BMAT Exercise help!

Hi all!!
Can anyone please explain this BMAT Exercise question. I have tried a loot to solve it, but unfortunately I can't.
Thanks a lot!

15 Two radioactive sources X and Y have half-lives of 4.8 hours and 8.0 hours respectively. Both
decay directly to form only stable isotopes.
The activity of a sample of the source X is measured by a detector as 320 counts per minute,
and simultaneously the radioactivity of a sample of the source Y is measured as 480 counts per
minute. Immediately after the measurements, the two samples are combined.
What is the count rate when the activity of the combination of X and Y is measured 24 hours
later?
[Assume that all readings in this question have been corrected for background radiation.]

A 25 counts per minute
B 50 counts per minute
C 55 counts per minute
D 70 counts per minute
E 100 counts per minute
F 140 counts per minute

Reply 1

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Reply 2

Whizbox

You know both the original count rates, the half life of the isotope is the amount of time it takes the count rate to halve so for source X the count rate halves every 4.8 hours and for Y every 8 hours. So we know that in 24 hours, source X will halve itself 5 times (24/4.8) and source Y will halve itself 3 times (24/8). We can then work out the count rates individually after 24 hours: source X will have a count rate of 10, because 320 halved 5 times is 10. Source Y will have a count rate of 60 because 480 halved 3 times is 60. We then add 60 to 10 and get 70.
Therefore the answer is D

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Reply 3

bluevalkyrie88

Can anyone explain this?

In a laboratory experiment, protactinium-234 undergoes radioactive decay by β-emission into uranium-234.
The table below describes how the mass of uranium-234 present in the sample varies with time from the start of the experiment:

time / min mass of u-234 / mg
0.0 0.0
1.2 8.0
2.4 12.0
3.6 14.0
4.8 15.0
6.0 15.5
7.2 15.7
8.4 15.9
9.6 15.9
10.8 16.0
12.0 16.0
Using the information in the table, approximately what is the half-life of protactinium-234?

Reply 4

Larynx.pharynx

Original post by bluevalkyrie88

This is a bit of a trickily phrased question. The first thing to consider is that, despite the beta emission, an atom of uranium-234 and protactinium-234 can be considered to have the same mass. Therefore, we can use the mass of each in our samples as an analogue for the amount of atoms.

In beta emission, one atom of a substance gives becomes another, there's no change in the number of atoms. At the end of this experiment, we can see that the mass of uranium is no long increasing. We can assume, therefore, that all the protactinium has decayed. There are 16mg of uranium, so we began with 16mg of protactinium.

The half life is the amount of time for half the atoms in a sample to decay: our sample is 16mg, so we want the time it took for 8mg of the protactinium to become uranium. The table tells us that this took 1.2 minutes, so this is (approximately) the half-life of protactinium-234.

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