Question

How much of a radioactive kind of thorium will be left after 14,680 years if you start with

Answer 1

Answer:

8978 grams

Step-by-step explanation:

The equation to find the half-life is:

$N(t)= N_{0}e^{-kt}$

N(t) = amount after the time t

$N_{0}$ = 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.

$N(t)= N_{0}e^{-\frac{ln(\frac{1}{2}) }{t_{h} } t}$ or more simply $N(t)= N_{0}(\frac{1}{2})^{\frac{1}{t_{h} } }$

$t_{h}$ = time of the half-life

We know that $N_{0}$ = 35,912, t = 14,680, and $t_{h}$=7,340

Plug these into the equation:

$N(t) = 35912(\frac{1}{2})^{\frac{14680}{7340} }$

Using a calculator we get:

N(t) = 8978

Therefore, after 14,680 years 8,978 grams of thorium will be left.

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