Question

The decay of radioactive elements occurs at a fixed rate. The half-life of a radioisotope is the time required for one half of the amount of unstable material to degrade into a more stable material. The half-life of Carbon-14 is 5,730 years. Choose ALL the true statements regarding the Carbon-14 isotope. A) 100 grams of C-14 decays to 25 grams in 11,460 years. B) The C-14 isotope is only useful for dating fossils up to about 50,000 years old. C) A sample contained 3,360 atoms of C-14. 8 half-lives passed and 210 C-14 atoms remained. D) If an ancient bone contains 6.25% of its original carbon, then the bone must be 22,920 years old. E) A sample of 4,000 radioactive C-14 atoms undergoes decay. After 5 half-lives there are 800 radioactive atoms remaining.

Answer 1

100 grams of C-14 decays to 25 grams in 11,460 years.

The C-14 isotope is only useful for dating fossils up to about 50,000 years old

If an ancient bone contains 6.25% of its original carbon, then the bone must be 22,920 years old.

Step-by-step explanation:

We already know that the half life of C-14 is 5,730 years. After the first half life, we have 50 grams remaining. This takes 5,730 years. After the second half life (11,460 years now gone) we have 25 grams of C-14 left.

If a fossil material is older than 50,000 years an undetectable amount of 14C is left in the sample hence Carbon-14 is no longer suitable for dating the sample.

From;

0.693/5730 = 2.303/t log (No/0.0625No)

Where;

t = time taken and No = initial amount of C-14

0.693/5730= 2.77/t

t = 22,920 years