Minimum amount of energy required for the transference of electrons between atoms
11 Minimum amount of energy requiredfor the transference of electronsbetween atoms
Pillon, Matheus Barbiero
Institute of Bom Jesus IeluscJoinville, SC, Brazil
Abstract
The purpose of this article is to show a different way to calculate the electrontransfer between atoms. It can be used as a base for calculating the minimalelectricity, showed here by Joules, necessary for the transference of electrons.There is already a Table, in which you find the result of all of the electrictransfer necessary in most of the materials. In this article, we tried togeneralize the electricity necessary, but if you want the result in a specificfield or material, you can search the references and collaborates workers.
Keywords: Electron Transfer, Electrodynamics, Quantum Physics, Quantum mechanics.
1. Introduction
Quantum physics, also known as quantum mechanics, is one of the newest areas ofphysic. Created in 1900 by Max Planck, quantum mechanics is known as one of the hardestsubjects to learn and work with. The field deal with the behavior of matter and energy in thescale of atoms and subatomic particles/waves [2]. The quantum physic, seen as a difficult subject,is used every day by everyone. It can be regarded in actions as charging your cellphone, turningon your microwaves, or even clicking on the red bottom to watch your TV [3] [4].One of the subareas of quantum mechanics is electrodynamics, which is the centralspeech of this article. Already worked by famous scientists as
Richard Feynman, Sin-ItiroTomonaga and Julian Schwinger , the subarea deal with the reactions of the electron or radiativecorrelation on precisely quantum phenomena [5] . The main idea of this article is the minimalpurposeful transfer of electrons between atoms. It proposes the minimal amount of energynecessary to send the electron from one atom to other.This article is divided into four parts: Introduction, Collaborates workers, Proposal, andConclusion. Each part has details about the work’s ideas and ways to understand and prove them.
2. Collaborates workers
One of the main ideas of this article is based on the works of Bohr, in which he proposesone formula (Equation 1) that calculates the amount of energy necessary for changing electronsbetween atoms axes. I used it as a principle for creating the formula that cares about the energynecessary for the achievement of an electron on a different atom [1].In his work, Niels Bohr does speak about the changingof electrons in the same atom in different axes, shown in figure1, but he has never spoken about the transfer of electronsbetween atoms, which is the main idea of this article (Figure 1)[1]. One example of this technology nowadays is showed byprofessors at the Duke University and the University of Cyprus,named
David N. Beratan, Spirios S. Skourtis, Ilya A. Balabin,Alexander Balaeff, Shahar Keinan, Ravindra Venkatrammi,Dequan Xiao , in which they speak about the consequences ofthe electron transfer reaction in proteins, chemistry and biologyareas. They show and calculate, with graphics and images, howis the reaction and how the protein is modified with electrontransfer [6].We could do these works with the formula (Equation 2)showed in this article, which would help with the energy wastedand also the conduct of this observation in laboratory.Another group of physicians that speaks aboutelectron transfer is
Ziegler and Biersack (1985). Intheir article, they speak about how calculating thestopping and the final range distribution of ions inmatter. They use graphics and tables, in which theyshow the evolution of the ionized atoms stopping. Itis also calculated in the article, the hydrogen mass,and energy lost on the stopping [7] . They have usedtheir formula, which contains more difficult termsthan mine, but, on the other side, their formula ismore appropriate for their work, which requests moredetailed and approximate results [7] . It can be alsocited here, the article of
Cazaux , which speaks aboutthe ionizing radiation in electrodynamics, with moreprecise, the changing effects of transmission electronmicroscopy, with formula, figures, and graphics [8] .In his formula, there is the presence of the integral,because of the electrical transmission changing. Hedeals with the temperature changing and more thanone angle field [8].
Figure 1: The model made by Niels Bohr. Inthe image, it shows the axes from the atom,represented by the letter n . The letter Z isused as a representation of the atomicnumber. The positive signal ( + ) and the letter e are showing that the atom is ionized, whichmeans that it has fewer electrons in its axesthan normal.Based on Niels Bohr [1] Table 1: It is shown here the section of exogenous redoxmediators used for microbial fuel cells. In other words, it isa section of the microbial fuel cells, which are chemicalswith an electrochemical activity that are growing orcreating themselves outside of an organism or part of it.This table is showed in Uwe Shröder’s article.Font: Uwe Schröder [9]
On other hand, his formula has a lot of terms and deals with the changing, but not with astatic moment, which is carried by my formula [8].
