Fluorine-18, which has a half-life of 110 min, is used in PET scans. A.) If 180.
ID: 976728 • Letter: F
Question
Fluorine-18, which has a half-life of 110 min, is used in PET scans.
A.) If 180. mg of fluorine-18 is shipped at 7:00 A.M., how many milligrams of the radioisotope are still active after 110 min ? Express the mass to three significant figures and include the appropriate units.
B.) If 130. mg of fluorine-18 is shipped at 7:00 A.M., how many milligrams of the radioisotope are still active when the sample arrives at the radiology laboratory at 4:10 P.M.? Express the mass to three significant figures and include the appropriate units.
Explanation / Answer
A)
Given that half-life of 110 min
So after 110 min 180 mg/2 = 90 mg
Thus 90 mg radioisotope are still active after 110 min.
b)
Fluorine-18 has a half-life of 110 min therefore rate of reaction is given as
k = 0.693 / t1/2 = 0.693 / 110 min = 6.3 x 10^-3 /min
and
[F0] = 130 mg and t = ( 9 and 10 min ) = 550 min
using the following equation we get
k = 2.303 / t * ln [F0] / [Ft]
ln 130 mg / [Ft] = 6.3 x 10^-3 /min *550 min /2.303
ln 130 mg / [Ft] =1.505
130/ [Ft] = 4.504
[Ft] = 28.9 mg