Answer:
proof in explanation
Explanation:
First, we will calculate the number of half-lives:
[tex]n = \frac{t}{t_{1/2}}[/tex]
where,
n = no. of half-lives = ?
t = total time passed = 2100 million years
[tex]t_{1/2}[/tex] = half-life = 700 million years
Therefore,
[tex]n = \frac{2100\ million\ years}{700\ million\ years}\\\\n = 3[/tex]
Now, we will calculate the number of uranium nuclei left ([tex]n_u[/tex]):
[tex]n_u = \frac{1}{2^{n} }(total\ nuclei)\\\\n_u = \frac{1}{2^{3} }(6400\ million)\\\\n_u = \frac{1}{8}(6400\ million)\\\\n_u = 800\ million[/tex]
and the rest of the uranium nuclei will become thorium nuclei ([tex]u_{th}[/tex])
[tex]n_{th} = total\ nuclei - n_u\\n_{th} = 6400\ million-800\ million\\n_{th} = 5600\ million[/tex]
dividing both:
[tex]\frac{n_{th}}{n_u}=\frac{5600\ million}{800\ million} \\\\n_{th} = 7n_u[/tex]
Hence, it is proven that after 2100 million years there are seven times more thorium nuclei than uranium nuclei in the rock.
