Chapter 20.3, Problem 18R

To determine

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:

  $\mathrm{Number}ofhalf-lives=\frac{totaldays}{half-lifeofmaterial}$

Calculation:

Substitute the values and solve:

  $\mathrm{Number}ofhalf-lives=\frac{32}{8}=4$

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.