91影视

A nuclear reaction occurs when two atom nuclei or nuclei meet with a subatomic particle from outside the atom. Such reactions can occur spontaneously or artificially to provide 鈥渘uclear energy鈥� on demand in a regulated manner.

a. Student 2 is entirely accurate. The remaining fraction of ²³⁰U is equal to ^2sU divided by its starting value.

Therefore, student 2 is correct.

b.${}^{238}U=2(Pb-206)$

Let ${}^{238}U=2x$and $2(Pb-206)=x$;

Fraction of ²³⁸U:

$\frac{{}_{92}{}^{238}U}{{}_{92}{}^{238}U{+}_{82}^{206}Pb}=\frac{2x}{2x+x}=\frac{2}{3}$

We must use the half-life formula to find the constant (k) in this situation.

role="math" localid="1663609934846" $$\begin{gathered} t_{\frac{1}{2}}=\frac{\ln 2}{k}鈫�k=\frac{\ln 2}{t_{\frac{1}{2}}} \\ k=\frac{\ln 2}{t_{\frac{1}{2}}}=\frac{\ln 2}{4.5x{10}^{9}yr} \\ =\frac{1.540327脳{10}^{-10}}{yr} \end{gathered}$$

We can solve for the value of t using the expression for determining the number of nuclei remaining.

$\ln \frac{N_0}{N_t}=kt$

$$\begin{gathered} \ln \frac{1}{\frac{2}{3}}=\frac{1.540327脳{10}^{-10}}{yr}\left(t\right) \\ t=2.6323脳{10}^9 \end{gathered}$$

Therefore, the age is $2.6323脳{10}^9$years old.