How much of a sample remains after five half-lives have occurred?

1/5 of the original sample

1/25 of the original sample

1/32 of the original sample

1/64 of the original sample

BOB

1/32 of the original sample

Explanation:

We have to use the formula

N/No = (1/2) ^t/t1/2

N = amount of radioactive sample left after n number of half lives

No = original amount of radioactive sample present

t = time taken for the amount of radioactive samples to reduce to N

t1/2 = half-life of the radioactive sample

We have been told that t = five half lives. This implies that t = 5 (t1/2)

N/No = (1/2) ^5 (t1/2) / t1/2

Note that the ratio of radioactive samples left after time (t) is given by N/No. Hence;

N/No = (1/2) ^5

N/No = 1/32

Hence the fraction left is 1/32 of the original sample.