Q.28 Physics · Section A ⭐ 360° Option Elimination Active

NEET 2024 Physics Question 28 Solution

Topic: Nuclei · Official NTA Booklet Code T1

Question

²⁹⁰₈₂X →(α) Y →(e⁺) Z →(β⁻) P →(e⁻) Q. In the nuclear emission stated above, the mass number and atomic number of the product Q respectively, are:

✓

Verified Against NTA Final Answer Key

Option (2) : 286, 81

📚 Nuclei Easy

📋 Given Parameters & Problem Setup

Parent Nucleus ²⁹⁰₈₂X (A = 290, Z = 82)

Decay Step 1 α emission (alpha particle, ⁴₂He)

Decay Step 2 e⁺ emission (positron / β⁺ decay, ⁰₊₁e)

Decay Step 3 β⁻ emission (beta-minus particle, ⁰₋₁e)

Decay Step 4 e⁻ emission (electron / beta-minus decay, ⁰₋₁e)

⚡

The 30-Second Exam Hall Shortcut: ⚡ Mass Number Conservation Shortcut

⏱️ Save ~40 seconds

Only α decay changes mass number (drops by 4 -> 290 - 4 = 286)! Beta particles have mass 0 -> Final A = 286 (eliminates 1 & 3); Z: 82 - 2 - 1 + 1 + 1 = 81 -> (286, 81)!

1 Look at mass number A: Only α emission changes A (ΔA = -4).

2 Positron (e⁺) and electrons (β⁻, e⁻) have mass number 0.

3 Final mass number A = 290 - 4 = 286 (immediately eliminate options 1 and 3!).

4 Track atomic number Z: Z_initial = 82.

5 - After α: 82 - 2 = 80.

6 - After e⁺ (positron): 80 - 1 = 79.

7 - After β⁻: 79 - (-1) = 80.

8 - After e⁻: 80 - (-1) = 81.

9 Result: (A = 286, Z = 81) -> Option (2) in under 15 seconds!

🛡️

Why You Can 100% Trust This Shortcut: Soddy-Fajans Radioactive Displacement Laws (α decay: A-4, Z-2; β⁻ decay: A, Z+1; β⁺ decay: A, Z-1).

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Step 1: Alpha Decay (X -> Y)

An alpha particle is a helium-4 nucleus (⁴₂He). Emission of an alpha particle reduces the mass number by 4 and atomic number by 2:

^{290}_{82}X \xrightarrow{\alpha} ^{286}_{80}Y + ^4_2\text{He}

Step 2

Step 2: Positron (e⁺ / β⁺) Decay (Y -> Z)

In positron emission, a proton inside the nucleus transforms into a neutron, emitting a positron (⁰₊₁e) and a neutrino. The mass number remains unchanged, while the atomic number decreases by 1:

^{286}_{80}Y \xrightarrow{e^+} ^{286}_{79}Z + ^0_{+1}e + \nu

Step 3

Step 3: Beta-Minus (β⁻) Decay (Z -> P)

In beta-minus emission, a neutron transforms into a proton, emitting an electron (⁰₋₁e) and an antineutrino. The mass number is unchanged, while the atomic number increases by 1:

^{286}_{79}Z \xrightarrow{\beta^-} ^{286}_{80}P + ^0_{-1}e + \bar{\nu}

Step 4

Step 4: Electron (e⁻) Decay (P -> Q)

The final emission is an electron (e⁻, identical to β⁻). The mass number remains unchanged, and the atomic number increases by another 1:

^{286}_{80}P \xrightarrow{e^-} ^{286}_{81}Q + ^0_{-1}e + \bar{\nu}

Step 5

Final Nucleus Identification

The resulting product nucleus Q has mass number A = 286 and atomic number Z = 81.

A_Q = 286, \quad Z_Q = 81

⭐

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:

Incorrect mass number; subtracted 2 instead of 4 for alpha particle.

⚠️

Student Fallacy (Why candidates pick this trap): Confusing alpha mass number (4) with atomic number (2).

2 (2)

✓ 100% Correct

Verdict & Scientific Reason:

Flawless conservation of nucleons and charge: A = 286, Z = 81.

💡

Why this is airtight: None.

3 (3)

✗ Incorrect

Verdict & Scientific Reason:

Subtracts 10 from mass number.

⚠️

Student Fallacy (Why candidates pick this trap): Assuming beta particles have mass numbers.

4 (4)

✗ Incorrect

Verdict & Scientific Reason:

Misses the final electron emission (+1 to Z).

⚠️

Student Fallacy (Why candidates pick this trap): Stopping at nucleus P instead of Q.

⚠️

NTA Trap Alert: Positron (e⁺) vs Electron (e⁻ / β⁻) Sign Confusion

Students frequently subtract 1 for both e⁺ and e⁻, forgetting that emitting a negative charge increases the nuclear positive charge (Z increases by 1).

🛡️ How to avoid the -1 mark: Think charge conservation: If negative charge leaves, positive charge inside MUST increase: Z -> Z + 1.

📖

Core NEET Syllabus Standard

Physics Core Nuclear Physics · Nuclei Standard Benchmark

Core Scientific Principle Tested:

"In any nuclear transformation, total mass number (A) and total electric charge (Z) are conserved strictly."

Syllabus Focus: Radioactivity and Nuclear Decay Law

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

Alpha drops 4 from mass; Positron subtracts 1, Two electrons add 2 -> 81!

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NEET 2024 Physics Question 28 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Mass Number Conservation Shortcut

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1: Alpha Decay (X -> Y)

Step 2: Positron (e⁺ / β⁺) Decay (Y -> Z)

Step 3: Beta-Minus (β⁻) Decay (Z -> P)

Step 4: Electron (e⁻) Decay (P -> Q)

Final Nucleus Identification

360° Option Elimination Engine Key Feature

NTA Trap Alert: Positron (e⁺) vs Electron (e⁻ / β⁻) Sign Confusion

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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