(adsbygoogle = window.adsbygoogle || []).push({}); [SOLVED] Exponential decay

1. The problem statement, all variables and given/known data

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?

2. Relevant equations

N(t) = Noe[tex]^{-t/to}[/tex]

3. 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]

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Exponential decay

**Physics Forums | Science Articles, Homework Help, Discussion**