# Nuclear physics half-life MCQ

Hi Can anyone help with this question?
X and Y are two radioactive nuclides. X has a half-life of 3.0 minutes and Y has a half-life of 9.0 minutes.
Two freshly prepared samples of X and Y start decaying at the same time. After 18 minutes the number of radioactive nuclei in both samples is the same. The sample of Y initially contained N radioactive nuclei.
What was the initial number of radioactive nuclei in the sample of X?

A 4N
B 16N
C 32N
D 64N
Original post by Terry Li
Hi Can anyone help with this question?
X and Y are two radioactive nuclides. X has a half-life of 3.0 minutes and Y has a half-life of 9.0 minutes.
Two freshly prepared samples of X and Y start decaying at the same time. After 18 minutes the number of radioactive nuclei in both samples is the same. The sample of Y initially contained N radioactive nuclei.
What was the initial number of radioactive nuclei in the sample of X?

A 4N
B 16N
C 32N
D 64N

How many half-lives have each isotope undergone after 18 minutes?

Because you know how many nuclei of y there were at the start, you should be able to work out how many nuclei there are of y after 18 minutes.
Original post by Terry Li
Hi Can anyone help with this question?
X and Y are two radioactive nuclides. X has a half-life of 3.0 minutes and Y has a half-life of 9.0 minutes.
Two freshly prepared samples of X and Y start decaying at the same time. After 18 minutes the number of radioactive nuclei in both samples is the same. The sample of Y initially contained N radioactive nuclei.
What was the initial number of radioactive nuclei in the sample of X?

A 4N
B 16N
C 32N
D 64N

Another way of solving the question is as follows.

Do you know the exponential decay equation?
(number of remaining nuclei) N = N0 exp(- ln2/T0.5)
where N0 is the initial number of radioactive nuclei and T0.5 is the half-life.

You can write the decay equations for X and Y respectively and then equate them to solve for the initial number of radioactive nuclei in the sample of X.