Question

# The iodine isotope 131 53 I (half-life = 8 days, atomic mass = 131 u) is...

The iodine isotope 131 53 I (half-life = 8 days, atomic mass = 131 u) is used in hospitals for diagnosis of thyroid function. (1 u = 1.66 x 10-27 kg). If 682 μg (1 μg = 10-6 g) are ingested by a patient, determine the activity

(a) Immediately

(b) One hour later, when the thyroid is being tested

(c) Six months later (assume the iodine is still in the patient’s body)

number of Iodine nuclie present initially,

No = mass of the sample/mass of one nuclie

= 682*10^-9/(131*1.66*10^-27)

= 3.136*10^18

given
half life time, T1/2 = 8 days

= 8*24*60*60

= 691200 s

decay constant, lamda = 0.693/(T1/2)

= 0.693/691200

= 1.0016*10^-6 s^-1

a) Immediately,

initial activity, Ao = No*lamda

= 3.136*10^18*1.0016*10^-6

= 3.14*10^12 decay/s <<<<<<<---------Answer

b) one hour later,

t = 60*60 s

A = Ao*e^(-lamda*t)

= 3.12*10^12*e^(-1.0016*10^-6*60*60)

= 3.11*10^12 decay/s <<<<<<-----------Answer

c) six months later,

t = 6*30*24*60*60 s

A = Ao*e^(-lamda*t)

= 3.12*10^12*e^(-1.0016*10^-6*6*30*24*60*60)

= 5.36*10^5 decay/s <<<<<<-----------Answer

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