Dinosaur fossils are too old to be reliably dated using carbon-14, which has a half-life of about 5730 years. Suppose we had a 68 million year old dinosaur fossil. How much of the living dinosaur's 14C would be remaining today? (Round your answer to five decimal places.)

0.00000

Explanation:

The half-life of a radioisotope, in this case carbon-14, is the time that a sample requires to reduce its amount to half, and it is a constant for every radioisotope (it does not change with the amount of sample).

Then, the formula for the remaining amount of a radioisotope is:

A / A₀ = (1/2) ⁿ

Where:

A is the final amount of the element, A₀ is the initial amount of the element, A/A₀ is ratio of remaining amount to the original amount, and n is the number of half-lives elapsed

The number of half-lives for carbon-14 elapsed for the dinosaur fossil is:

n = 68 million years / 5730 years ≈ 11,867

Then, A / A₀ = (1/2) ⁿ = (1/2) ¹¹⁸⁶⁷ ≈ 0.00000.

The number is too small, and when you round to five decimal places the result is zero. That is why carbon-14 cannot be used to date dinosaur fossils, given that they are too old.