Respuesta :

jorel1380
(1/2)^x=1/16
ln 1/2^x=x ln 1/2=ln 1/16
x=4
4 half-lives in one hour=1/4 hour for the half-life of the isotope
☺☺☺☺

Answer:

[tex]t_{1/2} = 0.25 hours[/tex]

Explanation:

As we know that

[tex]N = N_o e^{-\lambda t}[/tex]

here we know that

[tex]\lambda = \frac{ln2}{t_{1/2}}[/tex]

so we will have

[tex]N = N_o e^{\frac{t ln2}{t_{1/2}}}[/tex]

so it will be

[tex]N = N_o(\frac{1}{2})^{\frac{t}{t_{1/2}}}[/tex]

now we know that

[tex]t = 1 hour[/tex]

[tex]N = \frac{N_o}{16}[/tex]

[tex]\frac{1}{16} = (\frac{1}{2})^{\frac{t}{t_{1/2}}}[/tex]

[tex]4 = \frac{1}{t_{1/2}}[/tex]

[tex]t_{1/2} = 0.25 hours[/tex]