Quantum Numbers and Orbitals Explained for NEET Students

🧠 Orbitals and Quantum Numbers (NEET Notes)

The four quantum numbers determine the shell, shape, orientation and spin of an electron in an atom.

- Dr.Sanjaykumar Pawar 

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🌌 Orbitals Concept

1. In an atom, a large number of orbitals are possible for electrons.

2. Orbitals are different based on:

   • Size
   • Shape
   • Orientation

3. Smaller orbital size means:

   • Electron is more likely to be found close to nucleus

4. Shape of orbital means:

   • Electron is more likely found in certain regions of space

5. Orientation of orbital means:

   • Direction in space where electron probability is higher

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🔢 Quantum Numbers

6. Every atomic orbital is described by three quantum numbers:
   • Principal quantum number (n)
   • Azimuthal quantum number (l)
   • Magnetic quantum number (mₗ)

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📏 1. Principal Quantum Number (n)

7. It is a positive integer:

   • n = 1, 2, 3, 4, …

8. It defines:

   • Size of orbital
   • Energy of orbital (mainly)

9. For hydrogen and hydrogen-like species:

   • Energy depends only on n

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🏠 Shell Concept

10. Principal quantum number also defines shells:

n	Shell
1	K
2	L
3	M
4	N

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11. As n increases:

• Size of orbital increases
• Electron is farther from nucleus
• Energy increases

12. Reason:

• Electron is attracted less strongly at larger distance

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13. Number of orbitals in a shell = n²

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14. All orbitals with same n form a shell

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🧩 2. Azimuthal Quantum Number (l)

15. Also called:

• Angular momentum quantum number
• Subsidiary quantum number

16. It defines:

• Shape of orbital

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📊 Values of l

17. For a given n:

• l = 0 to (n − 1)

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18. Examples:

• n = 1 → l = 0 only
• n = 2 → l = 0, 1
• n = 3 → l = 0, 1, 2

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🧱 Sub-shell Concept

19. Each shell has sub-shells.

20. Number of sub-shells = n

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🏷️ Sub-shell Notation

21. Values of l correspond to letters:

l value	Sub-shell
0	s
1	p
2	d
3	f
4	g
5	h

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22. Examples:

• n = 1 → 1 sub-shell → 1s
• n = 2 → 2 sub-shells → 2s, 2p
• n = 3 → 3 sub-shells → 3s, 3p, 3d

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🧭 3. Magnetic Quantum Number (mₗ)

23. It describes:

• Orientation of orbital in space

24. It depends on l

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📐 Values of mₗ

25. For a given l:

• mₗ = −l to +l

26. Total values = 2l + 1

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📊 Examples

27. If l = 0:

• mₗ = 0
• Orbitals = 1 (s orbital)

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28. If l = 1:

• mₗ = −1, 0, +1
• Orbitals = 3 (p orbitals)

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29. If l = 2:

• mₗ = −2, −1, 0, +1, +2
• Orbitals = 5 (d orbitals)

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🔗 Relationship Between Quantum Numbers

30. l depends on n
31. mₗ depends on l

👉 So hierarchy is: n → l → mₗ

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⭐ Quick Revision

• n → shell, size, energy
• l → sub-shell, shape
• mₗ → orientation
• Orbitals increase as n²
• Sub-shells: s, p, d, f...
• Orientation states = 2l + 1

🧠 Quantum Numbers, Orbitals & Electron Spin (NEET Notes)

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🌌 Definition of Orbital

1. Every atomic orbital is completely defined by three quantum numbers:
   • Principal quantum number (n)
   • Azimuthal quantum number (l)
   • Magnetic quantum number (mₗ)

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2. These three quantum numbers together describe:
   • Energy of orbital
   • Shape of orbital
   • Orientation of orbital

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📍 Example of Orbital Identification

3. An orbital with:

   • n = 2, l = 1, mₗ = 0

4. This means:

   • n = 2 → second shell
   • l = 1 → p subshell
   • mₗ = 0 → one of the p orbitals

5. So this orbital is: 👉 2p orbital

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📊 Subshell and Number of Orbitals

