Half-life Problem?
2017-02-27 3:04 pm
An isotope of a radioactive element has half-life equal to 9 thousand years. Imagine a sample that is so old that most of its radioactive atoms have decayed, leaving just 10 percent of the initial quantity of the isotope remaining. How old is the sample? (Give your answer correct to at least one decimal place.)
回答 (1)
2017-02-27 3:16 pm
Half-life = 9000 years
No. of half-lives = n/9000
(1/2)^(n/9000) = 10%
(0.5)^(n/9000) = 0.1
log[(0.5)^(n/9000)] = log(0.1)
(n/9000) log(0.5) = log(0.1)
n/9000 = log(0.1) / log(0.5)
n = 9000 × [log(0.1) / log(0.5)]
n = 29897.4 (years)
The sample is 29897.4 years old.
No. of half-lives = n/9000
(1/2)^(n/9000) = 10%
(0.5)^(n/9000) = 0.1
log[(0.5)^(n/9000)] = log(0.1)
(n/9000) log(0.5) = log(0.1)
n/9000 = log(0.1) / log(0.5)
n = 9000 × [log(0.1) / log(0.5)]
n = 29897.4 (years)
The sample is 29897.4 years old.
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https://hk.answers.yahoo.com/question/index?qid=20170227070455AANrF8e