# Chem alevel decay equation help!!!

3. The half-life of the radioactive isotope oxygen-15 is 2 minutes.
(b) If a quantity of 15O decays by positron emission, determine what fraction of 15O is left after 10 minutes.

Need help with this question !! Markscheme says 1/32 but idk how to get to that point
Original post by shesmycollar
3. The half-life of the radioactive isotope oxygen-15 is 2 minutes.
(b) If a quantity of 15O decays by positron emission, determine what fraction of 15O is left after 10 minutes.

Need help with this question !! Markscheme says 1/32 but idk how to get to that point

Fraction left = (1/2)^(number of half-lives)

If 1 half life is 2 mins, what is 10 mins in half lives?

Hence, what is the fraction?
(edited 1 year ago)
half life is the time taken for half the nuclei in the radioactive sample to decay
so in your question, after 2 mins, half of the 15O nuclei will have decayed, and half ("x") will not have decayed
after another 2 mins (4 mins from the start), half of "x" will have decayed, i.e. you are left with 1/4 of the original sample

effectively you are multiplying the original number by 0.5 for 1 half life; then by 0.5 again for the next half life... so size of sample after n half lives = (size of original sample) x (0.5 x 0.5 x ... n times)
which is the same as (size of original sample) x (0.5 ^n)

how many half lives are in 10 minutes?
(edited 1 year ago)