Question

In a clinical study, a patient intakes 10.0 μg of Iodine-131. After 5 days, it is found that the concentration of I-131 in the patient’s thyroid has declined to 6.50 μg.

What is the half-life of I-131?

	A.	5 days
	B.	8 days
	C.	7.2 days
	D.	0.086 days

Answer 1

i) Determine the rate constant

Decay of an isotope is first order reaction ,for first order reaction following is the integrated rate law

ln[A]_t = -kt + ln[A]₀

where,

[A]_t= amount at time t, 6.50g

[A]₀= initial amount , 10.0 g

k = rate constant,?

After rearranging the equation

2.303log([A]₀/[A]_t) = kt

substituting the values

2.303log(10.0g/6.50g)= k× 5days

0.4309= k × 5days

k = 0.0862day^-1

^{ii) Determination of half life}

  For first order reaction, half life(t_1/2) is calculated as follows

t_1/2 = 0.693/k

t_1/2= 0.693/0.0862day^-1

t_1/2 = 8 days

Therefore,

The answer is B