Question

An Egyptian mummy is discovered in which the amount of Carbon-14 present is only about twenty-nine fiftieths the amount found in living human beings. a. Using the half-life of Carbon-14, determine the decay constant for Carbon-14 (answer in decimal form and scientific notation, accurate to the tenth decimal place)? b. About how long ago did the Egyptian die? c. If this is a royal tomb, which Pharaoh is in the sarcophagus? Which dynasty and regnal years are recorded for this Pharaoh? In addition to showing the calculations that lead to your solution, write a synopsis of the tactic(s) you used to arrive at your solution(s) to this series of questions. Use clear and concise sentence structure and grammar. Your answer should be labelled with appropriate units and reflect the context used in this question.

Answer 1

Answer:)

a.) We have the radioactive decay equation as :

Where the left hand side is the ratio of C14 found in the mummy as compared to a live person, and the right hand side is the amount of decay, given by the decay rate and time t.

We are given that the left hand side is 29/50. Also, since half-life of carbon is 5730 years and the half-life and decay rate are related as:

b.) Thus, we have:

c.) Let us take roughly 4500 years as the lookback time, and thus, this corresponds to a time when it was around 2482 BC. This period corresponds to the period of the Fifth Dynasty of Egypt, particularly during the reign of king Nebkhau, who reigned from 2487 - 2475 BC. The entire fifth dynasty reigned from 2494 to 2345 BC.

In order to find these answers, one must realise that the decay of C-14 follows the decay law:

Which is solved, along with the initial condition that at t = 0 (when the person dies and stops taking in new carbon to offset the decay of radioactive C-14), N(t) = N(0). Also, given this ratio, we can immediately use the relation between the decay rate and the half-life. Following this, all it takes to identify the Egyptian King is to subtract the age of the mummy, which is roughly the year of death of the king. Then, one must look into an Egyptology reference, or use the internet to cross-reference the name of the king, and to which dynasty he belonged and so on.