The age of the rock can be calculated from the half life of Uranium - 238. The age of the rock sample is 9 million years.
The term radioactivity refers to the sponteanous decay of a material which leads to the production of daughter nuclei. We know that uranium 238 decays to lead 206 with a half life of 4.5 billion years.
Using;
0.693/t1/2 = 2.303/t log(No/N)
t1/2 = half life of uranium 238
t = age of the rock sample
No = initial amount of uranium 238
N = amount of uranium 238 after time t
Now;
0.693/4.5 * 10^9 = 2.303/t log (No/0.25No)
0.693/4.5 * 10^9 = 2.303/t log(1/0.25)
0.693/4.5 * 10^9 =1.387/t
1.54 * 10^-10 = 1.387/t
t = 1.387/1.54 * 10^-10
t = 9 million years
The age of the rock sample is 9 million years.
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