Iron-56; 126 pm (picometers = 10^-12 meters) Atomic Radius and allotropes (II)
In the previous post I gave links, images, and explanations for everyone to know where I found my reasoning which, in this post I’ll explain as simple as possible. In the event that you find something complicated or don’t know why I say so, you have two non mutually exclusive options: read this series previous post, or make a question.
I told you there are some allotropes for iron-56, the most abundant and stable isotope of this metal, commonly referred to as simply Fe, as we know it in school.
The radius for this element has a lenght of 126 picometers. By making some basic calculi you can reach the radius for Ni, one of the daughter isotopes for iron, whose value is 149 picometers, and also to the value for the radius of copper-63 [+1], Cu, also a daughter isotope of iron (which you can check in the previous post or in other source of your choice), whose radius is 145 picometers.
Copper, and Zinc appear in the same right-left order in my table and the IUPAC’s table, and the two along with others are daughter isotopes of iron, Fe.
However, there are some differences between both models (mine and IUPAC’s), being in my model a traditional s type orbital, whereas in IUPAC’s they pertain to a d type orbital.
Notice, there is no direct correspondence between my orbitals ordering and the IUPAC’s traditional orbital ordering, so you cannot conclude my S orbital is equivalent to IUPAC’s s orbital, so, to understand my model (which has a lot more things on account than only the chemical external properties of the valence shells), you must re-read my explanations on how my table works.
My [Capital] S orbital is that into which there are only two elements in each sub-level (row). In fact all my orbitals are easy to see, they are all in separate rows, being my sub-levels of, two, six, ten, and sixteen, evens on the right, odds on the left, and increasing in number from the central axis, to the right and left respectively.
The last level in my model, is the fifth level, it has an orbital more, which exceeds the 16 positions, and it is in that sublevel that Uuo, Uus… Cf, and Bk are. I do not propose any number of positions for this last sub-level.
To get from 126 to 149, which are in picometers the values for iron and nickel radiuses respectively, without using decimal values in order to find a direct ratio between one another, the only thing to do is to find how to increase the 23 picometers of difference between these two values, and add it to iron’s radius (or subtract them from nickel radius).
23 x (14/3) = 107.333333333333… this number never ends, as is the case for any third: 1/3 = 0.3333333333333…
However, if you multiply one third for three, it is not difficult to see it gives 1, but if you make the calculus with a computer, or a calculator, it will give 0.99999999999… instead of 1, which is easy to see in this example, is a wrong calculus, though it is accepted by all calculators’ inputs, throughputs, and outputs.
The same happens with the above number: 107.3333333333333… multiplied by 3, gives 321.999999999999, but the real quantity is not a pure periodic decimal, instead it is a one, to add to 321, thus the above calculus multiplied by 3 is indeed 322, despite all calculators in the world.
Analogous calculi can be made, but since I don’t want to make a long post just as the previous one is, I’ll give other calculi: those for the proportion IN LENGHT, not in weight, which is what commonly is done in chemistry calculi (and are denoted as wt% | tantos por ciento en peso, in Spanish), but in radius, so the percent values you will see, and peer-check yourselves are not for mass, but for length (area, and volume).
I’m a bit tired today, so I will explain better these values tomorrow.
92% iron and 8% nickel passing to 68% and 32%, and an overlenght of 10% of other elements and molecules.
And 76% and 24% and an overlenght of 10%
I leave it here because it is a process of transformation through various concentrations, I wrote about it in ‘New Tectonics’ series in January and February this year, search for it.
[December 28th 2015 update]
Before going on explaining, what I said in this post, I will upload some images in which you can see directly information on mononuclidic isotopes (the en.wikipedia to Isotopes article is long, but I think this is interesting), and also their positions in IUPAC’s table, and my table.
For the explanation on these type of isotopes read any text of your choice, regarding my and IUPAC’s ordering, I think the images are eloquent enough themselves.
And now I’ll go on explaining on iron-56, commonly known as, Fe.
I said previously in this post
‘92% iron and 8% nickel passing to 68% and 32%, and an overlenght of 10% of other elements and molecules.
And 76% and 24% and an overlenght of 10%’
In ‘New Tectonics’ I told this was a process of decay of iron into other elements, mainly nickel, silicon, and aluminium. The Moon has a composition in a proportion like that, according to data known by astronomers and astrophysicists, 92%Fe/8%Ni. This composition is also the composition of the Earth inner core (radius of about 3100 kms).
What happened, was a massive decay of iron giving as a result, the releasing of overheat in the core, by sending out a big amount of mass which kept hot and with those proportions, in the first place. That massive amount of mass is our satellite: the Moon (I’ll write something about two-body’s reduced mass, barycenters, and three-bodies being then the third body to consider the Sun).
You can multiply 92 by 126, on the one hand, and 8 by 149, on the other hand, and you will find, those numbers compared with astronomical distances between Earth, and the Moon, are in direct proportions, but there is an excess which resulted into today’s Earth radius + the excess: the Moon’s radius.
The Earth, had a radius millions of years ago, of a half the radius it has today, so, it tripled, ejecting the Moon, and then iron kept on decaying at a much slower pace, and formed the mantle, mainly compossed of silicon and aluminium.
Today’s update ends here, I’ll go on explaining more and better on all this (excuse me, but my schedule is a bit busy these days).
Anyway, I think you should know two important facts:
- One thing is heat getting out from the inside, and other thing is heat getting in from the outside.
- Decay from outside, can concentrate into the core, but at least the focus of the problem is already on the Earth’s outer crust.
[2016 January 5th]
I will give you another calculus here. This is for the 19 picometers of difference between iron-56, Fe, and Copper, Cu.
(19 x 14 x 15 )/ 3 = (19 x 14 x5) = 1330 =>19 = 1330 / (14 x 5) = 1330 / 70 = 133 / 7 = 19
These numbers when referring to atoms result in direct proportions. I learned it while studing chemistry in the University, to balance stechiometry equations: usually fractional numbers are not used, nor preferred to integers, which is how I calculated. This is why, I don’t simplify directly, and give long lines with transformations.
Had I put 133/7 = 19, wouldn’t be so clearly seen.
Instead of going on with this topic in this series (unless someone asks for specific aspects), I will start a new series ‘New Tectonics Revised’ in which, I will go on explaining this, and I will be updating some posts I wrote last year, making some corrections where necessary.
Last year I started writing about this, but left it aside, so, in ‘New Tectonics Revised’ I will give better (and in a more serious tone) explanations.