Q.58 Chemistry · Section A ⭐ 360° Option Elimination Active

NEET 2024 Chemistry Question 58 Solution

Topic: Structure of Atom · Official NTA Booklet Code T1

Question

The energy of an electron in the ground state (n = 1) for He⁺ ion is −x J, then that for an electron in n = 2 state for Be³⁺ ion in J is:

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Verified Against NTA Final Answer Key

Option (3) : -x

📚 Structure of Atom Easy

📋 Given Parameters & Problem Setup

He+ ion (Z = 2) ground state (n = 1) energy -x J

Be3+ ion (Z = 4) target state n = 2 state

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The 30-Second Exam Hall Shortcut: ⚡ (Z / n)² Ratio Cancellation Hack

⏱️ Save ~40 seconds

Energy E ∝ (Z / n)². For He+ (n=1): (2/1)² = 4 -> -x J. For Be3+ (n=2): (4/2)² = (2)² = 4 -> exactly -x J!

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

2 For He+ in ground state: Z = 2, n = 1 -> (Z/n)² = (2/1)² = 4 -> E_1 = -4 R_H = -x J.

3 For Be3+ in n = 2 state: Z = 4, n = 2 -> (Z/n)² = (4/2)² = 2² = 4 -> E_2 = -4 R_H.

4 Because both have the identical factor (Z/n)² = 4, their energies are identical: E_2(Be3+) = -x J.

5 Option (3) in 5 seconds!

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Why You Can 100% Trust This Shortcut: NCERT Chemistry · Structure of Atom (Bohr model formulation for hydrogen-like species: E_n = -2.18 × 10^-18 · Z²/n² J).

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Bohr Energy Equation for Hydrogen-like Species

For any one-electron hydrogen-like ion of atomic number Z, the energy of the stationary electron state with principal quantum number n is given by:

E_n = -R_H \frac{Z^2}{n^2}

Step 2

Relating Given Energy of He+ Ground State to Constant RH

For helium ion He+, Z = 2. In the ground state, n = 1:

E_1(\text{He}^+) = -R_H \frac{2^2}{1^2} = -4 R_H = -x \implies R_H = \frac{x}{4}

Step 3

Calculation for Be3+ in n = 2 State

For beryllium ion Be3+, Z = 4. For the n = 2 quantum level:

E_2(\text{Be}^{3+}) = -R_H \frac{Z^2}{n^2} = -R_H \frac{4^2}{2^2} = -R_H \left(\frac{16}{4}\right) = -4 R_H

Step 4

Equating and Concluding

Substituting -4 RH = -x directly into the expression:

E_2(\text{Be}^{3+}) = -4 R_H = -x\;\text{J}

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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:

Multiplies by (Z/n)² again instead of recognizing identical ratios.

⚠️

Student Fallacy (Why candidates pick this trap): Multiplying by 4² without dividing by n².

2 (2)

✗ Incorrect

Verdict & Scientific Reason:

Uses n = 3 in the denominator instead of n = 2.

⚠️

Student Fallacy (Why candidates pick this trap): Confusing the state index with n = 3.

3 (3)

✓ 100% Correct

Verdict & Scientific Reason:

Exact mathematical equality: (4/2)² = (2/1)² = 4.

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Why this is airtight: None.

4 (4)

✗ Incorrect

Verdict & Scientific Reason:

Unrelated scaling error.

⚠️

Student Fallacy (Why candidates pick this trap): Miscalculating squared quantum numbers.

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NTA Trap Alert: Squaring Only Z and Forgetting to Square n

Students frequently square the numerator Z² = 16 but forget to square the denominator (dividing by 2 instead of 4, obtaining 8 instead of 4).

🛡️ How to avoid the -1 mark: Always evaluate the grouped ratio (Z / n) first: for Be3+ at n=2, (4/2) = 2, so (Z/n)² = 4.

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Core NEET Syllabus Standard

Chemistry Core Physical Chemistry · Structure of Atom Standard Benchmark

Core Scientific Principle Tested:

"Energy of hydrogen-like species scales as Z²/n²: En = -RH · (Z/n)²"

Syllabus Focus: Bohr’s Model for Hydrogen Atom: Radii and Energy of Stationary States

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

Z over n is two in both: square is four, identical growth (-x J)!

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

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NEET 2024 Chemistry Question 58 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ (Z / n)² Ratio Cancellation Hack

Step-by-Step Rigorous Workflow & Mathematical Proof

Bohr Energy Equation for Hydrogen-like Species

Relating Given Energy of He+ Ground State to Constant RH

Calculation for Be3+ in n = 2 State

Equating and Concluding

360° Option Elimination Engine Key Feature

NTA Trap Alert: Squaring Only Z and Forgetting to Square n

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

🔗 Related Questions — Structure of Atom

Radial Wavefunctions and Identification of Radial Nodes

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

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

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