We have, decay constant ( ) = 0.693 / t 1/2
Where, t 1/2 is a half-life radioactive element.
Decay constant of I - 131 = = 0.693 / t 1/2 = (0.693 / 7.6 days ) = 0.09118 days-1
We have equation: t =2.303 / log (N 0 / N t)
Where, is a decay constant
N 0 is the initial amount of radioactive element,
N t is the amount of radioactive element after time t.
In this example, N 0 = [I - 131] 0 = 10.0 mCi
N t = [I - 131] t =?
t =38 days
Hence, 38 days = 2.303 / 0.09118 days-1 log 10.0 mCi / [I - 131] t
log 10.0 mCi / [I - 131] t = 38 days x 0.09118 days-1 / 2.303 = 1.5045
log 10.0 - log [I - 131] t = 1.5045
1.0 - log [I - 131] t = 1.5045
log [I - 131] t =1.0 -1.5045 =- 0.5045
[I - 131] t =10 - 0.5045 = 0.3130 mCi
ANSWER: Radiation remained in patient body after 38 days is 0.3130 mCi
PART 2
We have, decay constant ( ) = 0.693 / t 1/2
Where, t 1/2 is a half-life radioactive element.
Decay constant of P -32 = = 0.693 / t 1/2 = (0.693 / 14.1 days ) x ( 1 day / 24 hour ) = 2.048 x 10 -03 hr-1
We have equation: t =2.303 / log (N 0 / N t)
Where, is a decay constant
N 0 is the initial amount of radioactive element,
N t is the amount of radioactive element after time t.
In this example, N 0 = [P-32] 0 =6.0 mCi
N t = [P-32] t =?
t =169.2 hr
Hence, 169.2 hr = 2.303 / 2.048 x 10 -03 hr-1 log 6.0 mCi / [P-32] t
log 6.0 mCi / [P-32] t =169.2 hr x 2.048 x 10 -03 hr-1 / 2.303 = 0.1504
log 6.0 - log [P-32] t = 0.1504
0.7782 - log [P-32] t = 0.1504
log [P-32] t = 0.7782 - 0.1504 = 0.6278
[P-32] t = 10 0.6278 = 4.244 mCi
ANSWER: Radiation remained in patient body after 169.2 hrs is 4.244 mCi
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