# What is the half-life of a radioisotope if 25.0 grams of an original 200.-gram sample of the isotope remains unchanged after 11.46 days? (1) 2.87 d (3) 11.46 d (2) 3.82 d (4) 34.38 d

Chemistry · High School · Tue Nov 03 2020

llm

Answered on

Given :

K = rate constant

time taken for decay process, t = 11.46 days

Initial amount of the reactant, a = 200 grams

Amount of reactant after decay process, a - x = 25 grams

Formula :

K = 2.304/t log(a/a-x)

K = 2.303/11.46 log(200/25)

K = 0.1814

Now, half life of radioisotope

t½ = 0.693/K

= 0.693/0.1814

= 3.820

Hence, half life of radioisotope is 3.820 days.