There are also a lot of examples in specifics areas that wouldn’t handle in this article,even though I will cite some of them in different fields:
Uwe Schröder has shown in his article inApril of 2007 solutions of the problem to the electron transfer between microscopy beings andhas also proposed the energy efficiency of the anodic electron transfer mechanism. For his work,he needed to measure the electron’s energy between the two microbial full cells, which he couldhave used my formula [9].Besides, his job is related to mine by the electron transfer and the electrodynamics, evenso, he uses it in a subarea, where is more important the details that he has achieved with the
Table 1 and the
Table 2 [9]. The article of
Yan Jiao, Yao Zheng,Mietek Jaroniecb, and Shi Zhang Qiao promisethe Design of electrocatalysts oxygen- andhydrogen-involving energy conversionreactions. Their article’s main idea is to studyone way to reduce the climate change due to theenergy conversion reaction [10].Their works are related to mine becauseof the energy conversion reaction, which iscarried by electron transfer. The article workswith specific areas, because of the hydrogenand oxygen-involving energy and because ofbeing treated in the chemicals field [10].Another chemistry article, in which it isspoken all of the electron transfer reaction inthis area was written by
Rudolph A. Marcus.
Hetells us about all of the discoveries since the1940s and explains how to solve problems withsome specific applications and exceptionsshowed in these articles [11].
3. Proposal
Before we begin the explication, we need to show the condition for the function of theformula. In other words, I’ll show the necessary hypotheses. Opening, we need to consider thatthe two atoms are in a straight line and the electron needs to be static, in other words, with nospeed. This is necessary for the function of the formula, with this, the electron will go in astraight line between the atoms. This lets us see the next condition, we need to consider that theelectron follows the same steps and the same comportments inside and outside the atoms.Without that, the electron couldn’t be transferred to the next atom.
Table 2: It is the comparative of the Table 2. While the Table 2 has theinformation about the section of exogenous redox mediators used formicrobial fuel cells, this table shows the selection of extracellularbacterial (endogenous) redox mediators. It was used by Uwe Shröderfor his research, but what is the difference between the two tables?While the Table 2 speaks about exogenous microbial fuel cells, whichmeans antigens entering from outside of your body to inside of yourbody, and this table tells us about Endogenous, which means antigensthat are already inside of your organism and are causing problems.Font: Uwe Schröder [9]
Also, we need to suppose that we can measure the distancebetween atoms. If this is not possible, the whole idea of this article isfalse. Finally, we need to set the limits of the atom. As Niels Bohrhas shown us, the potential energy of an electron on axis one is −18
J, and, with his formula Equation 1, we can measure all of thepotential energy of the electron on all of the axes from the atom [1] .With this in mind, we can say that the minimum energy necessary ismore than −18 , since the electron needs to be a positron, anti-electron, to be guided to his final destiny, the next atom. We know thatthis is the energy necessary for the electron transform itself, because ofBohr’s formula Equation 1, which shows us the potential energy of theelectron, in this case, −18 , considering that the electron is on the first axis. It is alsoconsidered here that it needs to still use the kinetic energy for ruining in his straight line. If it isnot possible, he will be stopped in the vacuum [1] . Even though there is minimal energynecessary, there isn’t any limit, because this formula aims to transfer whatever electron atwhatever distance, the only thing necessary is the measurement of this distance.
The principle of this article, as the name suggests, is for searching for the minimalpurposeful transfer of electrons between atoms. It suggests that, with the formula, we could savethe electricity or use it differently way without put in more or less than necessary for theescaping of the electron in direction of another atom. We can apply it in laboratory on researches,in which we need a negative energy atom and, due to the lack of money or intending to saveenergy, we use the formula for finding what is the minimum necessary, showed in Equation 2.
