Thursday, September 11, 2025

Class 11 chemistry Atomic structure

 

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).

 Example: Nitrogen (N)

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 (m = +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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