- Dr.Sanjaykumar Pawar
 |
| Orbitals and Quantum Numbers explained with shells, subshells and orbital orientation for Class 11 Chemistry. |
ORBITALS AND QUANTUM NUMBERS
│
├── Orbitals
│ │
│ ├── Region of maximum electron probability
│ ├── Differ in:
│ │ ├── Size
│ │ ├── Shape
│ │ └── Orientation
│ │
│ └── Described by Quantum Numbers
│
├── Principal Quantum Number (n)
│ │
│ ├── Determines:
│ │ ├── Size of orbital
│ │ └── Energy of orbital
│ │
│ ├── Values:
│ │ └── 1, 2, 3, 4, ...
│ │
│ ├── Shell Names:
│ │ ├── n = 1 → K
│ │ ├── n = 2 → L
│ │ ├── n = 3 → M
│ │ └── n = 4 → N
│ │
│ ├── Increase in n:
│ │ ├── Size ↑
│ │ ├── Distance from nucleus ↑
│ │ └── Energy ↑
│ │
│ └── Number of Orbitals
│ └── n²
│
├── Azimuthal Quantum Number (l)
│ │
│ ├── Also called:
│ │ ├── Subsidiary Quantum Number
│ │ └── Orbital Angular Momentum
│ │
│ ├── Determines:
│ │ └── Shape of orbital
│ │
│ ├── Values:
│ │ └── 0 to (n − 1)
│ │
│ ├── Number of Subshells
│ │ └── Equal to n
│ │
│ └── Subshell Notation
│ ├── l = 0 → s
│ ├── l = 1 → p
│ ├── l = 2 → d
│ ├── l = 3 → f
│ ├── l = 4 → g
│ └── l = 5 → h
│
├── Magnetic Quantum Number (mₗ)
│ │
│ ├── Determines:
│ │ └── Orientation of orbital
│ │
│ ├── Values:
│ │ └── -l to +l
│ │
│ ├── Formula
│ │ └── Number of Orbitals = 2l + 1
│ │
│ ├── l = 0
│ │ ├── mₗ = 0
│ │ └── 1 s orbital
│ │
│ ├── l = 1
│ │ ├── mₗ = -1, 0, +1
│ │ └── 3 p orbitals
│ │
│ ├── l = 2
│ │ ├── mₗ = -2, -1, 0, +1, +2
│ │ └── 5 d orbitals
│ │
│ └── l = 3
│ ├── mₗ = -3 to +3
│ └── 7 f orbitals
│
└── Important Relationships
│
├── n → Shell
├── l → Shape/Subshell
├── mₗ → Orientation
│
├── Orbitals in Shell = n²
├── Subshells in Shell = n
├── Orbitals in Subshell = 2l + 1
│
└── n → l → mₗ
INTERNAL LINK
• Introduction to Structure of Atom • Thomson Atomic Model • Rutherford Atomic Model • Bohr's Atomic Model
• Electromagnetic Radiation • Photoelectric Effect • Dual Nature of Matter • Heisenberg Uncertainty Principle • Quantum Mechanical Model of Atom
• Shapes of Atomic Orbitals • Electronic Configuration • Aufbau Principle • Pauli Exclusion Principle • Hund's Rule
FAQ
Q. What are quantum numbers? A. Quantum numbers are numbers that describe the position, energy, shape and orientation of electrons in an atom.
Q. What does principal quantum number determine? A. It determines the shell, size and energy of an orbital.
Q. What does azimuthal quantum number represent? A. It determines the shape of the orbital.
Q. What does magnetic quantum number represent? A. It determines the orientation of the orbital in space.
Q. How many orbitals are present in the third shell? A. Nine orbitals are present in the third shell.
INTERNAL LINKS
/class11/chemistry/atomic-structure
/neet/chemistry/electronic-configuration
/chemistry/hunds-rule-exchange-energy
/neet/important-exceptions-cr-cu
/class11/chemistry/orbital-theory-basics
2.1 Orbitals and Quantum Numbers
Introduction
- An atom contains a large number of orbitals.
- Orbitals differ in size, shape, and orientation.
- An orbital is a region where the probability of finding an electron is maximum.
