Q1 How much time is required for a 6.55mg sample of 51Cr to decay to 0.600mg if
ID: 869234 • Letter: Q
Question
Q1
How much time is required for a 6.55mg sample of 51Cr to decay to 0.600mg if it has a half-life of 27.8 days? Express the time in days to one decimal place.
Q2
The cloth shroud from around a mummy is found to have a 14C activity of 9.4 disintegrations per minute per gram of carbon as compared with living organisms that undergo 16.3 disintegrations per minute per gram of carbon.
From the half-life for 14C decay, 5715 yr, calculate the age of the shroud.
Express your answer using two significant figures.
Explanation / Answer
Q1)Radioactive decay follows first order rate law.
the rate expression is k = 2.303/k .log (a/a-x)
substituting k = 0.693/27.8 and a= 6.55 and a-x = 0.600
we get time= 2.303 x27.8/ 0.693 log (6.55/0.6) = 95.88 years
Q2) Since activity is proportional to concentration of species,
time = 2.303/k log (initial acitivity/activity now)
substituting k = 0.693/5715 and A1= 16.3 and A2 = 9.4
we have time = 2.303x5715/0.693 log 16.3/9.4 = 4539.1 Yrs.
= 4.5 x103yrs as two significant figures
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