Nuclear Decay Calculator
Exponential decay of radioactive nuclei.
Formula first
Overview
The nuclear decay equation models the statistical decrease of radioactive nuclei within a sample over time. It demonstrates that the rate of decay is proportional to the number of nuclei present, resulting in a predictable exponential decay curve.
Symbols
Variables
N = Remaining Nuclei, N_0 = Initial Nuclei, \lambda = Decay Constant, t = Time
Apply it well
When To Use
When to use: Apply this equation when calculating the remaining mass or activity of a radioactive isotope after a specific duration. It assumes a sufficiently large sample size where the constant probability of decay (L) remains uniform across all atoms.
Why it matters: This formula is essential for carbon-14 dating to determine the age of organic artifacts and for nuclear medicine to calculate precise patient dosages. It also informs safety protocols for the storage and management of hazardous nuclear waste products.
Avoid these traps
Common Mistakes
- Using base⁻10 logs instead of natural logs.
- Mixing half-life and decay constant directly.
One free problem
Practice Problem
A laboratory sample initially contains 1000 radioactive nuclei. If the isotope has a decay constant of 0.05 s⁻¹, how many nuclei will remain after 10 seconds?
Solve for:
Hint: Calculate the exponent by multiplying the decay constant and time, then use the eˣ function.
The full worked solution stays in the interactive walkthrough.
References
Sources
- Halliday, Resnick, Walker - Fundamentals of Physics
- Wikipedia: Radioactive decay
- IUPAC Gold Book: Decay constant
- Halliday, Resnick, Walker, Fundamentals of Physics
- AQA A-Level Physics — Nuclear Physics