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Wherever you find potassium, the isotopes are present in a set percentage that exists the same everywhere in nature, but why is that? Does it have something to do with how the element is produced?

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    $\begingroup$ Define 'in nature'. Small isotopic differences can be used in archeology to determine where minerals and gemstones came from to track prehistoric trading routes. The natural abundance of even stable isotopes will likely be different in different solar systems. $\endgroup$ – Jon Custer Jun 18 '15 at 16:12
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    $\begingroup$ There are plenty of natural processes that alter the ratio of isotopes so the answer in general will be no. An example, evaporation of water alters the ratio of both deuterium and oxygen isotopes and this can lead to significant changes in the ratios depending on the source and history of the water you are examining. $\endgroup$ – matt_black Jun 18 '15 at 19:57
  • $\begingroup$ "presnt" -> "present" $\endgroup$ – Peter Mortensen Jun 18 '15 at 22:59
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The relative natural abundance of isotopes is not the same everywhere. Depending upon what you mean by "everywhere", there are two cases to consider.

  • Extraterrestial

Dust from before the sun was formed (stardust, presolar grains) has a very different elemental and isotopic composition than that found on earth. Depending where a star is in its life cycle different elements and isotopes will be created and destroyed, so it is not surprising that dust from different stars has a very different composition than what is found on earth. As Wikipedia notes,

In these materials, deviations from "natural abundance" are sometimes measured in factors of 100

  • Terrestial

When our solar system was forming, elements and isotopes were not uniformly distributed - close to uniform, but not exactly uniform. This is due to processes like diffusion in which a mass-dependent fractionation occurs. A heavier isotope won't travel as far as a lighter isotope in a given amount of time, so the resulting distribution of the two isotopes will not be exactly equal. While these mass-dependent processes account for most of the isotopic variation in our solar system, mass-independent processes can play a smaller role. It is also suggested that catastrophic events in nearby stars may have also influenced local elemental and isotopic homogeneity. These "original" inhomogeneities will be further altered by a continuation of the mass-dependent (diffusion, bond-breaking and making, etc.) and -independent processes. Natural radioactive decay processes can also lead to changes in local isotope ratios. For example, $\ce{^238U}$ ultimately decays to $\ce{^206Pb}$, so it wouldn't be surprising to find an altered lead isotope ratio (e.g. enriched in $\ce{^206Pb}$) around large uranium deposits.

This paper presents a study of the natural isotopic variation found on earth. Here is a table from the paper that gives an idea of the range in variation. As expected it is much smaller than the extraterrestial variation, but certainly not insignificant. For boron and copper, the isotopic variation is on the order of parts per hundred, but more typically isotopic variation is on the order of parts per thousand.

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    $\begingroup$ And of course, humans modify these ratios as well - the easiest visible example being nuclear power plants. Maybe not something you'd call natural, but it seems that there have been natural nuclear reactors on Earth in the past, working much the same way (though with vastly lower intensity). $\endgroup$ – Luaan Jun 19 '15 at 5:33
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    $\begingroup$ Yes, good point. $\endgroup$ – ron Jun 19 '15 at 13:58
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Short answer: it's not the same everywhere on earth.

Ron's answer is excellent, but the main point is that isotopic ratios vary from place to place and over time.

We can use these geographic variations with isotope analysis to track locations and dates of things.

The stable isotopic ratios of drinking water are a function of location, and the geology that the water percolates through. $\ce{^87Sr}$, $\ce{^88Sr}$ and oxygen isotope variations are different all over the world. These differences in isotopic ratio are then biologically 'set' in our hair as it grows and it has therefore become possible to identify recent geographic histories by the analysis of hair strands. For example, it could be possible to identify whether a terrorist suspect had recently been to a particular location from hair analysis.

Similarly, explosives and other compounds are tested for isotopic ratios to determine their origin (e.g., if the material at a crime scene matches the isotopes in a suspect's house).

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