Rounding to 2 significant digits, the time it would take for the sample to decay from 5.00 mg to 2.60 mg is approximately 4.3 minutes.
To find out how long it would take for the sample of Tin-129 to decay from 5.00 mg to 2.60 mg, we need to use the concept of half-life.
The half-life of Tin-129 is given as 2.23 minutes. This means that every 2.23 minutes, the amount of Tin-129 in the sample will decrease by half.
To calculate the time it takes for the sample to decay from 5.00 mg to 2.60 mg, we can set up a ratio using the initial amount, the final amount, and the half-life.
Initial amount: 5.00 mg
Final amount: 2.60 mg
Half-life: 2.23 minutes
First, let's find the number of half-lives it takes for the sample to decay from 5.00 mg to 2.60 mg. We can do this by dividing the initial amount by the final amount:
5.00 mg / 2.60 mg = 1.9231
This tells us that it takes approximately 1.9231 half-lives for the sample to decay from 5.00 mg to 2.60 mg.
Now, let's multiply the number of half-lives by the length of one half-life (2.23 minutes) to find the total time:
1.9231 half-lives * 2.23 minutes/half-life = 4.2904 minutes
Rounding to 2 significant digits, the time it would take for the sample to decay from 5.00 mg to 2.60 mg is approximately 4.3 minutes.