The half-life of C-14 is 5470 years. If a particular archaeological sample has one-quarter of its original radioactivity remaining, what is the best estimate for its age?

When there remains one-quarter of the sample, the age of the sample is 10940 years

Explanation:

Step 1: Data given

The half-life of C-14 is 5470 years.

The half - life time is the time required for a quantity to reduce to half of its initial value.

This means after 5470 years there remains half of the C-14 sample.

To remain a quarter of the sample, another cycle of 5470 years is required.

This means 2 half-lives should have passed to remain a quarter of the sample.

Step 2: Calculate it's age

t / (t/1/2) = 2

⇒ with t = the age (or time) of the sample

⇒ with t (1/2) = the half-life time of the sample = 5470 years

⇒ with 2 = the number of halvf - lives passed

t/5470 = 2

t = 2*5470 = 10940 years

When there remains one-quarter of the sample, the age of the sample is 10940 years