- Smaller orbital size means a greater chance of finding the electron near the nucleus.
- Shape and orientation tell us the direction in which the electron is most likely to be found.
Quantum Numbers
Quantum numbers are numbers that completely describe an electron and its orbital.
Every orbital is identified by three quantum numbers:
- Principal Quantum Number (n)
- Azimuthal Quantum Number (l)
- Magnetic Quantum Number (ml)
1. Principal Quantum Number (n)
Definition
- Represented by n.
- Always a positive integer.
Possible Values
n = 1, 2, 3, 4, 5, ...
Importance
- Determines the size of the orbital.
- Determines the energy of the orbital.
- For hydrogen and hydrogen-like species, energy depends only on n.
Examples of Hydrogen-like Species
- He+
- Li2+
- Be3+
Shells and n
| n | Shell Name |
|---|---|
| 1 | K |
| 2 | L |
| 3 | M |
| 4 | N |
Important Points
- Higher n → Larger orbital size.
- Higher n → Electron farther from nucleus.
- Higher n → Higher orbital energy.
| Shell | n | Number of Orbitals |
|---|---|---|
| K | 1 | 1² = 1 |
| L | 2 | 2² = 4 |
| M | 3 | 3² = 9 |
| N | 4 | 4² = 16 |
2. Azimuthal Quantum Number (l)
Other Names
- Orbital Angular Momentum Quantum Number
- Subsidiary Quantum Number
Definition
- Represented by l.
- Determines the shape of the orbital.
Possible Values
Examples
- For n = 1 → l = 0
- For n = 2 → l = 0, 1
- For n = 3 → l = 0, 1, 2
- For n = 4 → l = 0, 1, 2, 3
Subshells
Each shell is divided into subshells.
| n | Subshells |
|---|---|
| 1 | l = 0 |
| 2 | l = 0, 1 |
| 3 | l = 0, 1, 2 |
| 4 | l = 0, 1, 2, 3 |
Subshell Notation
| l Value | Subshell |
|---|---|
| 0 | s |
| 1 | p |
| 2 | d |
| 3 | f |
| 4 | g |
| 5 | h |
3. Magnetic Quantum Number (ml)
Definition
- Represented by ml.
- Determines the orientation of an orbital in space.
Possible Values
Number of Possible Values
Examples
For l = 0 (s-subshell)
ml = 0
Number of orbitals = 1
For l = 1 (p-subshell)
ml = -1, 0, +1
Number of orbitals = 3
For l = 2 (d-subshell)
ml = -2, -1, 0, +1, +2
Number of orbitals = 5
For l = 3 (f-subshell)
ml = -3, -2, -1, 0, +1, +2, +3
Number of orbitals = 7
Relationship Between Quantum Numbers
- n determines the shell.
- l is derived from n.
- ml is derived from l.
Quick NEET Revision Table
| Quantum Number | Symbol | Determines | Values |
|---|---|---|---|
| Principal | n | Size and Energy | 1, 2, 3, 4... |
| Azimuthal | l | Shape | 0 to (n−1) |
| Magnetic | ml | Orientation | −l to +l |
Most Important NEET Formulas
- Number of Orbitals in a Shell = n²
- Number of Subshells in a Shell = n
- Number of Orbitals in a Subshell = 2l + 1
- Values of l = 0 to (n − 1)
- Values of ml = −l to +l
NEET One-Line Summary
- n → Size and Energy
- l → Shape
- ml → Orientation
- Orbitals in shell = n²
- Subshells in shell = n
- Orbitals in subshell = 2l + 1
Structure of Atom: Orbitals and Quantum Numbers
A. Multiple Choice Questions (MCQs)
Q1. Which quantum number determines the size of an orbital?
a) l
b) ml
c) n
d) s
Answer: c) n
Q2. The shape of an orbital is determined by:
a) n
b) l
c) ml
d) spin
Answer: b) l
Q3. How many orbitals are present in the third shell?
a) 3
b) 6
c) 9
d) 18
Answer: c) 9
Q4. Which subshell corresponds to l = 2?
a) s
b) p
c) d
d) f
Answer: c) d
Q5. Number of orbitals in p-subshell is:
a) 1
b) 3
c) 5
d) 7
Answer: b) 3
B. Very Short Answer Questions
Q1. What is an orbital?
