Question

PLEASE HELP ME!!!!

A specific radioactive isotope is presented for our scientific evaluation for possible use of this isotope within the field of radioisotopic medical tracers. At 1 pm, there are 5.6 grams and at 7 pm, there are 3.2 grams. What's the half-life?

A) about 3.2 hrs
B) about 7.4 hrs
C) about 17.1 hrs
D) over 24 hrs

Answer 1

Answer: B) about 7.4 hrs

Explanation:

Rate law expression for first order kinetics is given by:

`t=(2.303)/(k)\log(a)/(a-x)`

where,

k = rate constant

t = time taken for decay process =6 hours

a = initial amount of the reactant = 5.6 g

a - x = amount left after decay process = 3.2 g

Putting values in above equation, we get:

`k=(2.303)/(6)\log(5.6g)/(3.2g)`

`k=0.09hours^(-1)`

To calculate the half life, we use the formula:

`k=(0.693)/(t_(1/2))`

`t_(1/2)=(0.693)/(0.09)=7.4hours`

Answer 2

Over a period of 6 hours, the substance went from 100% to about 60%, which is slightly less than one half life. One half life is therefore slightly more than 6 hours, with 7.4 hours being the most logical answer.