Question

Radiocarbon or 14C is a widely used tracer for groundwater movement for up to 30,000 years. 14C can be used to estimate recharge rates and horizontal flow rates important for water related policy decisions. 14C has a half-life of 5730 years and the ratio of 14C to all C from biological material is 1.3 × 10⁻¹². The atomic mass of carbon is 12.0107 g/mol. Your sample is 0.29 g of carbon. The activity of this sample, due to presence of radioactive 14C, is 0.043 Bq.

a) Convert the half-life of 14C from years to seconds and show each step of the unit conversion.

b) Determine the number of 14C nuclei present in this sample at the time it entered the ground. Hint: Avogadro’s number is 6.022 × 10²³ atoms/mol.

c) Calculate the radioactivity expected from this sample at the time it entered the ground.

d) Assuming that this organic carbon entered the groundwater just after it formed, how old is carbon in your sample?

Answer 1

(a) Nooq Number 23 -12 Decay constant, &z 0.693 T1/2 -12 Half life, y = 5730 year Half life in recovers = 5730 seconds in ayear - Half life in sunds 5730x( 365 x 24 x 60X60) seconds. -) T₂ (re) 1.807 x 10 seconds. (6) Nuclei, No = 0.29 x 6.022x10 4 1.3x10 0 (140) 1.3x1012 12.0107 1.890 23x 10° unelei Initial AchenlyNo 0-693 3.83509x10 1.807810 free .. Initial Activity, A.z 3.83509x10**1-89023X10°= 0.072492 / sve =) Acturity, A z 0.072492 Bq Present Actiurly, Az Ao ett Ext) 0.043 = 0.072492x e Ext) 0.872492 1:20942x107t 0.593169 е An(0.593169)in( 1:20942x1044) - 0.52227593 - -1-20942x10tt ta -0.52227543 - 1.20942 x 104 =) Age of sample is 4318.40 years. 0.643 573 0.043 ..693 5730 = 4318.40 years