Chapter 20, Problem 6STP

To determine

To Choose: The correct option.

Answer to Problem 6STP

Correct option is D.

One-eighth of the fraction of the radioactive material that will be left after 30 years.

Explanation of Solution

Give info:

Half-life of radioactive material = 10 years.

Total number of years = 30 years

Formula used:

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

Calculation:

  $\mathrm{Number}ofhalf-lives=\frac{30years}{10years}=3$

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.

Hence, after 30 years, only one-eighth of the fraction of the radioactive material that will be left.

Conclusion:

Thus, one-eighth of the fraction of the radioactive material that will be left after 30 years.