Radioactive Decay Calculator

About Radioactive Decay Calculator

Radioactive decay follows N = N₀(½)^(t/t½). Carbon-14 has t½ ≈ 5730 years, used in radiocarbon dating.

How to use this calculator

1. Enter the starting amount as \(N_0\).
2. Enter the elapsed time as \(t\).
3. Enter the half-life as \(t_{1/2}\).
4. Read the remaining amount \(N\) from the result.

The formula explained

The formula \(N = N_0 \left(\frac{1}{2}\right)^{t/t_{1/2}}\) computes how much radioactive material is left after time \(t\). Each half-life cuts the amount in half, so the exponent tells how many half-life periods have passed.

• \(N\) = remaining amount after time \(t\)
• \(N_0\) = starting amount
• \(t\) = elapsed time
• \(t_{1/2}\) = half-life, the time it takes for the amount to drop to half

Step by step method

1. Start with the initial amount \(N_0\).
2. Find how many half-lives have passed by calculating \(t/t_{1/2}\).
3. Raise \(\frac{1}{2}\) to that power, then multiply by \(N_0\).

Worked example

Problem. A sample starts with \(80\) grams and has a half-life of \(6\) hours. How much remains after \(18\) hours?

1. Compute the number of half-lives, \(18/6 = 3\).
2. Use the formula, \(N = 80 \left(\frac{1}{2}\right)^3\).
3. Simplify, \(N = 80 \cdot \frac{1}{8} = 10\).

Tips and common mistakes

• Make sure \(t\) and \(t_{1/2}\) use the same units, such as hours or years.
• A half-life does not mean the amount reaches zero, it keeps getting smaller by halves.

Frequently asked questions