Physicians use 18^F to study the brain by injecting a quantity of fluoro-substit
ID: 530996 • Letter: P
Question
Physicians use 18^F to study the brain by injecting a quantity of fluoro-substituted glucose into the blood of a patient. The glucose accumulates in the regions where the brain is active and needs nourishment. The decay of Flourine-18 can be described by the following reaction: 18_F^9 --> 18_O^8 + e^- t_1/2 = 109.7 min
Approximately how long does it take for 75.0% of the 18^F to decompose? The answer is 220 minutes but I don't know how to get that answer no matter how much I try. Please show step-by-step solutions. Thanks!
Explanation / Answer
HL = 109.7 min
find time for
75% of 18F to decompose
that is, 25% will be left
A = A0*(1/2)^(t/HL)
A = 25%
A0 = 100%
t = time required, HL = half life
0.25 = 1*(1/2)^(t/109.7)
t = 109.7*ln(0.25)/ln(0.5)
t = 219.4 minutes
nearest answer shown is 220 minutes