Free Physics Calculators — Unit Converter · Constants
Free Nuclear Physics Calculator

Half-Life & Radioactive Decay Calculator

N(t) = N₀ · (½)^(t/t½)

Find remaining quantity, fraction decayed, activity, or number of half-lives elapsed.

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☢ Radioactive Decay Calculator

Enter initial quantity, half-life, and elapsed time
Decay formula
1
Number of half-lives: n = t / t½
2
Remaining: N(t) = N₀ × (½)ⁿ = N₀ × e^(−λt)
3
Decay constant: λ = ln(2) / t½ ≈ 0.6931 / t½
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Understanding Radioactive Decay

Radioactive decay is a random quantum process in which unstable atomic nuclei emit particles or energy to reach a more stable state. The half-life t½ is the time for exactly half of a sample to decay — it is constant regardless of the amount present or external conditions.

Key Concepts

  • Half-life (t½): Time for Nâ‚€/2 to remain. After n half-lives: N = Nâ‚€ × (½)ⁿ
  • Decay constant (λ): λ = ln(2)/t½ ≈ 0.6931/t½. Probability of one atom decaying per unit time.
  • Activity (A): A = λN (Becquerels, Bq = decays/second). 1 Curie = 3.7 × 10¹⁰ Bq.
  • Carbon-14 dating: Uses t½ = 5730 years to date organic material up to ~50,000 years old.

Worked Example — Carbon Dating

A bone fragment contains 25% of its original C-14. How old is it?

1
N/N₀ = 0.25 → (½)ⁿ = 0.25 → n = 2 half-lives
2
Age = n × t½ = 2 × 5730 = 11,460 years
3
Verify: N = N₀ × (½)² = 0.25 N₀ ✓

📚 Recommended Textbooks

Introductory Nuclear Physics (Krane)
Kenneth S. Krane
Undergraduate
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Nuclear Physics (Blatt & Weisskopf)
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