Question
Gold (Au) has a synthetic isotope that is relatively unstable. After 25.5 minutes, a 128-gram sample has decayed to 2 g.
What is the half-life of this isotope?
8.5 minutes
2.25 minutes
1.5 minutes
4.25 minutes
What is the half-life of this isotope?
8.5 minutes
2.25 minutes
1.5 minutes
4.25 minutes
Answers
x = Xi e^-kt
2 = 128 e^-25.5 k
0.015625 = e^-25.5 k
ln 0.015625 = -25.5 k
-4.15888 = -25.5 k
k = 0.163
so
1 = 2 e^-0.163 t for half life
0.5 = e^-0.163 t
ln 0.5 = -0.693 = -0.163 t
t = 4.25 minutes
2 = 128 e^-25.5 k
0.015625 = e^-25.5 k
ln 0.015625 = -25.5 k
-4.15888 = -25.5 k
k = 0.163
so
1 = 2 e^-0.163 t for half life
0.5 = e^-0.163 t
ln 0.5 = -0.693 = -0.163 t
t = 4.25 minutes
128/2 = (1/2)^6
So, now you want
25.5/6 = 4.25
For a half-life of k minutes, your function is A = P*(1/2)^(t/k)
So, now you want
25.5/6 = 4.25
For a half-life of k minutes, your function is A = P*(1/2)^(t/k)
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