Question

Phosphorus-32, a radioisotope used in leukemia therapy, has a half-life of 14.26 days. How long will it take for a sample of 32P to decay to 18.3% of its original activity? O 3.5 days 4.2 days 15 days 35 days O 17.5 days

Answer 1

as radioactivity follow first order kinetics

given half life =14.26days

as we know for first order reaction

half life =0.693/K

then K =rate constant =0.693/half life =0.693/14.26

as K for first order is

K =(1/t)* ln(A°/A). ...... (1)

lets original activity =A° =100

then A =100-18.3 =81.7

now put in (1)

K =(1/t) ln(100/81.7) =0.693/14.26

from here t =(14.26/0.693)*ln(100/81.7) =4.2 days

thus second option is correct.

based on calculation, other options are incorrect.