The detector keeps its xenon at 167K, so it stays liquid. In this liquid volume,
ID: 1562446 • Letter: T
Question
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 (as per appendix B of the textbook).
Found N=2.93 X 10^26 atoms
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?
Found such to be 3.29 X 10^4
The question is: The detector was operational for 127.6 days. Using the results from last two parts, what would the measured half-life be?
Explanation / Answer
3)
from the given data
activity, A = 3.29*10^4 decays/(127.6 days)
= 3.29*10^4/(127.6*24*60*60) decay/s
= 2.98*10^-3 decay/s
let lamda is the decay constant.
we know, A = lamda*N
==> lamda = A/N
= 2.98*10^-3/(2.93*10^26)
= 1.02*10^-29 s^-1
half life time, T1/2 = 0.693/lamda
= 0.693/(1.02*10^-29)
= 6.79*10^28 s
= 6.79*10^28/(365*24*60*60)
= 2.15*10^21 years <<<<<<<<<<--------------Answer