Radioactive Decay Calculation Example
Calculating Remaining Mass of Sodium-22 After 15.6 Years
In this example, we are given a mass of 72.5 g of sodium-22 and asked to determine how much of this mass will remain after 15.6 years considering its half-life is 2.60 years.
Question:
If this decay has a half-life of 2.60 years, what mass of 72.5 g sodium-22 will remain after 15.6 years?
Answer: Remaining mass = 1.13 grams (3-sig figs) Explanation: All radioactive decay follows 1st order kinetics and is defined by the expression A = A₀e^⁻kt. Here, A represents the final mass activity, A₀ is the initial mass activity, k is the rate constant, t is the time of decay, and e is the base of the natural logarithm.- A = final mass activity
- A₀ = initial mass activity
- k = rate constant = 0.693/t(half-life) = 0.693/2.60 yrs = 0.2665 yrs⁻¹
- t = time of decay = 15.6 yrs
- A = (72.5 g)(e^[-(0.2665 yrs⁻¹)(15.6yrs)] = 72.5 grams x 0.0156
- = 1.13381331 grams (calculated answer) ≅ 1.13 grams (3 sig figs)