Question

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?
5470 years

10940 years

16410 years

21880 years

Answer 1

Answer:

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

Explanation:

Step 1: Data given

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

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

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

When there will pass another half-life cyclus, half of the sample will remain.

Half of 50 % = 25% = one- quarter

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 half- lives passed  to remain one quarter of sample

t/5470 = 2

t = 2*5470 = 10940 years

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

Answer 2

10940? Sorry if it isn’t correct