\[m=m_0e^{-\lambda t}\]
Variables
mremaining radioactive mass (kg)
m0initial radioactive mass (kg)
lambda[λ]decay constant (1/s)
ttime (s)
Description
What is this formula?
This formula calculates the remaining mass of a radioactive substance after a given time. Since the number of nuclei decreases exponentially, the total radioactive mass also follows an exponential decay law.
When to use it
Use this formula in radioactive material analysis, isotope decay calculations, nuclear waste management, and radiopharmaceutical studies.
Example
Given:
m0=0.50 kg
λ=0.001 s^-1
t=1000 s
Formula:
m=m0e^(-λt)
Substitution:
m=(0.50)e^(-(0.001)(1000))
Result:
m=0.184 kg
Applications
- Radioactive waste analysis
- Isotope studies
- Nuclear medicine
- Radiopharmaceutical calculations
- Nuclear engineering