Question #1f8ff

Question

Question #1f8ff

1 Answer

Impact of this question

930 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-01-12T05:39:03

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

$N (t) = N_{0} {(\frac{1}{2})}^{\frac{t}{\frac{t_{1}}{2}}}$ $N(t)=N_0(1/2)^(t/(t_1/2))$

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

$N_{0}$ $N_0$ is the original amount of the substance

$t$ $t$ is the time

$t_{\frac{1}{2}}$ $t_(1/2)$ 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

$N (t) = N_{0} {(\frac{1}{2})}^{\frac{t}{\frac{t_{1}}{2}}}$ $N(t)=N_0(1/2)^(t/(t_1/2))$

Dividing by $N_{0}$ $N_0$ gives us

$\frac{N (t)}{N_{0}} = {(\frac{1}{2})}^{\frac{t}{\frac{t_{1}}{2}}}$ $(N(t))/N_0=(1/2)^(t/(t_1/2))$

Using the logarithm properties, we get that

$\frac{t}{t_{\frac{1}{2}}} = {log}_{\frac{1}{2}} (\frac{N (t)}{N_{0}})$ $t/(t_(1/2))=log_(1/2)((N(t))/N_0)$ , and then we can inverse and get the reciprocal, which is

$\frac{t_{\frac{1}{2}}}{t} = \frac{1}{{log}_{\frac{1}{2}} (\frac{N (t)}{N_{0}})}$ $(t_(1/2))/t=1/log_(1/2)((N(t))/N_0)$

Solving for $t_{\frac{1}{2}}$ $t_(1/2)$ , we get

$t_{\frac{1}{2}} = \frac{t}{{log}_{\frac{1}{2}} (\frac{N (t)}{N_{0}})}$ $t_(1/2)=t/log_(1/2)((N(t))/N_0)$

Science

Math

Humanities

... and beyond

Question #1f8ff

1 Answer

Explanation:

Related questions

Impact of this question