Fluorine-18 is a radioactive isotope of fluorine that is used in medical imaging scans. It has a
half-life of approximately 110 minutes. If a patient has a medical imaging scan using an
injection of fluorine-18 at 9 am, at what time will there be less than 25% of the radioactive
isotope in her body?
a) 10 am
b) 12 pm
c) 1 pm
Answers
Given info : Fluorine-18 is a radioactive isotope of fluorine that is used in medical imaging scans. It has a half-life of approximately 110 minutes. If a patient has a medical imaging scan using an
injection of fluorine-18 at 9 am
To find : at what time will there be less than 25% of the radioactive isotope in her body ?
solution : half life of radioactive decay, T½ = ln2/λ
⇒λ = ln2/110 min¯¹
now initial amount = N₀
final remaining amount, N = 0.25N₀
using formula, t = 1/λ ln[N₀/N]
= 1/(ln2/110) × ln(1/0.25)
= 110/ln2 × ln4
= 220 minutes
= 3 hrs 40 minutes
so, definitely time taken to remain less than 25 % is more than 3 hrs 40 minutes.
only option (4) is satisfied above statement so option (4) is correct choice
half life of radioactive decay, T½ = ln2/λ
⇒λ = ln2/110 min¯¹
now initial amount = N₀
final remaining amount, N = 0.25N₀
using formula, t = 1/λ ln[N₀/N]
= 1/(ln2/110) × ln(1/0.25)
= 110/ln2 × ln4
= 220 minutes
= 3 hrs 40 minutes
so, definitely time taken to remain less than 25 % is more than 3 hrs 40 minutes.
only option (4) is satisfied above statement so option (4) is correct choice