How do you explain the ratio of lead-206 to uranium-235 in a sample and the sample's age?

Answer 1

It's called radiometric dating, and it's a convenient way to figure out how old rocks are. Radioactive elements have a "half-life," which means during a specific amount of time, half the atoms in that sample will decay into another element. Half-lives are different for every element; some are a fraction of a second and some are billions of years. Analyzing the ratio between parent element and daughter element (what it decays into) can give you the age of the rock it's in. This is how we know how old the earth is - about 4.6x109 years.

Answer 2

This question cannot be answered unequivocally:

Rocks do not have a half life. Radioactive isotopes of elements have. The half life of the radioactive isotope U235 is 704 million years.

The ratio of the two isotopes of lead 207 and uranium 235 is not enough to constrain an accurate age of a rock, because it might have contained a bit of lead 207 already when it formed.

Assuming that there had been absolutely no lead in the rock when it formed and no later processes like partial melting or recrystallization during metamorphic processes changed the budget of lead and uranium in the rock, one can apply the decay equation for radioactive materials:

C = Co * exp(-t*ln2/T)

With C = concentration of radioactive nuclide left

Co = concentration of radioactive nuclide at the beginning

t = time

T = half life

207 lead is only produced by the decay of U235 so the number of Pb 207 atoms in the rock is exactly equivalent to the number of atoms that completed the whole decay chain from U235 to Pb 207. When the ratio of Pb 207 to U 235 is 0.9 (number of Pb207 divided by number of U235 = 0.9), this means that slightly less than half of the Uranium 235 has decayed. The ratio would be 1 if half was Pb 207 and the other half was U 235.

From the given ratio we can get the ratio of C to Co; this is the amount of U235 atoms still present divided by the number of U 235 atoms at the time of rock formation. This ratio is 1 / (1+0.9) ~ 0.526

Now the only unknown in the decay equation is t (time):

C = Co * exp(-t*ln2/T) -->

C/Co = exp(-t*ln2/T) -->

ln(C/Co) = -t*ln2/T-->

ln(C/Co)/ln2*T = -t

-ln(C/Co)/ln2*T = t

and putting in the numbers results in an age of about 652 million years.

Answer 3

Use the the following formula: 206Pb/238U = eλ238t- 1 where lambda is the hal life of uranium 238 (4,470.109 years) and t is the age.

Answer 4

The age of the meteorite is 4,468.109 years.