6. Each value of l defines a subshell and number of orbitals:

l value	Subshell	Number of orbitals
0	s	1
1	p	3
2	d	5
3	f	7
4	g	9
5	h	11

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7. Key rule: 👉 Number of orbitals in a subshell = 2l + 1

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🧲 Electron Spin (New Quantum Number)

8. The three quantum numbers (n, l, mₗ) were not enough to explain all atomic spectra.

9. Some spectral lines appear as:

   • Doublets (2 lines)
   • Triplets (3 lines)

10. This showed the need for an extra property of electron.

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🧭 Spin Quantum Number (mₛ)

11. In 1925, scientists:

• George Uhlenbeck
• Samuel Goudsmit

proposed electron spin

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12. Electron spin means:

• Electron rotates around its own axis
• Like Earth rotating on its axis

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13. Electron has intrinsic property called: 👉 spin angular momentum

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🔄 Spin States

14. Spin quantum number is written as mₛ

15. It has only two possible values:

• +½
• −½

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16. These represent:

• ↑ spin (spin up = +½)
• ↓ spin (spin down = −½)

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17. Electrons with opposite spins:

• One +½
• One −½
  👉 called opposite spin electrons

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⚠️ Important Rule (Pauli Exclusion Principle idea)

18. One orbital can hold a maximum of 2 electrons only

19. These two electrons must have:

• Opposite spins (↑ ↓)

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🧠 Summary of All Quantum Numbers

20. n (Principal quantum number)

• Shell
• Size and energy of orbital

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21. l (Azimuthal quantum number)

• Subshell
• Shape of orbital
• Also affects energy in multi-electron atoms

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22. mₗ (Magnetic quantum number)

• Orientation of orbital
• Number of orbitals = 2l + 1

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23. mₛ (Spin quantum number)

• Spin direction of electron
• Values: +½ or −½

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⭐ Final Key Idea

24. Total quantum description means: 👉 Each electron in an atom is uniquely identified by 4 quantum numbers (n, l, mₗ, mₛ)

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🔥 Super Quick Revision

• n → shell
• l → subshell (s, p, d, f)
• mₗ → orbital orientation
• mₛ → electron spin (↑ ↓)
• Max 2 electrons per orbital with opposite spin

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Class 11 Chemistry (CBSE) – Orbitals & Quantum Numbers Question Bank

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1. Multiple Choice Questions (MCQs)

1. Which quantum number determines the size of an orbital?

A. l
B. mₗ
C. n
D. mₛ

Answer: C. n

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2. The shape of an orbital is determined by:

A. n
B. l
C. mₗ
D. mₛ

Answer: B. l

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3. For n = 3, the possible values of l are:

A. 0, 1
B. 0, 1, 2
C. 1, 2, 3
D. 0, 1, 2, 3

Answer: B. 0, 1, 2

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4. Number of p orbitals is:

A. 1
B. 3
C. 5
D. 7

Answer: B. 3

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5. Number of d orbitals is:

A. 3
B. 4
C. 5
D. 7

Answer: C. 5

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6. The spin quantum number can have values:

A. ±1
B. ±2
C. ±½
D. 0 and 1

Answer: C. ±½

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7. Maximum electrons in one orbital are:

A. 1
B. 2
C. 4
D. 8

Answer: B. 2

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8. Which subshell corresponds to l = 2?

A. s
B. p
C. d
D. f

Answer: C. d

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9. Number of orbitals in M-shell:

A. 3
B. 5
C. 7
D. 9

Answer: D. 9

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10. The value of mₗ for l = 1 are:

A. 0,1
B. -1,0,+1
C. -2,-1,0,+1,+2
D. +1 only

Answer: B. -1,0,+1

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2. Very Short Answer Questions (1 Mark)

Q1. What is an orbital?

Answer: An orbital is a region around the nucleus where the probability of finding an electron is maximum.

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Q2. What does principal quantum number represent?

Answer: It represents the shell, size, and energy of an orbital.

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Q3. How many orbitals are present in a p-subshell?

Answer: Three.

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Q4. Write the values of spin quantum number.

