Question

A 120 mg sample of technetium-99m is used for a diagnostic test. If technetium-99m has a half-life of 6.0 h, how many milligrams of the technetium-99m sample remains active 23 h after the test?

Answer 1

Step-by-step explanation:

Here, we want to get the number of mg of the atom that would remain

Half-life refers to the time taken for exactly half the mass of a radioactive isotope to be lost to radiation

From the question, the half-life is 6 hours

During the first six hours, we have a mass of 60 mg left

In the next 6 hours, which is the second half-life, we have 30 mg left

In the next 6 hours, which is the third half-life, we have 15 mg left

Now, for the next 5 hours, there will not be a complete decay

Thus, we get the decay constant using the following:

`\begin{gathered} t_{(1)/(2)}\text{ = }(0.693)/(k) \\ \\ 6\text{ = }(0.693)/(k) \\ \\ k\text{ = }(0.693)/(6)\text{ = 0.1155 h}^(-1) \end{gathered}`

Mathematically: