Question

Question #1f8ff

Answer 1

We can use a radioactive decay equation.

Explanation:

Radioactive decay is a random process, so we cannot exactly know which atom or the order that the atoms are going to decay. But, a formula can work to find the general half-life of a substance.

It is given by

`N(t)=N_0(1/2)^(t/(t_1/2))`

`N(t)` is the final amount of substance

`N_0` is the original amount of the substance

`t` is the time

`t_(1/2)` is the half-life of the substance

So, we can derive the half-life of the substance by rearranging the equation. Our original equation is

`N(t)=N_0(1/2)^(t/(t_1/2))`

Dividing by `N_0` gives us

`(N(t))/N_0=(1/2)^(t/(t_1/2))`

Using the logarithm properties, we get that

`t/(t_(1/2))=log_(1/2)((N(t))/N_0)`, and then we can inverse and get the reciprocal, which is

`(t_(1/2))/t=1/log_(1/2)((N(t))/N_0)`

Solving for `t_(1/2)`, we get

`t_(1/2)=t/log_(1/2)((N(t))/N_0)`