Question

Iodine-131 is a beta emitter used as a tracer in radio immunoassays in biological systems. It follows first order kinetics. The half-life if iodine-131 is 8.04 days. If you start with 8.0 grams of iodine-131, how many grams would remain at 39 days

Answer 1

Answer: The amount of Iodine-131 remain after 39 days is 0.278 grams

Explanation:

The equation used to calculate rate constant from given half life for first order kinetics:

$t_{1/2}=\frac{0.693}{k}$

where,

$t_{1/2}$ = half life of the reaction = 8.04 days

Putting values in above equation, we get:

$k=\frac{0.693}{8.04days}=0.0862days^{-1}$

Rate law expression for first order kinetics is given by the equation:

$k=\frac{2.303}{t}\log\frac{[A_o]}{[A]}$

where,

k = rate constant = $0.0862days^{-1}$

t = time taken for decay process = 39 days

$[A_o]$ = initial amount of the sample = 8.0 grams

[A] = amount left after decay process = ?

Putting values in above equation, we get:

$0.0862=\frac{2.303}{39}\log\frac{8.0}{[A]}$

$[A]=0.278g$

Hence, the amount of Iodine-131 remain after 39 days is 0.278 grams