Question

Question #03416

Answer 1

11460 years.

Explanation:

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

Where, `N_0` = Original amount of radioactive nuclei present.

`N` = Nuclei present at that instant.

`n = t/(T)`

`T` = Half life of Carbon-14
Half life of C-14 is 5730 years.

`t` = Time in which the particular number of nuclei has disintegrated.

`:. N/(N_0) = (25/100)`

Which is,

`(1/2)^n = (1/4)`

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

`t/T = 2`

`t = T × 2`

`t = 5730 × 2`

`t = 11460` years

Answer 2

`11460` years old

Explanation:

At time `t=0`, we have `100%` of the radioactive `""^14"C"` isotope.

The half-life of `""^14"C"` is `5730` years. This means that at `t=5730` years, only `50%` of the original `""^14"C"` remains.

Taking half of `50%`, we see that the next half life will occur at `t=2xx5730=11460` years. At this point in time, only `25%` of the `""^14"C"` will remain.