Question

Certain minerals exclude lead but not uranium from their crystal structure, so when the minerals form they have no lead, only uranium. As time goes on, the uranium decays to lead, so measuring the ratio of lead atoms to uranium atoms allows investigators to determine the ages of the minerals. If a sample of a mineral contains 3 atoms of 207Pb207Pb for every 1 atom of 235U235U, how many years ago was it formed

Answer 1

The answer is "
`1.4 \ \bold{ billion-years}`".

Step-by-step explanation:

Using formula:

`\to N_(Now) = N_(orige)e^(\lambda t) \\\\`

`\to` 1 U atom produces 1 Pb atom after decay.

`\to` U's original numbers are now the sum of U counts and Pb counts.

`\to N_U=(N_U+N_(pb))e^(\lambda Ut)`

`\to 1 = (1+3) \ exp[((-\ln(2))/(t_((half))) * t ]\\\\\to t = [(\ln(4))/(\ln(2))] * t_((half))`

`= 14 * 10^8 \ \ years\\\\=1.4 \ billion \ \ years`