One isotope of holmium, 162Ho, has a half life of 22 minutes. The half-life of a second isotope, 164Ho, is 37 minutes. Starting with a sample containing equal amounts, find the ratio of the amounts of 162Ho to 164Ho after one hour. Rounded to three decimal

Answer 1

after t minutes, the two isotopes have remaining amounts of

2^(-t/22) and 2^(-t/37)

So, after one hour (60 minutes), the ratio of 162Ho/164Ho is just

2^(-60/22) / 2^(-60/37)
= 2^(-60/22 + 60/37)
= 2^(-450/407)
= 2^-1.10565
= 0.465