Question
Radium decays exponentially. Its half-life is 1,690 years. How long will it take for a 50-gram sample of radium to be reduced to 5 grams?
1/2P = Pe^(-1690k)
(ln1/2)/(-1690) = k
4 x 10^-4 = k
5 = 50e^-kt
ln0.1 = -kt
ln0.1/-k = t
5,630 years = t
...but textbook answer is 5,614 years. Where did I go wrong?
1/2P = Pe^(-1690k)
(ln1/2)/(-1690) = k
4 x 10^-4 = k
5 = 50e^-kt
ln0.1 = -kt
ln0.1/-k = t
5,630 years = t
...but textbook answer is 5,614 years. Where did I go wrong?
Answers
Damon
I got 5616 using 4.1 * 10^-4 for k
You did it right but did not carry the same number of significant figures.
it is easier to use a^-b = 1/a^b in a case like this
1/10 = e^-kt
becomes
e^kt = 10
t = ln 10/k = 2.303/.00041
You did it right but did not carry the same number of significant figures.
it is easier to use a^-b = 1/a^b in a case like this
1/10 = e^-kt
becomes
e^kt = 10
t = ln 10/k = 2.303/.00041
bobpursley
your calculator. Set it on scientific, so the k is equal to 4.101E-4
With that, I get 5615 years.
With that, I get 5615 years.
DrBob222
I, too, get 5615.