Question

Radiocarbon Dating. A sample from timbers at an archeological site containing 830 g of carbon provides 2010 decays/min. The initial concenration of radioactive carbon-14 is 1 part in 1.0×1012. The half-life of carbon-14 is 5730 year. What is the age of the sample?

Answer 1

Activity is given by,

A = A0*e^(-*t)

here,

A0 = initial activity = activity of atmospheric carbon = 255 Bq/kg

A = activity of sample = 2010 decays/min = 2010/(60*0.500)

A = 67 Bq/kg

t = age of sample = ??

= ln(2)/t_1/2

given,

t_1/2 = half-life of carbon = 5730 years

then, = ln(2)/(5730) = 1.21*10-4 y^-1

So,

67 = 255*e^(-1.21*10^-4*t)

-1.21*10^-4*t = ln(67/255)

t = ln(255/67)/(1.21*10^-4)

t = 11046 years

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