Answer: +½ and –½.

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Q5. What is the value of l for an s orbital?

Answer: 0.

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Q6. What is the maximum number of electrons in an orbital?

Answer: Two.

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Q7. Which quantum number determines orientation?

Answer: Magnetic quantum number (mₗ).

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Q8. Name the shell represented by n = 2.

Answer: L-shell.

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3. Short Answer Questions (2–3 Marks)

Q1. Explain principal quantum number.

Answer:

• Represented by n.
• Determines shell, size, and energy.
• Values are 1, 2, 3, 4...
• Number of orbitals in a shell = n².

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Q2. What is azimuthal quantum number?

Answer:

• Represented by l.
• Determines shape of orbital.
• Values range from 0 to (n−1).
• Subshells are s, p, d, f.

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Q3. Explain magnetic quantum number.

Answer:

• Represented by mₗ.
• Determines orientation of orbitals.
• Values range from −l to +l.
• Number of values = 2l+1.

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Q4. Why was spin quantum number introduced?

Answer: Spin quantum number was introduced to explain splitting of spectral lines into doublets and triplets, which could not be explained by the first three quantum numbers.

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4. Long Answer Questions (5 Marks)

Q1. Explain all four quantum numbers.

Answer:

1. Principal Quantum Number (n)

• Defines shell.
• Determines size and energy.
• Values: 1,2,3,4...

2. Azimuthal Quantum Number (l)

• Defines shape.
• Values: 0 to n−1.
• Subshells: s,p,d,f.

3. Magnetic Quantum Number (mₗ)

• Defines orientation.
• Values: −l to +l.

4. Spin Quantum Number (mₛ)

• Defines electron spin.
• Values: +½ and −½.

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Q2. Explain the relation between n, l and mₗ.

Answer:

• n determines shell.
• l depends on n and determines subshell.
• mₗ depends on l and determines orbital orientation.
• Number of orbitals = 2l+1.

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5. Assertion and Reason Questions

Q1.

Assertion (A): The shape of an orbital is determined by azimuthal quantum number.

Reason (R): The azimuthal quantum number identifies the subshell.

Answer: Both A and R are true and R is the correct explanation.

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Q2.

Assertion (A): An orbital can contain more than two electrons.

Reason (R): Two electrons in the same orbital must have opposite spins.

Answer: Assertion is false but Reason is true.

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Q3.

Assertion (A): For l = 2, there are five orbitals.

Reason (R): Number of orbitals = 2l+1.

Answer: Both A and R are true and R is the correct explanation.

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6. Fill in the Blanks

1. Principal quantum number is represented by ______.

Answer: n

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2. Shape of orbital is determined by ______ quantum number.

Answer: azimuthal

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3. The value of spin quantum number is ______ or ______.

Answer: +½, −½

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4. Number of orbitals in a d-subshell is ______.

Answer: 5

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5. For n = 2, the shell is called ______.

Answer: L

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6. Maximum number of electrons in one orbital is ______.

Answer: 2

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7. Statement-Based Questions

Statement I:

The number of orbitals in a p-subshell is three.

Statement II:

The value of l for p-subshell is 1.

Choose the correct answer:

A. Both statements are true.
B. Both statements are false.
C. Statement I is true, Statement II is false.
D. Statement I is false, Statement II is true.

Answer: A

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Statement I:

An orbital can contain two electrons.

Statement II:

Both electrons must have opposite spins.

Answer: Both statements are true.

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8. Case Study Questions

Case Study

An electron in an atom has: n = 3, l = 2, mₗ = +1 and mₛ = +½.

Answer the following:

Q1. Which shell does the electron belong to?

Answer: M-shell

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Q2. Which subshell does the electron belong to?

Answer: d-subshell

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Q3. How many orbitals are present in this subshell?

Answer: 5

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Q4. What is the spin state?

