Question

A 200-gram sample of a radioactive nuclide is left to decay for 60 hours. At the end of 60 hours, only 25 grams of the sample is left. What is the half-life of the nuclide sample?

60 hours
30 hours
40 hours
20 hours ---> I think 20??

Answer 1

Half life is the time taken by a radioactive isotope to decay by half its original mass.
The original mass is 200 g
Time taken is 60 hours
Final mass is 25 g
Therefore;
Final mass = Original mass × (1/2)^n; where n is the number of half lives.
25 = 200 (1/2)^n
1/8 = (1/2)^n
n = 3
Three half lives = 60 hours
1 half lives = 20 hours
Therefore; the half life of the radioactive nucleus is 20 hours