What is the half life, in minutes, of a sample that shows a decay from 87.12 grams of radioactive material to 21.87 grams in a time period of 19.4 minutes? (answer to two decimal places)

Question

What is the half life, in minutes, of a sample that shows a decay from 87.12 grams of radioactive material to 21.87 grams in a time period of 19.4 minutes? (answer to two decimal places)

BlackTom AI · Accepted Answer

To analyze the decay, we use the exponential decay model N(t) = N0 * (1/2)^(t / T1/2), where N0 is the initial amount, N(t) is the amount after time t, and T1/2 is the half-life.

Step 1: Determine the ratio after 19.4 minutes.
Calculate N(t)/N0 = 21.87 / 87.12 ≈ 0.2510. This means the sample has about 25.10% of its initial mass after 19.4 minutes.

Step 2: Relate the ratio to the half-life.
We have (1/2)^(t / T1/2) = 0.2510. Taking natural logs on both sides gives (t / T1/2) * ln(1/2) = ln(0.2510).

Step 3: Solve for t / T1/2.
(t / T1/2) = ln(0.2510) / ln(0.5). Since ln(0.2510) ≈ -1.383 and ln(0.5) ≈ -0.6931, the quotient is ≈ 1.994.

Step 4: Solve for the half-life T1/2.
T1/2 = t / 1.994 = 19.4 / 1.994 ≈ 9.73 minutes.

Step 5: Round appropriately.
Rounding to two decimal places yields T1/2 ≈ 9.73 minutes.

Summary: The half-life of the sample is about 9.73 minutes based on the observed decay from 87.12 g to 21.87 g in 19.4 minutes.

What is the half life, in minutes, of a sample that shows a decay from 87.12 grams of radioactive material to 21.87 grams in a time period of 19.4 minutes? (answer to two decimal places)简答题

类似问题

About half of a sample of K-40 will decay into Ar-40 in 1 billion years. Suppose we find a rock sample that has 12% K-40. Approximately how old must it be?

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?

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

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

更多留学生实用工具

智能学习助手

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