# Question about calculating age of a uranium and lead containing object, based on the ratio of uranium-to-lead

I realize this is probably going to sound so stupid, but... here goes:

• As Bill N said, breaking a rock into smaller pieces does not change the ratio of uranium to lead. All of the individual pieces will still the same uranium to lead ratio if the two metals are evenly dispersed. Perhaps the question you're really struggling with is what does "age" mean in the case of radioactive decay testing with uranium? "Age" of the rock as measured from what event?
– user93237
Commented Feb 22, 2016 at 22:19
• The simple answer is that it wasn't one scientist going out there one day and collecting one rock to take one little sample. It was thousands of geologists collecting millions of samples and comparing the results to verify that the sampling biases are understood. Science is tough, sweaty work. It takes a hundred measurements to confirm the one crucial one. Sometimes it takes trillions and millions of trillions. Commented Feb 22, 2016 at 22:43
• This appears to be a misunderstanding of what a ratio is. One glass of 2% skim milk is still 2% skim milk; a shot of 90 proof vodka is still 90 proof vodka. Commented Feb 22, 2016 at 23:17
• Re: @MSalters-- Lol, perhaps you're right! I think I'm going to need some 90 proof vodka after trying to wrap my head around this! ;'-D Commented Feb 23, 2016 at 20:41
• Re: @SamuelWeir-- Hi Samuel, thanks for taking the time to reply. No, I think I'm struggling with the ratio concept, like MSalters suggested. Although I am familiar with what a ratio is, I am just trying to understand how it all fits together, lol. Commented Feb 23, 2016 at 20:43

When these techniques are used, there is an assumption that the distribution of minerals/elements is uniform throughout the object. The whole point of using a ratio technique is that the size of the sample becomes unimportant.

It's like a food company making pancake mix: they don't mix each box individually. If they have mix 20 lbs of flour to 1 lb of sugar, every box is still going to have a 20:1 ratio of flour to sugar.

Breaking the rock into smaller pieces is assumed to not change the ratio (what argument can you make that it should?) and it definitely doesn't change the decay rates.

• That the nuclear composition of rocks is homogenous can be experimentally tested. You take a large piece of rock and you break it up in a hundred samples. Repeat the measurement and calculate the variance. Rinse, repeat with many different geological formations, strata and samples and the assumption turns into quantified information about the sampling bias of the techniques used to collect, prepare and analyze the samples. That's the "boring", decade long work of many scientists that the public never gets to see. Commented Feb 22, 2016 at 22:41
• Yep. the experiments support the assumptions Commented Feb 22, 2016 at 23:56
• Hi @BillN, Thanks for your answer. So, if I am understanding you correctly, if we accept the assumption that the uranium/lead concentration is evenly distributed throughout an object, then taking a small sample of the object can inform us as to the age of the greater whole (i.e., because the ratio of uranium-to-lead deterioration will be the SAME in both the sample and the parent object)? Commented Feb 23, 2016 at 20:52
• @E.N.B.: Science is a method and it's a complicated one. To produce high quality science takes many different consistency checks and constant critical thinking about all possible error sources. Every measurement we make has to be consistent with previous measurements, or many red flags go up. As a general rule: there are no unjustified assumptions in science. If you can't quantify the limit of validity of your assumptions about your measurement with control measurement, then you don't have valid data. Commented Feb 23, 2016 at 22:01
• @E.N.B. Yes, you understood correctly. Your question about the small grain indicates that you don't know how small atoms are. A sample of uranium ore the size of a piece of sand (2 mm diameter) is going to have on the order of $10^{19}$ atoms. I don't you have to worry about slicing the sample too small. A small sample will require a longer counting time to reduce the uncertainties in the statistics, but that's true in every type of counting experiment. Commented Feb 23, 2016 at 22:46

Well your apprehensions are there but the geologists working on this method have taken precautions for comparing their results through a variety of radioactive decay series and using zircon in crystal forms

The followung details may be seen in the citations listed (from Wikipedia):

Undamaged zircon retains the lead generated by radioactive decay of uranium and thorium until very high temperatures (about 900 °C), though accumulated radiation damage within zones of very high uranium can lower this temperature substantially.

Zircon is very chemically inert and resistant to mechanical weathering—a mixed blessing for geochronologists, as zones or even whole crystals can survive melting of their parent rock with their original uranium-lead age intact.

Zircon crystals with prolonged and complex histories can thus contain zones of dramatically different ages (usually, with the oldest and youngest zones forming the core and rim, respectively, of the crystal), and thus are said to demonstrate inherited characteristics.

Unraveling such complications (which, depending on their maximum lead-retention temperature, can also exist within other minerals) generally requires in situ micro-beam analysis via, say, ion microprobe (SIMS) or laser ICP-MS.>

References: