Uranium-235 decays to thorium-231 with a half-life of 700 million years. When a rock was formed, it contained 6400 million uranium-235 nuclei and no thorium-231 nuclei. Show that after 2100 million years there are seven times more thorium nuclei than uranium nuclei in the rock.

proof in explanation

Explanation:

First, we will calculate the number of half-lives:

where,

n = no. of half-lives = ?

t = total time passed = 2100 million years

= half-life = 700 million years

Therefore,

Now, we will calculate the number of uranium nuclei left ():

and the rest of the uranium nuclei will become thorium nuclei ()

dividing both:

Hence, it is proven that after 2100 million years there are seven times more thorium nuclei than uranium nuclei in the rock.