1.The remains of an old camp?re are unearthed and it is found that there is only
ID: 795886 • Letter: 1
Question
1.The remains of an old camp?re are unearthed and it is found that there is only 80% as much radioactive carbon-14 in the charcoal samples from the camp?re as there is in modern living trees. If the half-life of carbon- 14 is 5730 years, how long ago did the camp?re burn?
2. A bacteria population grows exponentially with growth rate k=2.5 how long it would take for the bacteria population to double its size?
3. The half-life of a certain drug in the human body is 8 hours how long it would take for a dose of this drug to decay to 0.1% of its initial level?
Explanation / Answer
1)t1/2 = 0.693/K1
5730 = 0.693/K1
K1 = 0.693/5730 = 1.21*10^-4 year^-1
but we know
K1 = 2.303/t log(a/a-x)
1.21*10^-4 =2.303/t log(100/80)
t = 1.71*10^4 years ago the tree had burnt
2)K1 = 2.303/t log(a/a-x)
2.5 = 2.303/t log(1/2)
t = 0.27 sec
3)t1/2 = 0.693/K1
8 = 0.693/K1
K1 = 0.0866 hour^-1
K1 = 2.303/t log(a/a-x)
0.0866 = 2.303/t log(100/0.1)
t = 79.78 hours
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