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
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To calculate the remaining amount of technetium-99m after a given time interval, we need to understand the concept of half-life.
1) One half-life: A half-life is the time it takes for half of the radioactive material to decay. In this case, the half-life of technetium-99m is 6.0 hours.
To calculate the remaining amount after one half-life, divide the given amount by 2:
Remaining amount after one half-life = 200mg / 2 = 100mg.
Therefore, 100mg of technetium-99m would remain after one half-life.
2) Two half-lives: To calculate the remaining amount after two half-lives, repeat the process. Remember that after each half-life, the remaining amount is halved once again.
Remaining amount after two half-lives = (200mg / 2) / 2 = 50mg.
Therefore, 50mg of technetium-99m would remain after two half-lives.
3) 18 hours: To calculate the remaining amount after 18 hours (3 half-lives), divide the given interval by the half-life and apply the formula.
Remaining amount after 3 half-lives = 200mg / (2^3) = 200mg / 8 = 25mg.
Therefore, 25mg of technetium-99m would remain after 18 hours.
4) 30 hours: To calculate the remaining amount after 30 hours (5 half-lives), divide the given interval by the half-life and apply the formula.
Remaining amount after 5 half-lives = 200mg / (2^5) = 200mg / 32 = 6.25mg.
Therefore, 6.25mg of technetium-99m would remain after 30 hours.