How do we know the natural abundance of isotopes on Earth?

Without knowing the Average Atomic Mass or the percent abundance, how do we know that Protium is the most prevalent hydrogen isotope? What methods did scientists use to come to this conclusion? How did they reach such a conclusion?

I'm still starting out in learning chemistry and I felt like I hit a boulder. I know the formulas and how to get the natural abundance, but I haven't heard a concrete explanation of the concept. I know that it's impossible to survey all the hydrogen elements on Earth to see which isotope is abundant, so what method did scientists use?

• Same as with everything else in life. Do we have to bite every apple in a crate to find out they aren't rotten? – Ivan Neretin Mar 5 at 6:10
• Sampling and lab measurements. // The mass of individual isotopes is known with far greater precision than the averaged mass of a particular element because of isotope variation. Look at copper for instance. – MaxW Mar 5 at 6:22
• Side note: Equally see IUPAC's committee working on this (example, their biennial reports example), or more recently, https://www.isotopesmatter.com/. – Buttonwood Apr 4 at 13:39
• Isotopic ratios in rhino horns. Trade and diet. luna.cas.usf.edu/~rtykot/NPR2%20-%20Rhino%20Horn.pdf – user55119 May 4 at 15:59

Because we can sample the environment with great precision

You seem to assume that we can't know the exact makeup of a sample unless we already know the components. This is wrong. Mass spectroscopy can reliably measure the exact mass of every isotope in a sample and the relative abundance of each. If, for example, a sample of sea-water is measured, we can reliably tell the exact proportion of all the hydrogen isotopes and all the oxygen isotopes in it.

Given that his is possible, estimating the true natural abundance is a matter of statistical sampling. Ocean and river water is fairly well mixed so this is easier than it sounds (at least when there are no processes that radically alter the isotopic composition). So we have a lot of samples, for example, from different oceans and different locations in those oceans. Given that, we can be fairly confident that the isotopic composition doesn't vary a lot and, therefore, we can get a good estimate of the "natural" abundance of each isotope.

But the techniques we use are precise enough to notice that there are some (small) variations in that composition. Some processes do (very slightly) alter the isotopic ratios. Evaporation tends to happen slightly faster for lighter isotopes, for example, as do some biological processes. Some of those processes are temperature dependent leading to the ability to identify the ambient temperature preset when some fossils were alive by measuring the ratio of oxygen isotopes in them.

The key point is that we do have tools that can measure isotope ratios very precisely. So we know the ratios in any sample very precisely. With a very large number of samples, we can generate a reliable picture of the typical abundance of each isotope which is what we refer to as the natural abundance.

These numerical values have been determined by mass spectrometry.

In brief, it starts form a box like a match box in the vacuum. No air in the room around the box. There are many plates and tubes in this box. First a small tube is introduced for delivering some hydrogen gas in the box. Second two thin metallic points have been introduced in advance one through the roof and one through the bottom of the box. Then a high tension is applied between the two points : a spark is produced that breaks the $$\ce{H2}$$ molecules into parts, producing $$\ce{H}$$ atoms, electrons, $$\ce{H2^+}$$ and $$\ce{H+}$$ ions. These fragments will soon recombined as soon as they get out of the spark. Except if they are prevented to do it by applying an outer tension. And indeed there are two vertical metallic plates on the lefthand and righthand sides of the box.

One of these vertical plates is charged positively and the other negatively. This last one attracts positive ions like $$\ce{H+}$$ and $$\ce{H2+}$$. They will move and fall on this plate. Not all ! Because this plate plate is pierced in its middle, and just on the other side there is another plate which is charged at a higher voltage. So the positive ions arriving in the middle of this hole are more strongly attracted by the second plate and they cross the hole.

Well ! This second plate is also pierced in its center, and it is followed by a third pierced plate, etc. The last plate is not pierced but it is far away from the last but one plate. This whole system of plates produces a thin beam of charged particules crossing all holes before being discharged when hitting the last plate. But between the last plate and the last but one plate, a big magnet is approached that is strong enough to deflect the trajectories of the ions in the beam. Small ions like $$\ce{H+}$$ are more deviated than heavier ions like $$\ce{H2+}$$. So by dividing the last plate into many independent small parts, you may know whether and how many ions have been slightly or strongly deviated. So you may know the proportion of isotopes in the beam.

OK ?