Answer :
Answer:
103.3 %
Explanation:
For a radioactive isotope, the number of radioactive nuclei left (parent nuclei) after a time t, N(t), is
[tex]N(t)=N_0 (\frac{1}{2})^{\frac{t}{\tau}}[/tex]
where
N0 is the initial number of radioactive nuclei
t is the time
[tex]\tau[/tex] is the half-life of the isotope
Here we have
[tex]t=4.5 \cdot 10^9 y\\\tau = 4.6\cdot 10^9 y[/tex]
So we find
[tex]\frac{N(t)}{N_0}=(\frac{1}{2})^{\frac{4.5\cdot 10^9}{4.6\cdot 10^9}}=0.508[/tex]
Which means that the fraction of parent nuclei left after this time is 0.508 (50.8% of the initial value). So the fraction of daugther nuclei at this time is
[tex]\frac{N_d}{N_0}=1-0.508=0.492[/tex]
So the percentage of parent to daughter isotopes is
[tex]\frac{N(t)}{N(d)}=\frac{0.508}{0.492}=1.033[/tex]
Which corresponds to 103.3 %.
Answer:
More than 50 percent of its parent isotope
Explanation:
Since Uranium-238 has a half-life of 4.5 billion years, basically when the Earth was created, we know there is going to be more than 50% of its parent isotope! Unlike potassium-40, which has a half-life of 1.25 billion years and less than 50% of its parent isotope left!