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 two hour. Rounded to three decimal

Answer 1

To solve this problem, we need to use the exponential decay formula:

A = A0 * (1/2)^(t/h)

Where A is the amount of isotope remaining after time t, A0 is the initial amount of the isotope, t is the time elapsed, and h is the half-life of the isotope.

Let's start by calculating the number of half-lives that have passed after two hours for each isotope.

For 162Ho:
Hours to minutes: 2 * 60 = 120 minutes
Number of half-lives: 120 / 22 = 5.454

For 164Ho:
Hours to minutes: 2 * 60 = 120 minutes
Number of half-lives: 120 / 37 = 3.243

Now, let's calculate the remaining amount of each isotope.

Remaining 162Ho = (1/2)^(5.454) = 0.0425
Remaining 164Ho = (1/2)^(3.243) = 0.1569

Finally, let's find the ratio of the amounts of 162Ho to 164Ho after two hours.

Ratio = Remaining 162Ho / Remaining 164Ho
Ratio = 0.0425 / 0.1569
Ratio ≈ 0.270