I was in History class the other day and I asked how people are able to get “accurate” dates for how old certain objects are. He said something along the lines of there are certain elements in materials and they decay overtime, half life this so we know roughly how long ago it was made.
I’m a mathematics major and am proficient in physics. I understand the concept of exponential decay and half-life’s. My questions is how do we know how much of a material we are measuring there initially was? To me, without knowing that, we could say that something was made whenever we want it to be made. Clearly I’m missing something but I can’t quite figure it out.
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That depends! If you’re asking about specifically carbon dating, that’s what this answer will be, but history is all about corroborating between as many sources as possible.
Carbon-14 is an unstable isotope of carbon in our atmosphere. It forms when cosmic rays from space interact with carbon in our atmosphere. This maintains a steady ratio of C-14 to other isotopes of carbon, where it forms as fast as it decays. When carbon is taken from the atmosphere, such as by plants, the C-14 will decay but no more is being created, so we can measure how much C-14 remains when compared to other carbon isotopes. This tells us how long it has been since that carbon was in the atmosphere.
While the C-14 balance in the atmosphere is a decent starting point, it *does* change over time. We can also study how much C-14 can be expected at different ages based on carbon samples of a known age, to further improve our estimates.
Really depends on what you’re looking at. Carbon dating is one method. Another method would be, if you dug something up, to look at how much sediment is on top of the object and use geological data to determine how long it took to get buried. Another method would be by comparing it to known objects of the same time period.
It depends on the type of radioactive dating being used, but essentially (to my understanding) is that it comes down to measuring the ratio of parent isotopes to daughter isotopes. In the case of carbon dating the carbon-14 is coming from the sun and being absorbed by living cells. But of course the amount of carbon-14 I get could be very different from the amount you get. To control for this you can measure the ratio of carbon-14 to nitrogen-14 in the sample.
Likewise, for longer-term dating, you can use uranium and measure the ratio of lead to uranium to control for different amounts of sample.
There are also other radioisotope dating methods like potassium-argon.
As with carbon dating, there are calibration curves. Those were made over long periods of time using samples for which we knew the dates. There will always be some uncertainty associated with those methods too.
For example, you can use tree rings and ^14 C measurements of those samples to make a calibration curve: https://www.ansto.gov.au/news/new-radiocarbon-calibration-curves-for-a-better-dating-method
You can also use other objects of known ages for which we have historical records.
Along with the radio dating what archaeologists also note what coins are found in digs so you know the date range of objects that are found on that dig. After a few digs they can then say certain types of pottery are from a certain date when found so can then associate other items found at the being from the same general time period.
Well, it was pretty easy for me. We were about the same age and looking for someone to spend time with. The dating just followed naturally.
Along with isotope dating, we use microscopic amounts of atmospheric gas trapped inside polar ice cores, laid down in clear annual layers, to cross check that the ratios of initial isotopes are known. This is cross checked again against tree rings (dendrochronology) that go back thousands of years, as trees that die and fall in peat swamps are very well preserved for many ages.
Measuring via the method you describe is only one of the way we are able to date things, with different methods being good for different range and overlapping in some ranges and reinforcing each other.
We known that for example the ratio of Carbon-13 to Carbon-14 in our atmosphere is more or less fixed. Carbon-14 constantly disappears due to decay, but it also gets constantly created new in the upper atmosphere.
Living things breath in and eat things that have breathed in CO2 from the atmosphere and thus the ratio of C-13 to C-14 in living things stays fixed.
Dead things no longer take in new Carbon. So as time goes by the ratio changes. decay still happens but no new C-14 gets added.
By itself this would not be very good as it relies on the assumption that new C-14 was always created at the same rate it is today. Thanks to the existence of other dating methods we can see ho well that assumption does and does not match up with reality and calibrate measurements accordingly.
> My questions is how do we know how much of a material we are measuring there initially was?
Geochronology has developed methods where the initial amounts can either remain as an unknown, or become part of the solution when determining the age.
The former relies upon using systems where the initial decay product in the mineral being measured is zero or close to zero. This is achieved by selecting a mineral which does not include the daughter product in its crystalline structure, eg. using the U-Pb system to date zircons, which routinely include trace amounts of U in them but reject Pb as it is not compatible with the crystalline structure of Zircon.
The idea is that any Pb is thus the product of U decay. Nature is messier than that, and contamination with Pb (or loss of Pb somewhere along the way) *is* possible, but this can be accounted for using the Concordia method, which relies on the fact that there are two different decay chains between U238 and U235 to different isotopes of Pb. The rate that these progress at dictates a set curve when the two parent-daughter ratios are plotted against each other. If the ratios measured are concordant with the curve the it’s a valid age. If not then the direction of discordance indicates Pb contamination or Pb loss, [something like this.](https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcRpl_6EPostwtL-9mxH_bxUMddDvXFQiKD2yw&usqp=CAU) The two for one decay system gives a kind of internal check of itself and the U-Pb Concordia method is pretty much the gold standard for geochronology (of large ages anyway) in part for this reason.
The other key technique — where the initial isotope amounts are solved for as well as the age — is the isochron method. This relies on measuring isotope ratios in several different minerals and plotting the results on a graph using a reference isotope in the ratios so you have D:R against P:R (where D = daughter, R = reference, and P = parent). The straight line plotted will intersect the y-axis at the initial value of D:R, something like [this](https://upload.wikimedia.org/wikipedia/commons/4/4e/Isochron.jpg). The age can be determined from the slope of the isochron, which is shown as equal to the exponential factor in that diagram. So the whole thing essentially gets reduced to a *y = mx + c* type problem; though it requires some careful field sampling to put into geological context, some very high precision measurements usually using a mass spec, then application of a least squares regression method to measured values in order to get a meaningful final result.
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