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Pomico
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[SOLVED] Exponential decay
A certain amount of the radioactive isotope of thorium [tex]^{232}[/tex]Th was produced during a supernova explosion 2 billion years ago. This isotope decays according to the exponential law N(t) = Noe[tex]^{-t/to}[/tex], where No and N are the initial number of atoms and the number of atoms after time t respectively, and to = 2x10[tex]^{10}[/tex] years. Calculate the fraction of initial atoms that have not decayed since the explosion.
What time is needed for one half of the initial atoms of thorium to decay?
N(t) = Noe[tex]^{-t/to}[/tex]
I have an answer, I'd just like to check it.
Using t = 2x10[tex]^{9}[/tex] years,
N = Noe[tex]^{-(2x10^{9})/(2x10^{10})}[/tex] = Noe[tex]^{-1/10}[/tex] years
For the second part,
0.5 = e[tex]^{-t/(2x10^{10})}[/tex]
ln0.5 = [tex]\frac{-t}{2x10^{10}}[/tex], t = 1.386 x 10[tex]^{10}[/tex]
Homework Statement
A certain amount of the radioactive isotope of thorium [tex]^{232}[/tex]Th was produced during a supernova explosion 2 billion years ago. This isotope decays according to the exponential law N(t) = Noe[tex]^{-t/to}[/tex], where No and N are the initial number of atoms and the number of atoms after time t respectively, and to = 2x10[tex]^{10}[/tex] years. Calculate the fraction of initial atoms that have not decayed since the explosion.
What time is needed for one half of the initial atoms of thorium to decay?
Homework Equations
N(t) = Noe[tex]^{-t/to}[/tex]
The Attempt at a Solution
I have an answer, I'd just like to check it.
Using t = 2x10[tex]^{9}[/tex] years,
N = Noe[tex]^{-(2x10^{9})/(2x10^{10})}[/tex] = Noe[tex]^{-1/10}[/tex] years
For the second part,
0.5 = e[tex]^{-t/(2x10^{10})}[/tex]
ln0.5 = [tex]\frac{-t}{2x10^{10}}[/tex], t = 1.386 x 10[tex]^{10}[/tex]