Question

Question #5d643

Answer 1

4052 years old.

Explanation:

`2^.5` = 1.414

25% is half of half life. so 2 to the .5 of a half life.

So the amount of the carbon left. is `1/1,414 xx 5730` = 4052 years.

Answer 2

The sample is 2380 years old.

Explanation:

We can express the rate law for a first-order decay as

`N_t/N_0 = (1/2)^n`

where

`N_t` is the amount remaining after time `t`.
`N_0` is the amount present at the start (`t = 0`).
`n` is the number of half-lives (`t_½`)

We can rewrite this as

`N_0/N_t = 2^n`

If the concentration of carbon-14 has decreased by 25 %, then 75 % remains.

`100/75 = 2^n`

`ln(100/75) = nln2`

`n = 0.2877/ln2 = 0.4150`

The sample has decayed for 0.4150 half-lives.

`0.4150t_½ = "0.4150 × 5730 yr" = "2380 yr"`