K-ar dating calculation

So we need to figure out what our initial amount is. We know what k is, and then we can solve for t. How old is this sample? We saw that in the last video. So if you want to think about the total number of potassiums that have decayed since this was kind of stuck in the lava. And we learned that anything that was there before, any argon that was there before would have been able to get out of the liquid lava before it froze or before it hardened.

So maybe I could say k initial-- the potassium initial-- is going to be equal to the amount of potassium 40 we have today-- 1 milligram-- plus the amount of potassium we needed to get this amount of argon We have this amount of argon 0. The rest of it turned into calcium And this isn't the exact number, but it'll get the general idea. And so our initial-- which is really this thing right over here.

I could call this N0. This is going to be equal to-- and I won't do any of the math-- so we have 1 milligram we have left is equal to 1 milligram-- which is what we found-- plus 0. And then, all of that times e to the negative kt. And what you see here is, when we want to solve for t-- assuming we know k, and we do know k now-- that really, the absolute amount doesn't matter. What actually matters is the ratio. Because if we're solving for t, you want to divide both sides of this equation by this quantity right over here.

So you get this side-- the left-hand side-- divide both sides. You get 1 milligram over this quantity-- I'll write it in blue-- over this quantity is going to be 1 plus-- I'm just going to assume, actually, that the units here are milligrams. So you get 1 over this quantity, which is 1 plus 0. That is equal to e to the negative kt. And then, if you want to solve for t, you want to take the natural log of both sides.

This is equal right over here. You want to take the natural log of both sides. So you get the natural log of 1 over 1 plus 0. And then, to solve for t, you divide both sides by negative k. So I'll write it over here.

And you can see, this a little bit cumbersome mathematically, but we're getting to the answer. So we got the natural log of 1 over 1 plus 0. Well, what is negative k? We're just dividing both sides of this equation by negative k. Negative k is the negative of this over the negative natural log of 2 over 1. And now, we can get our calculator out and just solve for what this time is. And it's going to be in years because that's how we figured out this constant.

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So let's get my handy TI First, I'll do this part. So this is 1 divided by 1 plus 0. So that's this part right over here. That gives us that number. In these materials, the decay product 40 Ar is able to escape the liquid molten rock, but starts to accumulate when the rock solidifies recrystallizes. The amount of argon sublimation that occurs is a function of the purity of the sample, the composition of the mother material, and a number of other factors.

Time since recrystallization is calculated by measuring the ratio of the amount of 40 Ar accumulated to the amount of 40 K remaining. The long half-life of 40 K allows the method to be used to calculate the absolute age of samples older than a few thousand years. The quickly cooled lavas that make nearly ideal samples for K—Ar dating also preserve a record of the direction and intensity of the local magnetic field as the sample cooled past the Curie temperature of iron. The geomagnetic polarity time scale was calibrated largely using K—Ar dating.

Potassium naturally occurs in 3 isotopes: Conversion to stable 40 Ca occurs via electron emission beta decay in Conversion to stable 40 Ar occurs via electron capture in the remaining Argon, being a noble gas , is a minor component of most rock samples of geochronological interest: When 40 K decays to 40 Ar argon , the atom typically remains trapped within the lattice because it is larger than the spaces between the other atoms in a mineral crystal.

Entrained argon—diffused argon that fails to escape from the magma—may again become trapped in crystals when magma cools to become solid rock again. After the recrystallization of magma, more 40 K will decay and 40 Ar will again accumulate, along with the entrained argon atoms, trapped in the mineral crystals.

Measurement of the quantity of 40 Ar atoms is used to compute the amount of time that has passed since a rock sample has solidified. By forcing out the naturally occurring Ar 40, the clock of the dating mechanism is reset or set to zero. Later, when we start discussing the K-Ar dating technique from a Creationary perspective, we will see that this reseting of the clock is a major issue.


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The clock might not always be reset by the heat in the Rock. There are other factors which might not allow the Argon to coming out of the rock as well. An interesting point to make is that the Potassium-Argon process does not date the age of the rock. What it does, is to tell you how long ago the rock was reset, or set to zero.


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  • Potassium-Argon Dating?
  • K–Ar dating.

In addition, some rocks may have been reheated so that the clock was partially reset or fully reset at a later date. So if there are multiple heatings of the rock, the K-Ar dating process may give the researcher a number that is not what the researcher expects to find. Another issue is atmospheric Argon However, this contamination can easily be accounted for in the calculations. Since Argon 40 exists in the atmosphere, there is a possibility that rock samples could be contaminated with atmospheric Argon.

K-Ar dating calculation (video) | Khan Academy

Because the atmospheric Argon is a mix of three different isotopes of Argon: Since there is more Ar than Ar, the amount of Ar is measured to determine the amount of atmospheric Argon that is inserted in the rock. So this factor can be used to estimate the amount of Argon 40 that has come into the rock via Atmospheric contamination.

In any kind of a historical science, assumptions have to be made in the assessing of historical dates. Because it is assumed that man, for example, has ascended over a long period of time, researchers would automatically want to lengthen the amount of time indicated by the artifacts uncovered in archeological digs. They are looking for answers that would fit their present model. I am not trying to say that they are falsifying their data. On the contrary they wouldn't need to falsify anything.

