Q.14 Physics ⭐ 360° Option Elimination Active

NEET 2021 Physics Question 14 Solution

Topic: Nuclei · Official NTA Booklet Code M1

Question

A radioactive nucleus ᴬ_ZX undergoes spontaneous decay in the sequence ᴬ_ZX → Z−1B → Z−3C → Z−2D, where Z is the atomic number of element X. The possible decay particles in the sequence are:

✓

Verified Against NTA Final Answer Key

Option (3) : β+, α, β-

📚 Nuclei Easy

📋 Given Parameters & Problem Setup

Decay Step 1 {}_Z^A X -> {}_{Z-1} B (ΔZ = -1)

Decay Step 2 {}_{Z-1} B -> {}_{Z-3} C (ΔZ = -2)

Decay Step 3 {}_{Z-3} C -> {}_{Z-2} D (ΔZ = +1)

⚡

The 30-Second Exam Hall Shortcut: ⚡ ΔZ Tracker: -1 is β+, -2 is α, +1 is β-

⏱️ Save ~20 seconds

Track the change in atomic number Z at each decay step: 1. $Z \to Z-1$ ( $\\Delta Z = -1$ ) $\implies \beta^+$ decay! 2. $Z-1 \to Z-3$ ( $\\Delta Z = -2$ ) $\implies \alpha$ decay! 3. $Z-3 \to Z-2$ ( $\\Delta Z = +1$ ) $\implies \beta^-$ decay! The sequence is $\beta^+, \alpha, \beta^-$ ! Match Option (3)!

1 Step 1: Atomic number decreases by 1 (

Z \to Z-1

)

\implies

positron emission (

\beta^+

decay).

2 Step 2: Atomic number decreases by 2 (

Z-1 \to Z-3

)

\implies

alpha particle emission (

\alpha

decay).

3 Step 3: Atomic number increases by 1 (

Z-3 \to Z-2

)

\implies

electron emission (

\beta^-

decay).

4 Sequence of emitted particles:

\beta^+, \alpha, \beta^-

5 Match Option (3).

🛡️

Why You Can 100% Trust This Shortcut: Canonical nuclear charge conservation in radioactive alpha and beta decay.

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Conservation of Nuclear Charge (Atomic Number Z)

In all nuclear reactions, the total electric charge (atomic number $Z$ ) is strictly conserved. Let $\Delta Z$ be the change in atomic number of the daughter nucleus relative to the parent nucleus.

Step 2

Analyzing Step 1: X -> B

The atomic number changes from $Z$ to $Z-1$ (decreases by 1). This occurs when a proton converts into a neutron, emitting a positron ( $\beta^+$ ):

{}_Z^A X \longrightarrow {}_{Z-1}^A B + {}_{+1}^0 e (\beta^+) + \nu_e \implies \mathbf{\beta^+\text{ decay}}

Step 3

Analyzing Step 2: B -> C

The atomic number changes from $Z-1$ to $Z-3$ (decreases by 2). This occurs when an alpha particle ( ${}_2^4\text{He}$ ) is emitted:

{}_{Z-1}^A B \longrightarrow {}_{Z-3}^{A-4} C + {}_2^4\text{He} (\alpha) \implies \mathbf{\alpha\text{ decay}}

Step 4

Analyzing Step 3: C -> D

The atomic number changes from $Z-3$ to $Z-2$ (increases by 1). This occurs when a neutron converts into a proton, emitting an electron ( $\beta^-$ ):

{}_{Z-3}^{A-4} C \longrightarrow {}_{Z-2}^{A-4} D + {}_{-1}^0 e (\beta^-) + \bar{\nu}_e \implies \mathbf{\beta^-\text{ decay}}

⭐

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:

Starts with alpha decay (which would reduce $Z$ by 2 to $Z-2$ , not $Z-1$ ).

⚠️

Student Fallacy (Why candidates pick this trap): Assuming

\alpha

decay is always the first step in a decay chain.

2 2

✗ Incorrect

Verdict & Scientific Reason:

Incorrect first step ( $\alpha$ instead of $\beta^+$ ).

⚠️

Student Fallacy (Why candidates pick this trap): Misreading

\Delta Z = -1

as an alpha decay.

3 3

✓ 100% Correct

Verdict & Scientific Reason:

Exact match with the nuclear charge changes: $\Delta Z = -1$ ( $\beta^+$ ), $\Delta Z = -2$ ( $\alpha$ ), $\Delta Z = +1$ ( $\beta^-$ ).

💡

Why this is airtight: None; rigorous nuclear bookkeeping.

4 4

✗ Incorrect

Verdict & Scientific Reason:

Inverts $\beta^-$ and $\beta^+$ : $\beta^-$ increases $Z$ by 1, which would produce $Z+1$ , not $Z-1$ .

⚠️

Student Fallacy (Why candidates pick this trap): Confusing

\beta^-

with

\beta^+

charge changes.

⚠️

NTA Trap Alert: Beta-Plus vs. Beta-Minus Sign Confusion Trap

Students frequently remember "beta decay changes Z by 1" and mix up the signs: $\beta^-$ emission INCREASES $Z$ by 1 ( $n \to p + e^-$ ), while $\beta^+$ emission DECREASES $Z$ by 1 ( $p \to n + e^+$ ).

🛡️ How to avoid the -1 mark:

\Delta Z = -1 \implies \beta^+

(positron).

\Delta Z = +1 \implies \beta^-

(electron).

\Delta Z = -2 \implies \alpha

📖

Core NEET Syllabus Standard

NCERT Physics · Nuclei Standard Benchmark

Core Scientific Principle Tested:

"In $\alpha$ -decay, $Z$ decreases by 2; in $\beta^+$ -decay, $Z$ decreases by 1; in $\beta^-$ -decay, $Z$ increases by 1."

Syllabus Focus: Radioactivity (Alpha and Beta Decay)

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

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NEET 2021 Physics Question 14 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ ΔZ Tracker: -1 is β+, -2 is α, +1 is β-

Step-by-Step Rigorous Workflow & Mathematical Proof

Conservation of Nuclear Charge (Atomic Number Z)

Analyzing Step 1: X -> B

Analyzing Step 2: B -> C

Analyzing Step 3: C -> D

360° Option Elimination Engine Key Feature

NTA Trap Alert: Beta-Plus vs. Beta-Minus Sign Confusion Trap

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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