Answer: Spin up (+½)

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9. Match the Columns

Column A	Column B
A. n	1. Orientation
B. l	2. Spin
C. mₗ	3. Shape
D. mₛ	4. Shell

Answer:

A → 4
B → 3
C → 1
D → 2

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Important CBSE Exam Formula Sheet

• Number of orbitals in shell = n²
• Maximum electrons in shell = 2n²
• Number of subshells = n
• Number of orbitals in subshell = 2l + 1
• s = 1 orbital
• p = 3 orbitals
• d = 5 orbitals
• f = 7 orbitals
• Electron spin = +½ or −½
• Maximum electrons per orbital = 2 (opposite spins) ✔️

ORBITALS & QUANTUM NUMBERS

│

├── Atomic Orbitals

│   │

│   ├── Defined by 3 Quantum Numbers

│   │   ├── n (Principal)

│   │   ├── l (Azimuthal)

│   │   └── mₗ (Magnetic)

│   │

│   └── Example

│       └── n=2, l=1, mₗ=0 → 2p Orbital

│

├── Principal Quantum Number (n)

│   │

│   ├── Defines Shell

│   ├── Determines Size of Orbital

│   ├── Determines Energy of Orbital

│   ├── Values → 1, 2, 3, 4...

│   │

│   ├── Shell Names

│   │   ├── n=1 → K

│   │   ├── n=2 → L

│   │   ├── n=3 → M

│   │   └── n=4 → N

│   │

│   └── Number of Orbitals = n²

│

├── Azimuthal Quantum Number (l)

│   │

│   ├── Defines Shape of Orbital

│   ├── Values → 0 to (n−1)

│   │

│   ├── Subshell Notation

│   │   ├── l=0 → s

│   │   ├── l=1 → p

│   │   ├── l=2 → d

│   │   ├── l=3 → f

│   │   ├── l=4 → g

│   │   └── l=5 → h

│   │

│   └── Number of Subshells = n

│

├── Magnetic Quantum Number (mₗ)

│   │

│   ├── Defines Orientation of Orbital

│   ├── Values → −l to +l

│   └── Number of Orbitals = 2l + 1

│

├── Orbitals in Each Subshell

│   │

│   ├── s → 1 Orbital

│   ├── p → 3 Orbitals

│   ├── d → 5 Orbitals

│   ├── f → 7 Orbitals

│   ├── g → 9 Orbitals

│   └── h → 11 Orbitals

│

├── Electron Spin Quantum Number (mₛ)

│   │

│   ├── Proposed by

│   │   ├── George Uhlenbeck

│   │   └── Samuel Goudsmit

│   │

│   ├── Defines Spin of Electron

│   ├── Values

│   │   ├── +½ → ↑ Spin Up

│   │   └── −½ → ↓ Spin Down

│   │

│   └── Opposite Spins

│       ├── ↑ ↓

│       └── Required in Same Orbital

│

├── Orbital Capacity

│   │

│   ├── Maximum Electrons = 2

│   └── Must Have Opposite Spins

│

└── Four Quantum Numbers Summary

    │

    ├── n  → Shell, Size, Energy

    ├── l  → Subshell, Shape

    ├── mₗ → Orientation

    └── mₛ → Electron Spin

MEMORY TRICK

│

├── n  → Name of Shell

├── l  → Look (Shape)

├── mₗ → Map Direction

└── mₛ → Spin Direction 

🔗  Internal Links

Atomic Structure Series

/atomic-structure-introduction

/hydrogen-atom-schrodinger-equation

/quantum-numbers-and-orbitals

/shapes-of-atomic-orbitals

/electronic-configuration

/aufbau-principle

/pauli-exclusion-principle

/hund-rule

NEET Chemistry Resources

/neet-chemistry-short-notes

/neet-chemistry-mcqs-atomic-structure

/class-11-chemistry-revision-notes

/important-neet-chemistry-formulas

Related Topics

/bohr-model-of-atom

/wave-function-and-probability-density

/hydrogen-spectrum-explained

/electron-spin-and-magnetic-properties

Recommended Anchor Texts

"What are Quantum Numbers?"

"Hydrogen Atom Notes"

"Atomic Orbitals Explained"

"Electron Spin Quantum Number"

"NEET Atomic Structure MCQs"

"Aufbau Principle Guide"

"Pauli Exclusion Principle Notes"