A radioactive sample has a half-life of 10 min. What fraction of the sample is left after 40 min?

Question

A radioactive sample has a half-life of 10 min.  What fraction of the sample is left after 40 min?

BlackTom AI · Accepted Answer

To solve this, we use the concept of half-life: after each half-life period the amount remaining is halved. Since the half-life is 10 minutes, 40 minutes corresponds to four half-lives (40 / 10 = 4).
Option 1: 1/16. This matches (1/2)^4 = 1/16, so this is consistent with the half-life decay model.
Option 2: 1/8. If the sample were reduced to 1/8, that would imply three half-lives have passed (since (1/2)^3 = 1/8). Four half-lives are required to reach 1/16, so this is not correct for 40 minutes.
Option 3: 1/4. This would correspond to two half-lives (40 minutes would be 4 half-lives, not 2). Therefore this undervalues the decay.
Option 4: 1/32. This would be five half-lives (since (1/2)^5 = 1/32). That would require 50 minutes, not 40, so it overestimates the decay.
Option 5: 1/2. This would mean zero half-lives have occurred, i.e., no decay, which is incorrect for 40 minutes at a 10-minute half-life.
In summary, the decay pattern for four half-lives yields 1/16, while the other fractions correspond to fewer or more half-lives than the 40-minute interval specifies.

PHYSICS 1201 SU2025 (10585) Final Exam- Requires Respondus LockDown Browser

A radioactive sample has a half-life of 10 min. What fraction of the sample is left after 40 min?

查看解析

登录即可查看完整答案

类似问题

Which of the following statements is/are true regarding and radioactive isotope's half-life? (there are three correct answers)

A radioactive isotope has a half-life of 10 years. If you start with a 200-gram sample, how much of the substance will remain after 30 years?

If you start with 16 atoms of a parent radioisotope, after how many half-lives will only 2 atoms of the parent remain, on average?

What percentage of a radioactive isotope would remain after three half-lives?

If you have 200.0 g of radioisotope with a half-life of 5 days, how much isotope would remain after 15 days?

What happens to the half-life of a radioactive substance as it decays?

The half-life of radon-222 is 2.8 days. A homeowner used a radon test-kit to sample the air in his home, but forgot to send it for processing for 30 days. If the level of radon was actually 100 counts, what value would be reported by the test lab?

If pure polonium-210 (k = 5.02 × 10−3 day−1) were used in a crime, based on radioactive disintegration alone, how long would it take for half the original isotope to disappear?

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单