Technetium-99m is an ideal radioisotope for scanning organs because it has a half-life of 6.0 {\rm hr} and is a pure gamma emitter. Suppose that 280{\rm mg} were prepared in the technetium generator this morning. How many milligrams would remain after the following intervals?
You still gave no intervals; however, look at your earlier post. I showed you how to do it there.
To find the amount of technetium-99m remaining after a given time interval, we need to use the half-life of the substance.
The half-life of technetium-99m is 6.0 hours, which means that after every 6.0 hours, the amount of technetium-99m remaining is reduced by half.
The amount remaining after a time interval can be calculated using the formula:
Amount remaining = Initial amount * (1/2)^(time elapsed / half-life)
Let's calculate the amounts remaining after the given time intervals.
1. After 6.0 hours:
Amount remaining = 280 mg * (1/2)^(6.0 / 6.0) = 280 mg * (1/2)^1 = 140 mg
2. After 12.0 hours:
Amount remaining = 280 mg * (1/2)^(12.0 / 6.0) = 280 mg * (1/2)^2 = 70 mg
3. After 18.0 hours:
Amount remaining = 280 mg * (1/2)^(18.0 / 6.0) = 280 mg * (1/2)^3 = 35 mg
4. After 24.0 hours:
Amount remaining = 280 mg * (1/2)^(24.0 / 6.0) = 280 mg * (1/2)^4 = 17.5 mg
Therefore, after the given intervals, the amounts of technetium-99m remaining would be:
1. After 6.0 hours: 140 mg
2. After 12.0 hours: 70 mg
3. After 18.0 hours: 35 mg
4. After 24.0 hours: 17.5 mg