Concept explainers
Amount of the radioactive material that will be left in a 5.0 g sample after 32 days which have half-life of 8 days.
Answer to Problem 18R
Only 0.3125 g of material remained in a 5.0 g sample after 32 days which have half-life of 8 days.
Explanation of Solution
Give info:
Half-life of radioactive material =8 days
Total number of days = 32 days
Formula used:
Calculation:
Substitute the values and solve:
Now,
Half-life is the amount of time it takes for half the lives in a sample of an isotope to decay.
After each half-life, the number of remaining undecayed nuclei decrease rapidly.
- After one half-life the number of remaining undecayed nuclei reduced to half.
- And after two half-lives the number of remaining undecayed nuclei reduced to one-fourth.
- And after 3 half-lives the number of remaining undecayed nuclei reduced to one-eighth.
- And after 4 half-lives the number of remaining undecayed nuclei reduced to one-sixteenth.
Hence, after 32 days, only one- sixteenth of the 5 g of the radioactive material will be left that means only 0.3125 g of material remained.
Conclusion:
Thus,0.3125 g of material remained in a 5.0 g sample after 32 days which have half-life of 8 days.
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