Carbon-14 is a radioisotope that is used for dating biological organisms. The ha

Question

Carbon-14 is a radioisotope that is used for dating biological organisms. The half-life of C-14 is 5730 years. When a one-gram sample of carbon from fresh peat is measured for radioactivity, 900 beta decays are recorded every hour A one-gram sample of carbon is obtained from a peat deposit and is measured for radioactivity. If 450 beta decays are observed every hour, how many half-lives of C-14 have passed since the deposit was formed? ? 450 O 1/2 Approximately how old is the peat deposit? O 11460 years O 5280 years O 2865 years O 5730 years Another one-gram sample is obtained from a different peat deposit at a different site. If 28 beta decays are measured every hour, about how old is this sample? O 160440 years O 28650 years O 5702 years O 183360 years

Explanation / Answer

a) 1
we know, activity is proportional to number of radiactive nuclei present in the sample.

when t = T1/2 number of nuclei becomes half.

so, A = Ao/2 (450 = 900/2)

b) 5730 years

because, Activity has become half.

it happens, t = T1/2

= 5730 years

c) 28650 years

decay constant, lamda = 0.693/(T1/2)

= 0.693/5730

= 1.209*10^-4 year^-1

let time t,

A = Ao*e^(-lamda*t)

A/Ao = e^(-lamda*t)

ln(A/Ao) = -lamda*t

t = -ln(A/Ao)/lamda

= -ln(28/900)/(1.209*10^-4)

= 28702 yesrs

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