Q.69 Chemistry ⭐ 360° Option Elimination Active

NEET 2023 Chemistry Question 69 Solution

Topic: Structure of Atom · Official NTA Booklet Code G5

Question

The relation between nₘ (nₘ = the number of permissible values of magnetic quantum number (m)) for a given value of azimuthal quantum number (l), is

✓

Verified Against NTA Final Answer Key

Option (2) : l = (n_m - 1) / 2

📚 Structure of Atom Easy

📋 Given Parameters & Problem Setup

Azimuthal quantum number l

Permissible values of magnetic quantum number m n_m

Standard relation n_m = 2l + 1

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The 30-Second Exam Hall Shortcut: ⚡ Simple Algebraic Inversion: n_m = 2l + 1 ⟹ l = (n_m - 1) / 2

⏱️ Save ~25 seconds

For any subshell l, there are 2l + 1 magnetic values (e.g., p-subshell l=1 has 3 orbitals: 3 = 2(1)+1). Rearranging n_m = 2l + 1 gives l = (n_m - 1) / 2 in 5 seconds!

1 Recall the number of orbitals in a subshell: For a given value of l, magnetic quantum number m ranges from -l through 0 to +l.

2 The total count of permissible values is: n_m = 2l + 1.

3 Rearrange this linear equation to isolate l:

4 n_m - 1 = 2l ⟹ l = (n_m - 1) / 2.

5 Compare with the options: Option (2) exactly matches l = (n_m - 1) / 2.

6 Lock Option (2) immediately!

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Why You Can 100% Trust This Shortcut: Atomic Structure · Quantum Numbers (The number of spatial orientations of an orbital for a given azimuthal quantum number l is n_m = 2l + 1).

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Definition and Range of Magnetic Quantum Number m

For an electron in an atom, the azimuthal (orbital angular momentum) quantum number l defines the subshell shape. For any given value of l, the magnetic orbital quantum number m_l designates the spatial orientation of the orbital and can take all integer values from -l to +l, including zero:

m_l \in \{-l, -(l-1), \dots, 0, \dots, +(l-1), +l\}

Step 2

Counting the Number of Permissible Values (n_m)

The total number of permissible orientations n_m in a subshell of azimuthal quantum number l is given by counting all values in this range:

n_m = l + 1 + l = 2l + 1

Step 3

Algebraic Inversion to Express l in Terms of n_m

The question asks for the relation expressing l in terms of n_m. Subtract 1 from both sides and divide by 2:

n_m - 1 = 2l \implies l = \frac{n_m - 1}{2}

Step 4

Verification with Concrete Quantum Subshells

Check for s (l=0), p (l=1), and d (l=2) subshells:

\begin{aligned} s\text{-subshell: } &l = 0 \implies n_m = 1 \implies l = \frac{1 - 1}{2} = 0 \quad (\text{Matches}) \\[4pt] p\text{-subshell: } &l = 1 \implies n_m = 3 \implies l = \frac{3 - 1}{2} = 1 \quad (\text{Matches}) \\[4pt] d\text{-subshell: } &l = 2 \implies n_m = 5 \implies l = \frac{5 - 1}{2} = 2 \quad (\text{Matches}) \end{aligned}

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360° Option Elimination Engine Key Feature

Diagnose every choice: Know exactly why the right option works and why distractors fail.

4-Option Deep Scan

1 (1)

✗ Incorrect

Verdict & Scientific Reason:

Arbitrary linear formula that fails for all subshells.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate guessed a linear relation without multiplying by 2.

2 (2)

✓ 100% Correct

Verdict & Scientific Reason:

Accurate algebraic inversion of the fundamental relation n_m = 2l + 1.

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Why this is airtight: None. Candidate performed correct algebraic transposition.

3 (3)

✗ Incorrect

Verdict & Scientific Reason:

Inverted variable positions (states l = 2n_m + 1 instead of n_m = 2l + 1).

⚠️

Student Fallacy (Why candidates pick this trap): Candidate swapped the dependent and independent variables.

4 (4)

✗ Incorrect

Verdict & Scientific Reason:

Erroneously introduces a quadratic term l².

⚠️

Student Fallacy (Why candidates pick this trap): Candidate confused number of orbitals with formulas for maximum electron capacity.

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NTA Trap Alert: Confusing n_m = 2l + 1 with l = 2n_m + 1 (Option 3)

Under exam pressure, students see "2" and "1" and hastily pick Option (3) l = 2n_m + 1, not realizing that l is the subject of the equation in the options, which requires (n_m - 1) / 2.

🛡️ How to avoid the -1 mark: Plug in numbers: For p-subshell, l = 1 and n_m = 3. Test Option 2: (3 - 1)/2 = 1 (Works!). Test Option 3: 2(3)+1 = 7 ≠ 1 (Fails!).

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Core NEET Syllabus Standard

National Eligibility cum Entrance Test (NEET UG) · Structure of Atom Standard Benchmark

Core Scientific Principle Tested:

"For a given value of l, there are (2l + 1) values of m_l, so n_m = 2l + 1, which inverts to l = (n_m - 1)/2."

Syllabus Focus: Quantum Mechanical Model of Atom – Quantum Numbers

Preserved in Rationalized Curriculum Syllabus & Academic Standards ↗

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NEET 2023 Chemistry Question 69 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Simple Algebraic Inversion: n_m = 2l + 1 ⟹ l = (n_m - 1) / 2

Step-by-Step Rigorous Workflow & Mathematical Proof

Definition and Range of Magnetic Quantum Number m

Counting the Number of Permissible Values (n_m)

Algebraic Inversion to Express l in Terms of n_m

Verification with Concrete Quantum Subshells

360° Option Elimination Engine Key Feature

NTA Trap Alert: Confusing n_m = 2l + 1 with l = 2n_m + 1 (Option 3)

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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