Q.50 Chemistry ⭐ 360° Option Elimination Active

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NEET 2025 Chemistry Question 50 Solution

Topic: Structure of Atom · Official NTA Booklet Code 45

Question

Energy and radius of first Bohr orbit of He⁺ and Li²⁺ are [Given R_H = 2.18×10⁻¹⁸ J, a₀ = 52.9 pm]

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Verified Against NTA Final Answer Key

Option (1) : E_n(Li²⁺) = -19.62 × 10⁻¹⁸ J; r_n(Li²⁺) = 17.6 pm; E_n(He⁺) = -8.72 × 10⁻¹⁸ J; r_n(He⁺) = 26.4 pm

📚 Structure of Atom Easy

📋 Given Parameters & Problem Setup

Rydberg Constant (R_H) 2.18 × 10⁻¹⁸ J

Bohr Radius (a₀) 52.9 pm

Quantum Level First Bohr orbit (n = 1)

Species He⁺ (Z = 2) and Li²⁺ (Z = 3)

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The 30-Second Exam Hall Shortcut: ⚡ Z² Energy and 1/Z Radius Shortcut

⏱️ Save ~40 seconds

E ∝ -Z² ⟹ He⁺ (Z=2) has -2.18 × 4 = -8.72 × 10⁻¹⁸ J; Li²⁺ (Z=3) has -2.18 × 9 = -19.62 × 10⁻¹⁸ J! Radius r = 52.9/Z ⟹ He⁺ is 52.9/2 = 26.45 pm; Li²⁺ is 52.9/3 = 17.6 pm!

1 Recall Bohr energy formula for single-electron species: E_n = -R_H (Z² / n²).

2 For n = 1: E(He⁺) = -2.18 × 10⁻¹⁸ × 2² = -2.18 × 4 = -8.72 × 10⁻¹⁸ J.

3 For n = 1: E(Li²⁺) = -2.18 × 10⁻¹⁸ × 3² = -2.18 × 9 = -19.62 × 10⁻¹⁸ J.

4 Notice energy exponent is 10⁻¹⁸ J, eliminating Options (3) and (4) which write 10⁻¹⁶ J.

5 Recall Bohr radius formula: r_n = a₀ (n² / Z) = 52.9 / Z pm.

6 For He⁺: r = 52.9 / 2 = 26.45 ≈ 26.4 pm.

7 For Li²⁺: r = 52.9 / 3 = 17.63 ≈ 17.6 pm.

8 Option (1) pairs Li²⁺ with 17.6 pm and He⁺ with 26.4 pm correctly.

9 Match Option (1) in under 15 seconds!

🛡️

Why You Can 100% Trust This Shortcut: Bohr’s Model of Hydrogen-like Atoms (NCERT Chemistry · Structure of Atom: r_n ∝ n²/Z).

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Energy Calculation for First Bohr Orbit of He⁺ and Li²⁺

The energy of a stationary state in a hydrogen-like species is given by Bohr’s formula:

E_n = -R_H \frac{Z^2}{n^2} \implies E_1 = -2.18 \times 10^{-18} \times Z^2\text{ J}

• For He⁺ (Z = 2): E₁(He⁺) = -2.18 × 10⁻¹⁸ × 4 = -8.72 × 10⁻¹⁸ J.
• For Li²⁺ (Z = 3): E₁(Li²⁺) = -2.18 × 10⁻¹⁸ × 9 = -19.62 × 10⁻¹⁸ J.

Step 2

Radius Calculation for First Bohr Orbit of He⁺ and Li²⁺

The radius of a Bohr orbit is inversely proportional to the atomic number Z:

r_n = a_0 \frac{n^2}{Z} \implies r_1 = \frac{52.9\text{ pm}}{Z}

• For He⁺ (Z = 2): r₁(He⁺) = 52.9 / 2 = 26.45 pm ≈ 26.4 pm.
• For Li²⁺ (Z = 3): r₁(Li²⁺) = 52.9 / 3 = 17.63 pm ≈ 17.6 pm.

Step 3

Consolidate and Select Matching Option

Compare with the multiple choice options:

E_n(\text{Li}^{2+}) = -19.62 \times 10^{-18}\text{ J}, \; r_n(\text{Li}^{2+}) = 17.6\text{ pm}; \; E_n(\text{He}^+) = -8.72 \times 10^{-18}\text{ J}, \; r_n(\text{He}^+) = 26.4\text{ pm}

• Option (1) has the exact values and proper order of magnitude (10⁻¹⁸ J).

⭐

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 A

✓ 100% Correct

Verdict & Scientific Reason:

100% correct. Exact evaluation of E ∝ -Z² and r ∝ 1/Z with 10⁻¹⁸ J.

💡

Why this is airtight: None; flawless physical calculations.

2 B

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. Assigns Z=3 values to He⁺ and Z=2 values to Li²⁺.

⚠️

Student Fallacy (Why candidates pick this trap): Swapping atomic numbers of He and Li.

3 C

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. Order of magnitude error (10⁻¹⁶ J instead of 10⁻¹⁸ J).

⚠️

Student Fallacy (Why candidates pick this trap): Selecting wrong power of 10.

4 D

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. Both values swapped and incorrect order of magnitude.

⚠️

Student Fallacy (Why candidates pick this trap): Multiple errors.

⚠️

NTA Trap Alert: Exponent Trap: 10⁻¹⁸ J vs 10⁻¹⁶ J

Options 3 and 4 feature identical digits (19.62 and 8.72) but with exponent 10⁻¹⁶ J instead of 10⁻¹⁸ J. Candidates working hastily often overlook the exponent!

🛡️ How to avoid the -1 mark: Always verify the exponent: R_H is 2.18 × 10⁻¹⁸ J, so energies must be on the scale of 10⁻¹⁸ J!

📖

Core NEET Syllabus Standard

NEET Chemistry Core Syllabus · Structure of Atom Standard Benchmark

Core Scientific Principle Tested:

"E_n = -R_H Z² / n² and r_n = a₀ n² / Z."

Syllabus Focus: Bohr’s Model of Hydrogen-Like Atoms

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

He is Z=2 (×4, /2); Li is Z=3 (×9, /3) ⟹ Exponent 10⁻¹⁸ J (Option 1)!

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Mathematical Relation Between Number of Magnetic Orbitals (n_m) and Azimuthal Quantum Number (l)

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NEET 2025 Chemistry Question 50 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Z² Energy and 1/Z Radius Shortcut

Step-by-Step Rigorous Workflow & Mathematical Proof

Energy Calculation for First Bohr Orbit of He⁺ and Li²⁺

Radius Calculation for First Bohr Orbit of He⁺ and Li²⁺

Consolidate and Select Matching Option

360° Option Elimination Engine Key Feature

NTA Trap Alert: Exponent Trap: 10⁻¹⁸ J vs 10⁻¹⁶ J

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

🔗 Related Questions — Structure of Atom

Radial Wavefunctions and Identification of Radial Nodes

Physical Significance of the Four Quantum Numbers

Bohr Energy Levels in Hydrogen-like Mononuclear Ions

Mathematical Relation Between Number of Magnetic Orbitals (n_m) and Azimuthal Quantum Number (l)

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