The Enriched Xenon Observatory - 200 kg (EXO-200) collaboration has a detector u

Question

The Enriched Xenon Observatory - 200 kg (EXO-200) collaboration has a detector underground in New Mexico, studying in detail the radioactive decay of 13654Xe. Here, we will use the results of the experiment to calculate the half-life of 13654Xe.

a) The detector keeps its xenon at 167K, so it stays liquid. In this liquid volume, a portion of it is instrumented so that decays in that volume can be detected. This volume contains 66.20 kg of 136Xe . How many atoms of xenon-136 is this? The atomic mass of a xenon-136 atom is 135.907220 amu.

b) The detector has an efficiency of 57.88% for detecting these special decays of xenon (this was very carefully measured). If 19042 decays are detected, how many decays happened in the detector's sensitive volume?

c) The detector was operational for 127.6 days. Using the results from last two parts, what would the measured half-life be?

Explanation / Answer

a.

given:

The atomic mass of a xenon-136 atom is 135.907220 amu.

so 1 mole i.e. 6.023 x 1023 number of atoms weigh 135.9072 g.

so 66.2 kg or 66.2 x 1000 =66200 g ( as 1kg=1000g) contains 66200/135.9072 moles = 487.097 moles or

487.097 x 6.022 x 1023 = 2.9333 x 1026 no of atoms

so the no of Xenon-136 atoms in 66.20 kg is 2.9333 x 1026

b. The detector has an efficiency of 57.88% for detecting these special decays of xenon.

That means only 57.88 deays are detected whereas the actual no of decays are 100.

In this case only 19042 decays are detected, so no of decays happened = 19042 x 100/57.88= 328899.1

so no of decays happened in the detector's sensitive volume = 328899.1

c. Although it is not clear from the question regarding initial amount and final amount of Xenon, let us assume that

initial amount of Xenon= 200 kg

final amount of Xenon after decay = 200-66.2= 133.8 kg

so, 133.8=200 x e^(- decay constant x t)

so, 133.8 = 200 x e^(-decay constant x 127.6)

so, decay constant=0.00315

so half life = ln 2/decay constant= 220.04 days

so half life of Xenon = 220.04 days

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