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

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

93.2 ml + 3920 ml = 4013 ml total  

(93.2 ml) * (2.03 m) / (4013 ml) = 0.0471 m

the volume in in l of the diluted solution would be 0.0471 m.