Question

Question #406c5

Answer 1

The half-life of the isotope is 2.5 min.

The number of half-lives `n = t/t_½`

For each half-life, you divide the total amount of the isotope by 2.

Amount remaining = original amount × `1/2^n` or

`A = A_0/2^n`

`A_0/A = 2^n`

`ln(A_0/A) = nln2`

`n = (ln(A_0/A))/ln2`

`n = (ln((100" mg")/(1.50" mg")))/ln2 = ln66.7/ln2 = 4.20/0.693` = 6.06

So 15 min = 6.06 half-lives

1 half-life = `(15 min)/6.06` = 2.5 min