Historical data can be so inconclusive that a host of positions is possible from almost any set of data that is collected. Man is thought to have progressed through a long period of prehistory cave man's experience before some sort of civilization is started. Only after civilization begins can we begin to gather some sort of data from the discovery of the artifacts that are found Pieces of pottery, etc. The artifacts according to today's traditional thinking should be slowly progressing in complexity as it is thought that man is progressing in his abilities and ideas that he uses.

If man is thought to have progressed over long periods of time, even within the later civilization phase of his existence, than surely as the artifacts are recovered from archaeological sites, the theories and ideas developed will reflect the scientist's own original thinking. This is how science normally works. They normally work within a fairly well defined set of theories that have become a paradigm. A paradigm is a theory that is so well accepted that no one seriously questions it. This way of doing science is most prominent when the evidence is fragmentary at best. Assumptions throughout the scientific process are extremely important because they must hold the facts together.

Only when specific data comes that either substantiates or falsifies the previously held assumption, can it be known if the thinking was originally correct. Unfortunately, with fragmentary data, the artifact that might falsify a theory is extremely hard in coming or it could easily be overlooked. So the problem must be solved by a host of assumptions that will probably never be tested. There is also the danger that good data could be thrown out because it doesn't fit with established thinking. For instance, I am told that there are sometimes found in the same level both "early" forms and "modern" forms of man.

Because of what is considered to be an impossibility, the modern forms are assumed to have been examples of intrusions. The modern form is considered to have been buried much later in spite of the fact that the specimens are found in the same level. The areas of science, which are the most successful, which the public notices, are the amazing discoveries in medicine, biology, space exploration, and the like.

These are the areas that deal with the here and now. If an experiment is conducted and the information needed to answer the problem is not forthcoming, then another experiment can be designed to answer the problem. The process can continue until some answer to the problem is understood. The problem is only limited by money, ingenuity, and the technical difficulties that have to be surmounted. In addition to the above limitations of science, historical science is limited by the fragmentary nature of the artifacts it is able to find.

In effect, the accuracy of ideas is limited by the assumptions chosen by the researchers. K-Ar dating is not based on irrefutable data alone. It has as its basis of understanding, various assumptions which concern the conditions of the Earth for hundreds of millions of years. These assumptions were originated within an atmosphere of long age preexisting ideas. Scientists almost never look for indicators in nature that might speak of a very young age for the world's history.

Most scientists do not believe that the short chronology of the Bible has any validity at all and most would consider it counterproductive to pursue such a course of investigation. If in fact such an answer were found, it would be quickly dismissed. It would be assumed that there was something wrong with the idea or the data, and a new scenario would be sought. Some papers give evidence of presenting filtered data. What is meant by filtered data, is that they only present the data that agrees with evolutionary thinking. The other data is eliminated.

Potassium-argon dating and the Cenozoic mammalian chronology of North America. Am J Sci ; This paper is now considered to be a classic paper. Yet they use biotite in an uncritical manor in other areas where the dates they obtained matched their expectations. On Page , we can also note: Thus, of some 65 samples collected by M. Skinner, only 10 could be used. Sometimes the whole rock basalt date is reported, but sometimes only a mineral fraction is reported from the basalt, like biotite or sanidine.

Why is it that one type of date is used one time and not at another time, is not discussed in the paper. As Paul Giem notes: Thus one could pick the dates that fit one's expectations and create a very impressive list of dates with close agreement without there being more than a general correlation of most dates with one's expectations. It should be remembered that these researchers are not being dishonest in their actions.

They think of the long age scenario of evolution as being fact. They do not believe that there is any alternative way to look at history.

K-Ar dating calculation

So when the data does not come out right, it is only natural that they assume that there is something wrong with the dates that do not fit the long age viewpoint. However, when they turn around and say that the data supports the evolutionary viewpoint and not the Creationary viewpoint. This is not right! The data does not support long ages. So, many people try to say something like: But this is not true either, the weight of evidence does not prove anything.

We do not have an issue of weight of evidence. Rather, what we have is weight of interpretation!


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  8. This controversy is not over data. The data can go either way. Very intelligent people believe in the long history of the earth and they have good data to support them. There is no question about it. However, I look at that same data and I come to very different conclusions. This process is legitimate! There is such a thing as multiple interpretation to the data base.

    .K. A R OG Y A M

    There is no proof for either position. On this web page I want to discuss a possible scenario that would allow K-Ar dates to indicate a short age chronology. Such a discussion might never be allowed in normal scientific circles because of the assumptions they choose to believe as being true. There is such a strong consensus of opinion on K-Ar dating and other similar topics that deal with the history of the Earth that alternative viewpoints are probably viewed as being counterproductive.

    Before we start, lets look at the specific K-Ar dating assumptions. The rate of decay half-life , and the branching ratio, of K have not changed. The material in question lost all its argon at an identifiable time, the reset time. No argon has been lost since the time the rock was reset, or set to zero. No potassium has been gained or lost since the reset time, except by decay.

    The ratio of K to total K is constant. The total K, Ar, and Ar in the material in question can all be measured accurately. The seventh assumption is one that scientists are doing their best to fulfill. We should also be able to safely make this assumption. The sixth assumption is also fairly secure.

    When the concentrations of the various K isotopes are measured, the results are always the same. The fifth assumption is fairly safe.