Answer:
The fraction remaining of a sample that is 5 half lives old is 0.03125.
Step-by-step explanation:
- It is known that the decay of a radioactive isotope isotope obeys first order kinetics.
- Half-life time is the time needed for the reactants to be in its half concentration.
- If reactant has initial concentration [A₀], after half-life time its concentration will be ([A₀]/2).
- Also, it is clear that in first order decay the half-life time is independent of the initial concentration.
- Suppose the initial concentration of the sample is 1:
So, it will decay as:
1.0 → (first half life) 0.5 → (second half-life) 0.25 → (third half-life) 0.125 → (fourth half-life) 0.0625 → (fifth half-life) 0.03125.
So, the rraction remaining of a sample that is 5 half lives old is 0.03125.