Radioactive Decay Calculator

Calculate radioactive decay using N = N0*e^(-lambda*t). Find remaining activity, decay constant from half-life, or time for a sample to reach a target activity or amount.

☢️ Nuclear Chemistry📐 N = N0·e^(-λt)🧪 Chemistry
Initial amount N0 (atoms or Bq)
Half-life t1/2 (same time units as t)
Time elapsed t
Please enter valid values.

Formula & Reference

VariableSymbolFormulaUnits
Radioactive Decay Calculator—N = N0·e^(-λt)atoms or Bq

Step-by-Step Examples

Example 1
Carbon-14 Dating

C-14 half-life=5730 years. Sample has N0=1000 atoms. How many after 11460 years?

  • 11460 = 2 x 5730 = 2 half-lives
  • N = 1000 x (0.5)^2 = 250 atoms
  • Or: lambda=0.6931/5730; N=1000xe^(-lambda x 11460)
✓ 250 atoms (25% remains after 2 half-lives)
Example 2
Iodine-131

I-131 t1/2=8.02 days. 100 mCi initial. Activity after 24 days?

  • lambda = 0.6931/8.02 = 0.0864 day^-1
  • N = 100 x e^(-0.0864 x 24) = 100 x e^-2.073
  • N = 100 x 0.1259 = 12.59 mCi
✓ 12.59 mCi remains after 24 days (~ 3 half-lives)
Example 3
Radon-222

Rn-222 t1/2=3.82 days. Find activity after 7.64 days.

  • 7.64/3.82 = 2 half-lives
  • N = N0 x (0.5)^2 = 0.250 N0
  • 25% remains
✓ 25% of initial radon remains

Real-World Applications

☢️
Radiocarbon Dating
C-14 (t1/2=5730 y) dating of organic materials up to ~50,000 years old.
🏥
Nuclear Medicine
I-131 (thyroid), Tc-99m (imaging), Ga-67: decay rates determine dose and imaging window.
♀️
Food Irradiation
Co-60 gamma irradiation sterilizes food. Activity calculated from decay for dose control.
🌍
Radiological Safety
Decay calculations determine when contaminated areas are safe after nuclear incidents.

Common Mistakes to Avoid

⚠️
Lambda = 0.693/t1/2

Decay constant lambda = ln(2)/t1/2 = 0.6931/t1/2. Same time units as t1/2.

⚠️
Time and half-life in same units

If t1/2 in years, t must be in years. Never mix days and years.

⚠️
After n half-lives: N = N0 x (0.5)^n

Quick calculation: after 1 HL: 50%, 2 HL: 25%, 3 HL: 12.5%, 7 HL: 0.78%, 10 HL: 0.098%.

Frequently Asked Questions

What is radioactive decay? ▾
Spontaneous transformation of unstable nucleus to more stable form, emitting alpha, beta, or gamma radiation. Follows first-order kinetics.
What is a Becquerel (Bq)? ▾
SI unit of radioactivity: 1 Bq = 1 disintegration per second. 1 Curie (Ci) = 3.7x10^10 Bq = original unit.
How does C-14 dating work? ▾
Living organisms exchange C-14 with atmosphere (maintained at ~1.2x10^-12 of C). After death, C-14 decays (t1/2=5730 y). Measure C-14/C-12 ratio to find age.
What is activity? ▾
A = lambda x N = dN/dt. Activity = decay constant x number of atoms. Units: Bq or Ci. Activity decreases as N decreases.
What is secular equilibrium? ▾
When a long-lived parent produces a shorter-lived daughter, eventually daughter activity equals parent activity. Activity of daughter grows in over several daughter half-lives.

Related Chemistry Calculators

⏱️ Chemical Half-Life⏱️ Integrated Rate Law☢️ Isotope Abundance☢️ Nuclear Equation☢️ Nuclear Symbol

Formula Explorer connections

Interpretation: This relationship connects isotopic composition, decay, radiation, mass defect or nuclear energy to a measurable quantity. Assumption: Use the correct nuclide, decay constant, branching behavior and time units. Radiation estimates also depend on geometry, shielding and detector response.

Specific Activity Calculator →Atomic Mass Calculator →Carbon-14 Dating Calculator →Chemistry Formula Explorer →