Zircon crystals and rock age?

Question

Zircon crystals in a sample of rock were analysed and found to have a daughter to parent (D/P) ratio of 1.8 for the decay scheme 235U to 207Pb. Can someone please esitimate the age of the rock to two significant figuresand comment on the uncertainties and limitations on this estimate.

Answer 1

The answer is right there and I just can't quite get it.

Answer 2

U235 decays to Pb207, so we can modify the equation for radioactive decay to give the following:

parent + daughter=initial parent

parent + daughter=parent/(e^-lt)

where e is the exponetial constant, l is the decay constant, and t is time

Rearrange and take logs to get t

1 +daughter/parent=e^lt

ln(1+daughter/parent)/l=t

if you do the calculation assuming the decay constant for U235 is 9.85E-10 then you get an answer of about 970 million years.

There are then basically two different uncertainties on the age: analytical, and geological.

The analytical uncertainty comes down to how well the Pb207/U235 ratio was measured (and the uncertainly arising from certain small corrections which have to be made).

Geological uncertainty basicaly relates to whether the measured Pb207/U235 ratio is meaningfull. Quite commonly zircon gets damaged be the radiation from the decay of the uranium, and some of the Pb escapes, in which case the age appears younger than it really is. Or alternatively the zircon has a core of older zircon which didn't form in the rock that it is now in, bug got accidentally incorporated when the rock formed. In this case the ages can apper older.

Fortunatly we can test this to some extent, because there is also U238, which decays into Pb206 (and Th232 which decays into Pb208), for which ages can also be calculated. If the Pb207/U235 age and Pb206/U238 age (and Pb208/Th232 age) agree, the zircon is said to be 'concordant' and the age is then usually accepted as being correct. If lead has escaped, or the zircon has a core, the Pb206/U238 age and Pb207/U235 age generally will not agree with each other. So without also knowing the Pb206/U238 ratio it is difficult to comment specifically on the uncertainty of the age.