Answer:
8978 grams
Step-by-step explanation:
The equation to find the half-life is:
[tex]N(t)= N_{0}e^{-kt}[/tex]
N(t) = amount after the time t
[tex]N_{0}[/tex] = initial amount of substance
t = time
It is known that after a half-life there will be twice less of a substance than what it intially was. So, we can get a simplified equation that looks like this, in terms of half-lives.
[tex]N(t)= N_{0}e^{-\frac{ln(\frac{1}{2}) }{t_{h} } t}[/tex] or more simply [tex]N(t)= N_{0}(\frac{1}{2})^{\frac{1}{t_{h} } }[/tex]
[tex]t_{h}[/tex] = time of the half-life
We know that [tex]N_{0}[/tex] = 35,912, t = 14,680, and [tex]t_{h}[/tex]=7,340
Plug these into the equation:
[tex]N(t) = 35912(\frac{1}{2})^{\frac{14680}{7340} }[/tex]
Using a calculator we get:
N(t) = 8978
Therefore, after 14,680 years 8,978 grams of thorium will be left.
Hope this helps!! Ask questions if you need!!