Answer: An orbital is a region around the nucleus where the probability of finding an electron is maximum.
Q2. What does principal quantum number represent?
Answer: It represents the shell, size and energy of an orbital.
Q3. Write the value of l for p-subshell.
Answer: l = 1
Q4. How many orbitals are present in s-subshell?
Answer: One orbital.
Q5. Write the formula for number of orbitals in a shell.
Answer: Number of orbitals = n²
C. Short Answer Questions
Q1. What are quantum numbers?
Answer:
- Quantum numbers are numbers used to describe the position and energy of electrons in an atom.
- They specify the shell, shape and orientation of orbitals.
Q2. Write the possible values of l for n = 4.
Answer:
- l = 0, 1, 2, 3
- Corresponding subshells are 4s, 4p, 4d and 4f.
Q3. Differentiate between principal and azimuthal quantum numbers.
Answer:
| Principal Quantum Number (n) | Azimuthal Quantum Number (l) |
|---|---|
| Determines size and energy. | Determines shape of orbital. |
| Values: 1, 2, 3... | Values: 0 to n−1 |
D. Long Answer Questions
Q1. Explain Principal Quantum Number.
Answer:
- Represented by n.
- Values are 1, 2, 3, 4....
- Determines shell number.
- Determines size of orbital.
- Determines energy of orbital.
- Number of orbitals in a shell = n².
Shell Names:
| n | Shell |
|---|---|
| 1 | K |
| 2 | L |
| 3 | M |
| 4 | N |
As n increases, size and energy of orbitals increase.
Q2. Explain Azimuthal Quantum Number and Magnetic Quantum Number.
Answer:
Azimuthal Quantum Number (l)
- Determines shape of orbital.
- Values range from 0 to n−1.
- Subshells are represented as s, p, d and f.
Magnetic Quantum Number (ml)
- Determines orientation of orbital.
- Values range from -l to +l.
- Number of orbitals = 2l + 1.
E. Fill in the Blanks
1. Principal quantum number is represented by ______.
Answer: n
2. Shape of orbital is determined by ______.
Answer: l
3. Orientation of orbital is determined by ______.
Answer: ml
4. Number of orbitals in p-subshell is ______.
Answer: 3
5. Number of orbitals in a shell is ______.
Answer: n²
F. Assertion and Reason Questions
Q1.
Assertion (A): Number of orbitals in third shell is 9.
Reason (R): Number of orbitals in a shell is given by n².
Answer: Both Assertion and Reason are true and Reason correctly explains Assertion.
Q2.
Assertion (A): p-subshell contains three orbitals.
Reason (R): For l = 1, ml values are -1, 0 and +1.
Answer: Both Assertion and Reason are true and Reason correctly explains Assertion.
G. Match the Columns
| Column A | Column B |
|---|---|
| 1. n | a. Orientation |
| 2. l | b. Shape |
| 3. ml | c. Size and Energy |
| 4. d-subshell | d. Five orbitals |
Answer:
1 → c
2 → b
3 → a
4 → d
H. Case Study Questions
Passage:
Quantum numbers describe orbitals in an atom. Principal quantum number determines shell, size and energy. Azimuthal quantum number determines shape while magnetic quantum number determines orientation. Number of orbitals in a shell is n² and number of orbitals in a subshell is 2l+1.
Q1. Which quantum number determines shape?
Answer: Azimuthal quantum number (l)
Q2. How many orbitals are present in M-shell?
Answer: 9 orbitals
Q3. How many orbitals are present in d-subshell?
Answer: 5 orbitals
Q4. What is the value of l for p-subshell?
Answer: 1
Q5. What is the value of ml for s-orbital?
Answer: 0
I. Important One-Mark Questions
Q. Number of orbitals in fourth shell?
Answer: 16
Q. Number of subshells in third shell?
Answer: 3
Q. Number of d orbitals?
Answer: 5
Q. Number of f orbitals?
Answer: 7
Q. Value of l for s orbital?
Answer: 0
Q. Formula for orbitals in shell?
Answer: n²
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