Sure, here's how to solve this problem:

Step 1: Understand the concept of half-life. The half-life of a radioactive substance is the time it takes for half of the atoms in a sample to decay. In this case, the half-life of barium-137 is 3 minutes.

Step 2: Determine the number of half-lives that have passed. In this case, 9 minutes have passed, so 9 minutes / 3 minutes/half-life = 3 half-lives.

Step 3: Calculate the remaining amount of the isotope. Start with the initial amount and halve it for each half-life that has passed.

- After 1 half-life (3 minutes), half of the 36 mg will remain, so you have 36 mg / 2 = 18 mg.
- After 2 half-lives (6 minutes), half of the 18 mg will remain, so you have 18 mg / 2 = 9 mg.
- After 3 half-lives (9 minutes), half of the 9 mg will remain, so you have 9 mg / 2 = 4.5 mg.

So, after 9 minutes, 4.5 mg of the barium-137 isotope will remain in the source.

Question

Sure, here's how to solve this problem:

Step 1: Understand the concept of half-life. The half-life of a radioactive substance is the time it takes for half of the atoms in a sample to decay. In this case, the half-life of barium-137 is 3 minutes.

Step 2: Determine the number of half-lives that have passed. In this case, 9 minutes have passed, so 9 minutes / 3 minutes/half-life = 3 half-lives.

Step 3: Calculate the remaining amount of the isotope. Start with the initial amount and halve it for each half-life that has passed.

- After 1 half-life (3 minutes), half of the 36 mg will remain, so you have 36 mg / 2 = 18 mg.
- After 2 half-lives (6 minutes), half of the 18 mg will remain, so you have 18 mg / 2 = 9 mg.
- After 3 half-lives (9 minutes), half of the 9 mg will remain, so you have 9 mg / 2 = 4.5 mg.

So, after 9 minutes, 4.5 mg of the barium-137 isotope will remain in the source.

Knowee AI · Accepted Answer

Sure, here's how to solve this problem:

Step 1: Understand the concept of half-life. The half-life of a radioactive substance is the time it takes for half of the atoms in a sample to decay. In this case, the half-life of barium-137 is 3 minutes.

Step 2: Determine the number of half-lives that have passed. In this case, 9 minutes have passed, so 9 minutes / 3 minutes/half-life = 3 half-lives.

Step 3: Calculate the remaining amount of the isotope. Start with the initial amount and halve it for each half-life that has passed.

- After 1 half-life (3 minutes), half of the 36 mg will remain, so you have 36 mg / 2 = 18 mg.
- After 2 half-lives (6 minutes), half of the 18 mg will remain, so you have 18 mg / 2 = 9 mg.
- After 3 half-lives (9 minutes), half of the 9 mg will remain, so you have 9 mg / 2 = 4.5 mg.

So, after 9 minutes, 4.5 mg of the barium-137 isotope will remain in the source.

An isotope of barium-137 has a half life of 3 minutes. A radioactive source contains 36 mg of this isotope. Calculate the mass of the isotope that remains in the source after 9 minutes.

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