Dates of these events have proposed that the plagues coincided with a huge erupt

Question

Dates of these events have proposed that the plagues coincided with a huge eruption of the volcano Thera in the Aegean Sea. Radiocarbon dating suggests that the eruption occurred 1360 BC, though other records place the eruption of There in the year 1628 BC. What is the percent difference in the^14C (t_v2 = 5730 yr) decay rate in biological samples from these two dates? Assuming that the year is 2007, what is the^14C/^12C ratio for the grain harvested in 2007? Radiocarbon dating of blackened grains from the site of ancient Jericho provides a date of 1315 BC plusminus 13 years for the fall of the city. What is the^14C/^12C ratio in the blackened grains compared with that of the grain harvested in 2007? Calculate the percent decrease in^14C/^12C ratio comparing grain from 1315 BC to 2007 AD. |^14C/^12C|_2097 AD = |^14C/^12C|_1315 BC = % decrease =

Explanation / Answer

(a.) Time Difference between the two evidences = 268years.

Since the half life is given as 5730 yrs, we can say that: ln(1/2) = -k*(5730) . Then , k = 1.2096 x 10^(-4).

Now, let No be the number of C14 atoms inititially , and Nt be the number of C14 left at time t(years), then by using:

ln(Nt/No) = -kt, and thus, Nt = No*exp(-kt)

and the rate equation r = k[Nt],

we get the relation for comparing the two durations as:

rt / rt+268 = exp{k(268-0)} = 0.0324 or 3.24%

(b.) At any particular time all living organisms have approximately the same ratio of carbon 12 to carbon 14 in their tissues. Thus, initial C12/C14=1 (at t=0,or 2007 AD).

Considering the blackened grains; after 1315+2007 = 3322 years, we can suppose x% of c14 getting decayed to c12. Then the new ratio will be C14/c12 = (1-x/1+x).

Now, in 3322 years, the fraction of C14 decayed can be calculated using the relations in part (a.):

ln(Nt/No) = -kt,

then, Nt/No = exp(-kt) = 0.6691, and The fraction of C14 decayed(x) will be 1- Nt/No = 0.3309 = x

Then, 1-x/1+x = 0.669/1.6691 = 0.4008 = C14/C12 for blackened grains obtained from 1315B.C.

Then , percent decrease = 1- 0.4008 / 1 = 0.5992 or ~ 60% .

** The answer corresponds to my perception of the question. Please let me know in the comments if an alternative perception gives a different answer, or if my answer is incorrect.

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.