Question

Carbon-14 is a radioactive isotope. It is found in the air in carbon dioxide molecules. The amount of carbon-14 in the air has stayed the same for thousands of years. There is a small amount of radioactive carbon-14 in all living organisms because it enters the food chain.
Once an organism dies, it stops taking in carbon-14. The carbon-14 it contained at the time of death decays over a long period of time, and the radioactivity of the material decreases.



The approximate time since the organism died can be worked out by measuring the amount of carbon-14 left in its remains compared to the amount in living organisms.


In 1991, two hikers discovered a mummified man, preserved for centuries in the ice on an alpine mountain. Small samples from his body were carbon dated by scientists and found to contain 50% carbon-14 remaining. Based on this finding, how old are the remains of the body estimated to be?



A.
About 5,700 years

B.
About 11,400 years

C.
About 22,800 years

D.
Over 30,000 years

Answer 1

Answer: A. About 5,700 years

Explanation:

Expression for rate law for first order kinetics is given by

$t=\frac{2.303}{k}\log\frac{a}{a-x}$

where,

k = rate or decay constant  

t = age of sample

a = let initial amount of the reactant  

a - x = amount left after decay process  

Half life is the amount of time taken by a radioactive material to decay to half of its original value.

Thus the time taken to carbon-14 to reduce to 50% is called as half life.

From the graph, it comes out to be 5750 years which is close to 5700 years