Living Will Sample Forms
How would you do this problem?
I have been trying this problems for so long, but I couln’t get it.
Can you help me to get these answers. The answers are given.
This is a Calculus Problems.
1) Mean Life of Radioactive Nuclei, Physicists using the radioactive decay equation y=ae^(-kt) call teh number 1/k the mean life of a radioactive nuclues. The mean life of a radon-222 nucleus is about 1/0.18 = 5.6 days. The mean life of a carbon-14 nuclues is more than 8000 years. Show that 95% of the radioactive nuclei originally present in any sample will disintegrate within three mean lifetimes, that is, by time t = 3/k. Thus, the mean life of a nuclues gives a quick way to estimate how long the radioactive of a sample will last.
2) Dating Crater Lake, The charcoal from a tree killed in the volcanic eruption that formed Crater Lake in Oregon contained 44.5% of the carbon-14 found in living matter. About how old is Crater Lake?
Answers:
1) y=ae^(-kt) = ae^[-k(3/k)] = ae^(-3) < 0.05a
2) 6658 years
(1)
y = a·e^(- k·t)
at t₀= 0
y₀= a·e^(- k·0) = a
the fraction of the initial amount decayed at time t is
η = (y₀ – y) / y₀
= 1 – y/y₀
= 1 – a·e^(- k·t) / a
= 1 – e^(- k·t)
at t₁ = 3/k
η₁ = 1 -e^(- k·(3/k))
= 1 – e^(- 3)
= 0.9502… >0.95
q.e.d.
(2)
The fraction of original amount present in a sample is
µ = y/y₀
= e^(- k·t )
<=>
t = – (1/k)·ln(µ)
= – 8266y · ln( 0.445 )
= 6693y
Because the mean life of C14 is not given precisely, i calculated it from half life, given in wikipedia as t1/2 = 5730 y:
1/k = t1/2 / ln(2) = 8266y
**Trance Channeling with Aimée Lyndon-Adams** on BEYOND THE LIVING SHOW-RCRN
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