L
n = 3 → M
n = 4 → N, etc.
Importance of Principal
Quantum Number (n)-
( a ) Determines Energy and
Distance
Higher n means:
Electron is at a higher energy level
Electron is located farther from the nucleus
As n increases, the size of the orbital increases.
( b ) Determines Maximum
Number of Electrons in a Shell-
The maximum number of electrons a shell can hold is
given by: 2n²
For n = 1 → 2(1)² = 2 electrons
For n = 2 → 2(2)² = 8 electrons
For n = 3 → 2(3)² = 18 electrons
Azimuthal Quantum Number ( l ):
It defines the type of subshell in which the orbitals
resides. it is denoted by l.
The Azimuthal Quantum Number, also known as the
angular momentum quantum number.
* It Depends on Principal Quantum Number (n)-
For a given value of n, l can have integer values from 0 to (n − 1).
If n = 3, then ℓ = 0, 1, 2.
Importance of Azimuthal Quantum
Number ( l ):
( a ) It determines
Subshell/Orbital Type-
Each value of ℓ corresponds to a type of subshell:
ℓ = 0 → s-
subshell
ℓ = 1 → p-
subshell
ℓ = 2 → d-
subshell
ℓ = 3 → f-
subshell
( b ) It determines Number of
Orbitals per Subshell
number of orbitals in that subshell= 2ℓ + 1
s (ℓ = 0) → 1 orbital
p (ℓ = 1) → 3 orbitals
d (ℓ = 2) → 5 orbitals
f (ℓ = 3) → 7 orbitals
( c ) It determines Orbital Shape-
ℓ = 0 (s) → spherical shape
ℓ = 1 (p) → dumbbell shape
ℓ = 2 (d) → cloverleaf shape
ℓ = 3 (f) → complex shape
( d ) It determines Orbital Angular Momentum-
Angular momentum of an electron is given by:
√[ℓ(ℓ + 1)] × ħ,
where ħ is the reduced Planck’s constant.
It give Subshell Notation-
The combination of n and ℓ gives subshell names:
n = 2, ℓ = 1 → 2p
n = 3, ℓ = 2 → 3d, etc.
(e) It tells Maximum Electrons
in a Subshell-
Each type of orbital can hold a maximum number of
electrons:
s → 2 electrons
p → 6 electrons
d → 10 electrons
f → 14 electrons
Magnetic Quantum Number (m )
The Magnetic Quantum Number describes the
orientation of an orbital in space within a given subshell.
It depends on Azimuthal Quantum Number (ℓ)-
For a given value of ℓ, m can have integer values
from −ℓ to +ℓ, including 0.
Example: If ℓ = 1 → m = −1, 0, +1
Importance of Magnetic Quantum
Number ( m ):
(a) It determines Orbital Orientation:
It Specifies the direction or orientation of the
orbital around the nucleus.
For p-orbitals (ℓ = 1):
m = −1 → px
m = 0 → py
m = +1 → pz
Each orbital defined by a value of m can hold up to 2 electrons (with opposite spins).
(b) Affects Electron Behavior
in Magnetic Fields
The value of m determines how orbitals are affected when placed in
an external magnetic field (basis of Zeeman effect).
Spin Quantum Number (s)
Definition:
The spin quantum number describes the intrinsic
angular momentum (spin) of an electron within an atom.
*It is represented by s
*An electron can have only two possible spin
values:
+½ (spin-up),
−½ (spin-down)
*Electron spin resonance and the splitting of
spectral lines in magnetic fields (Zeeman effect).
What is Hund’s Rule?
Hund’s Rule states:
Electrons fill empty orbitals of the same energy with parallel spins first before
pairlng in the same orbital.
In simpler terms:Hund’s Rule tells us:
*Place one electron in each orbital before pairing up.
*Make sure all have parallel spins (same direction).
Why is Hund’s Rule Important?
Hund's Rule helps us to:
1. Predict How Electrons Fill
Orbitals
It gives specific arrangement of electrons in p, d, and f
subshells.
2. Determine Magnetic
Properties
Atoms with unpaired electrons exhibit magnetic behavior. Hund's Rule
helps us identify which atoms are:
Paramagnetic or Diamagnetic
- Paramagnetic: Attracted to a magnetic field (due to
unpaired electrons).
- Diamagnetic: Not attracted to a magnetic field (all
electrons are paired).
Atomic Details:
- Atomic Number: 7
- Number of Electrons: 7
- Electron Configuration: 1s² 2s² 2p³
We focus on the 2p subshell (the highest-energy occupied subshell
here), which contains 3 electrons.
Applying Hund’s Rule:
The 2p subshell has three orbitals:
- px, py, and pz
So, the electron filling looks like this:
px: ↑ py:
↑ pz: ↑
Each orbital has one unpaired electron.
Magnetic Properties of Nitrogen
Since nitrogen’s 2p electrons are unpaired, the atom is:
- Paramagnetic
- It will be attracted to a magnetic field
This is a direct consequence of Hund’s Rule.
Aufbau
Principle-
The term
"Aufbau" is derived from the German word meaning "building
up."
The Aufbau
Principle states that:
Electrons
occupy the lowest energy orbitals first before filling higher energy orbitals.
*This
principle helps determine the electron configuration of atoms in their ground
state.
Order
of Orbital Filling
Electrons
are added to atomic orbitals in a specific sequence based on increasing energy
levels. The typical order in which orbitals are filled is:
1s → 2s → 2p
→ 3s → 3p → 4s → 3d → 4p → 5s → 4d → 5p → 6s → 4f → 5d → 6p → 7s → 5f → 6d → 7p
Exceptions
to the Aufbau Principle
There are
notable exceptions to the Aufbau Principle, especially among transition metals.
These exceptions arise because:
Half-filled
(e.g., d⁵) and Fully-filled (e.g., d¹⁰) subshells offer extra stability to
atoms.
Examples:
Chromium
(Cr):
Expected:
[Ar] 3d⁴ 4s²
Actual: [Ar]
3d⁵ 4s¹
Copper (Cu):
Expected:
[Ar] 3d⁹ 4s²
Actual: [Ar]
3d¹⁰ 4s¹
These
exceptions occur because such configurations lower the overall energy of the
atom.
Pauli
Exclusion Principle-
The Pauli
Exclusion Principle states:
No two
electrons in the same atom can have the same set of four quantum numbers.
* Each
electron in an atom is described by four quantum numbers:
n
(principal), l (azimuthal), m (magnetic), and m(spin).
* If two
electrons are in the same orbital (i.e., have the same values for n, l, and m),
then they must have opposite spins (mₛ = +½ and -½).
This
principle explains the maximum of 2 electrons per orbital.
Example:
In a 1s
orbital:
n = 1, l =
0, m = 0
It can hold
2 electrons, but only if:
One electron
has spin +½
The other
has spin -½
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