𝐸𝑎𝑡 = 𝑑𝑟𝑓|(𝑛 − 𝑛 + 1 )| × |𝐸𝑓| ÷ (𝑛 − 𝑛 + 1 ) Equation 2: Energy’s formula of minimal purposeful transfer of electrons between atoms
The letter “d” represents the distance between the two atoms, while the letter “n”represents the number of the axis the electron is. The “fs” after “E” and “r” mean fundamental,which is necessary for the functioning of the formula in more than one atom, you just need tofind the fundamental energy and radius.The module on the “Ef” is necessary because the electron needs to have positive energyto transform itself on a positron, anti-electron, and get out of the atom. The module is alsonecessary on the parentheses that are multiplied by “rf”, since the distance is never negative ifthere is progression. This formula can also be reduced with just three points, shown in Equation3.
𝐸𝑎𝑡 = 𝐷𝑎𝑑 × 𝑎𝐸
Equation 3:
Energy’s formula of minimal purposeful transfer of electrons between atoms in parts
The term “Eat” is named that way, because of its function. It means “Electric atomictransfer”, while the terms “ad” and “aE” mean axis distances and axis energy or axis potentialenergy. The isolated letter “D” tells us about the distance between the atoms. The calculus madein this article uses the hydrogen atoms, which the fundamental energy is −18 and the
𝐸𝑝 = 𝐸1𝑛 Equation 1: This is the formulaof Bohr, in which he showedhow to measure the potentialenergy of each electron on aspecific axis. The letter “n” isthe number of the axis and theletter “E” is the energy, in thiscase, E1 is −2.18 × 10 −18 .Font: Niels Bohr [1] fundamental radius is −11 , which are carried by the first axis. For finding thisinformation, you can search the table from Niels Bohr on the reference [1].
For the understanding of the formula, we can imagine one ordinary action where most ofus normally ask in a day by day. You need to go to the supermarket, where you will do yourmonthly shopping, but you live on a dangerous street, because of that, you should go with a car,you don’t have one, consequently, you take your brother’s car to go. When you join into the car,which is garbage near a lightbulb, you find out that the car has less than one eighth of your fuel.You know the distance between your house and the supermarket, since you have opened your
GPS and set your address and the location where you want to go, in this case, supermarket.The car that you are using is your brother’s automotive, by consequence of that, you donot know how much it loses per kilometer. How can you know if you will or not go to thesupermarket without needing to call an engineer because of the lack of fuel? In this situation, youwill probably call your brother and ask for the information or simply don’t go to the supermarket,but as this is an example, we cannot do such things. You drive from the lightbulb, where yourbrother’s car is garbage, to the door which you use for joining the street. When you achieve thedoor, you discover that you have lost 100 ml of gasoline.Subsequently, you drive until you achieve the first car garaged in your street and you seethat you lost, in total, 150 ml of gasoline. You subtract the two losses of gasoline and find outthat the fuel’s lost between the distance of your garage and the first car garaged in your street is50 ml.Knowing, due to the
GPS , that there are more than 50 meters to your destiny, and you drove just5 meters, you know that the total gasoline needed to the supermarket and the first car garaged inyour street is 500 ml. Let’s try to use the formula for calculating the example:
You have probably noted that I have used the module on this calculus, which are not usedon the formula (Equation 2). This is necessary in this case, because the result would be negative,without it, the result wouldn’t be correct.Even though, on an atomic scale,with more distance of the proton,more have the electron positiveenergy, which means, bigger numberof axis, less negative energy. If youwant a more scientific explication, Ishall show with images, for a betterunderstanding.We see in the Figure 2 thatthe atom A is a hydrogen atom, dueto its isolated proton, and it has an
Figure 2: The first atom is represented by the letter “A”, while the atom, which theelectron will be transferred, is represented by the letter “B”. The letter thatrepresents the electron that will be transferred is “ ”Font: The Author. electron. Let’s imagine that we want to throw the electron α into the atom B. For this to behappen, we need to first know which axis the electron is, in this case, it is on axis two.The second step is to discover the next axis. For example: axis 2+1= axis 3. The thirdstep is finishing the algebra from the formula with the information you already have.Continuing, you just have to find what is thedistance between the axis from the electron α and thenext axis.Then, you’ll finish the algebra of the formula.After finishing the part “ad”, the distance betweenaxis, and “aE”, the energy between axis, you need todivide the part “ad” by D, the distance between atoms.Finally, multiplying the result by the party“aE”, getting the final result.In Figure 3, there is a closer picture of thedistance of the axis one and two, which can be usedfor the understanding of the formula.You are probably asking why I would have tocalculate the distance between the axis if you want toknow the energy between the atoms. This is necessarybecause of the idea of the formula, I have used amechanism that takes the distance between the axisand divide all over the distance between the atoms,with that you just need to transcribe the energy. Theformula seems to be kind of difficult, but the idea isquite simple. The only thing that makes it look difficult is the Bohr’s formula that is needed inthese cases [1]. For the best knowlegdge of the formula, I will use it with imaginary numbers for theexample. We can suppose that the distance between the atom with electrons and the atom wewant to transfer is 1nm and the axis the electron stayed is the number three. With the formula, wefirst discovered the subtraction of the axis, in which the electron stayed, and the next axis.
