Technetium-99m is an ideal radioisotope for scanning organs because it has a half-life of 6.0 hr and is a pure gamma emitter. Suppose that 200mg were prepared in the technetium generator this morning. How many milligrams would remain after the following intervals?

1- One half life.
2- two half-lives
3- 18 hr
4- 30 hr

To determine the amount of Technetium-99m remaining after a certain interval, we need to use the concept of half-life decay. The half-life of an isotope is the time it takes for half of the initial amount to decay.

In this case, we are given that the half-life of Technetium-99m is 6.0 hours. Let's calculate the remaining amount for each interval:

1. One half-life (6.0 hours):
Since one half-life has passed, half of the initial amount will decay. Therefore, the remaining amount of Technetium-99m is 200mg / 2 = 100mg.

2. Two half-lives (12.0 hours):
Since two half-lives have passed, we apply the decay process twice. After the first half-life, we have 100mg remaining. After the second half-life, half of the remaining amount will decay, so the remaining amount is 100mg / 2 = 50mg.

3. 18 hours:
To calculate the remaining amount after 18 hours, we need to determine how many half-lives have passed. Since the half-life is 6.0 hours, we divide 18 hours by the half-life: 18 hours / 6.0 hours = 3 half-lives. Apply the decay process three times:

- After the first half-life: 200mg / 2 = 100mg.
- After the second half-life: 100mg / 2 = 50mg.
- After the third half-life: 50mg / 2 = 25mg.

After 18 hours, the remaining amount of Technetium-99m is 25mg.

4. 30 hours:
Similar to the previous case, we need to determine how many half-lives have passed. Divide 30 hours by the half-life: 30 hours / 6.0 hours = 5 half-lives. Apply the decay process five times:

- After the first half-life: 200mg / 2 = 100mg.
- After the second half-life: 100mg / 2 = 50mg.
- After the third half-life: 50mg / 2 = 25mg.
- After the fourth half-life: 25mg / 2 = 12.5mg.
- After the fifth half-life: 12.5mg / 2 = 6.25mg.

After 30 hours, the remaining amount of Technetium-99m is approximately 6.25mg.

You should go back and look for answers when you post. I worked this for you last night. I shouldn't need to work problems twice.