Science Calculator Radioactive Decay With Steps

Radioactive Decay Calculator with Steps

Use this radioactive decay calculator to calculate remaining amount, initial amount, elapsed time, decay constant, or half-life. This tool is useful for nuclear chemistry, radioactivity, carbon dating, medicine decay, and exponential decay problems.

Calculate Radioactive Decay

Result:
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What is Radioactive Decay?

Radioactive decay is the process where unstable atomic nuclei lose energy by emitting radiation. Over time, the amount of radioactive material decreases exponentially.

N = N₀e-λt
λ = ln(2) ÷ T½
T½ = ln(2) ÷ λ
  • N = remaining amount
  • N₀ = initial amount
  • λ = decay constant
  • t = elapsed time
  • T½ = half-life

Worked Example

A radioactive sample starts with 100 g. Its decay constant is 0.2 per year. How much remains after 5 years?

N = N₀e-λt
N = 100e-(0.2)(5)
N = 36.79 g

The remaining amount is approximately 36.79 g.

Practice Question

A radioactive sample starts with 80 g. Its decay constant is 0.1 per year. How much remains after 10 years?