𝐸𝑎𝑡 = 𝐷5.3 × 10 −11 | 𝑛 − 𝑛 + 1 | × 2.18 × 10 −18 ÷ (𝑛 − 𝑛 + 1 )𝐸𝑎𝑡 = 𝐷5.3 × 10 −11 |(3 − 3 + 1 )| × 2.18 × 10 −18 −18 −11 |(9 − 16)| × 34.88 × 10 −18
144 − 19.62 × 10 −18 −11 × 7 × 15.26 × 10 −18
𝐸𝑎𝑡 = 𝐷37.1 × 10 −11 × 15.26× 10 −18
𝐸𝑎𝑡 = 137.1 × 10 −11 × 15.26 × 10 −18 Figure 3: It is shown here the potential energy from theaxis one and axis two and the radius from the axis one andtwo to the proton, cited for the understanding of the idea ofsubtracting between the two axes and why used you use it.The two blue points are the electrons, while the big blackpoint is the proton. With this in mind, you can alreadyguess that this is a representation of a hydrogen atom, butthe formula can also be used with different atoms.Font: The Author
𝐸𝑎𝑡 = 15.26 × 10 −18 −11
𝐸𝑎𝑡 = 15.2637.1 × 10 −7 As we see, the Joules necessary from the axis three to four is −18 .Continuing our calculus, we shall look for the multiplication between −18 and 1/ −11 , getting the result of × 10 −7 J necessary for this distance.
There are always exceptions, in which there are problems that in some circumstances theformula won’t work, however, there are also problems where, with the adaption of the formula,the same one can be used.In their article,
William A. Tisdale, Kenrick J. Williams, Brooke A. Timp, David J. Norris,Eray S. and
Aydil, X.-Y. Zhu have shown the efficiency of nanocrystals in hot atoms. They haveshown the solution of high-energy photons transfer, but they have not mentioned what could bedone for solving the electron transfer [12].In these conditions, it is already known that one of the solutions is the addition of avariant “T” on the formula, but, more than that, the formula needs to be restored. Knowing that,with the solar cells, the photons are reduced by ~31%, cited by Tislade, the electron transfercould also change and knowing that it cools fast (~1 ps), also cited by Tislade, it would benecessary an equation with variation, including an integral. In whatever way, this is not the goalof this article, it will be carried in future works [12].In a different scenario, for example, the uses of artificial atoms, how could the electronsbehave? The answer is shown by [13] [14].The behave of the electron is not that different, even so, one detail is quite important:Some barriers are allowed for being cross on artificial’s atoms. This means that we need to becareful about which field and which interferences: pressure, temperature, etc., the two atoms thatwe chose that will be the ones are [14] [13].To find the solution for this problem, we will need to search for the conditions of theplace and then think about the changes that will need to be done. What could be done in futuresarticles, knowing that this is not the goal of this article.
4. Conclusion
In conclusion, we have seen in this article references and formulas for the minimalpurposeful transfer of electrons between atoms. It can be used by radiation conducted inlaboratory and it can also be used in futures research. It is pendent here what the electron will doif there are interferences of high or low temperature or high or low pressure between atoms,where the formula does not work or even if there are possibilities that with interference, theelectron couldn’t, with the minimal amount of energy calculated by the formula, achieve itsdestiny. The problem with the temperature could be solved with the variant “T”, but it is notmuch necessary if there aren’t many changes in the field, for example, a well-controlledlaboratory.It is also pendent in this article, the result with details and specific information in aspecific material or field. The formula can be useless if you are working in an area where youhave to show non-approximate results or a lot of details about electron transfer. Finally, all of thequestions that I have cited in the
Exception section, which I have already said the possiblesolution of the problems.
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