The half-life of a radioactive substance is 4 months. How much time it will take to decay 3/4th of the substance ?

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UKPSC Combined Upper PCS (Prelims) Exam (General Studies) Official Paper-I (Held On: 14 Jul, 2024)
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  1. 12 months
  2. 8 months
  3. 4 months
  4. 3 months

Answer (Detailed Solution Below)

Option 2 : 8 months
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The correct answer is option 2.

Key Points

  • Half-life (T₁/₂) = Time required for half of a radioactive substance to decay.
  • Let’s break it down:
    • After 1 half-life (4 months) → 50% of the substance remains.
    • After 2 half-lives (8 months) →
      • Half of the remaining 50% decays
      • So only 25% remains
      • That means 75% (3/4) has decayed.
  • Therefore, it takes 8 months to decay 3/4th of the substance. 
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