Q.2 Physics ⭐ 360° Option Elimination Active

NEET 2023 Physics Question 2 Solution

Topic: Nuclei · Official NTA Booklet Code G5

Question

The half life of a radioactive substance is 20 minutes. In how much time, the activity of substance drops to (1/16)th of its initial value?

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Verified Against NTA Final Answer Key

Option (1) : 80 minutes

📚 Nuclei Easy

📋 Given Parameters & Problem Setup

Half-life (T₁/₂) 20 minutes

Fractional Remaining Activity (A/A₀) 1/16

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The 30-Second Exam Hall Shortcut: ⚡ Powers of 2 Half-Life Ladder

⏱️ Save ~45 seconds

1/16 is (1/2)⁴, which means exactly 4 half-lives; 4 × 20 min = 80 min done in 5 seconds!

1 Write down the fraction: 1/16.

2 Express 16 as a power of 2: 16 = 2⁴.

3 The number of required half-lives is n = 4.

4 Multiply n by half-life: t = 4 × 20 min = 80 minutes.

5 Immediately bubble Option (1) without writing calculus exponential integrals.

🛡️

Why You Can 100% Trust This Shortcut: Fundamental Nuclear Physics · Radioactive Decay Law (Successive halving principle: N(t) = N₀(1/2)ⁿ where n = t/T₁/₂).

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Radioactive Activity Relation

The activity A of a radioactive sample at time t is related to its initial activity A₀ through the number of elapsed half-lives n:

A = A_0 \left(\frac{1}{2}\right)^n, \quad \text{where } n = \frac{t}{T_{1/2}}

Step 2

Determination of Number of Half-Lives

Given that the activity drops to 1/16th of its initial value:

\frac{A}{A_0} = \frac{1}{16} = \left(\frac{1}{2}\right)^4 \implies n = 4

Step 3

Calculation of Total Elapsed Time

Multiply the number of half-lives by the duration of one half-life:

t = n \times T_{1/2} = 4 \times 20\text{ min} = 80\text{ minutes}

⭐

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)

✓ 100% Correct

Verdict & Scientific Reason:

Exactly 4 half-lives of 20 minutes each equals 80 minutes.

💡

Why this is airtight: None. Correct deduction of (1/2)⁴.

2 (2)

✗ Incorrect

Verdict & Scientific Reason:

Represents only 1 half-life, where activity drops to 1/2, not 1/16.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate confused the elapsed time with the single half-life duration.

3 (3)

✗ Incorrect

Verdict & Scientific Reason:

Represents 2 half-lives, where activity drops to (1/2)² = 1/4.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate incorrectly assumed 1/16 requires 2 half-lives (confusing 4² = 16 with powers of 2).

4 (4)

✗ Incorrect

Verdict & Scientific Reason:

Represents 3 half-lives, where activity drops to (1/2)³ = 1/8.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate made an arithmetic counting error, stopping after 3 decay stages (1/2 → 1/4 → 1/8).

⚠️

NTA Trap Alert: Confusing 2ⁿ with n²

Aspirants often confuse powers of 2 (2, 4, 8, 16 -> n=4) with squares (4²=16 -> incorrectly picking n=2, leading to 40 minutes).

🛡️ How to avoid the -1 mark: Always draw a simple ladder: 1 → 1/2 (1) → 1/4 (2) → 1/8 (3) → 1/16 (4).

📖

Core NEET Syllabus Standard

National Eligibility cum Entrance Test (NEET UG) · Nuclei Standard Benchmark

Core Scientific Principle Tested:

"Every half-life reduces the remaining active nuclei and activity by an exact factor of 2."

Syllabus Focus: Radioactivity and Half-Life Determination

Preserved in Rationalized Curriculum Syllabus & Academic Standards ↗

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NEET 2023 Physics Question 2 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Powers of 2 Half-Life Ladder

Step-by-Step Rigorous Workflow & Mathematical Proof

Radioactive Activity Relation

Determination of Number of Half-Lives

Calculation of Total Elapsed Time

360° Option Elimination Engine Key Feature

NTA Trap Alert: Confusing 2ⁿ with n²

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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