Helium Electrons

  
  • After hydrogen, helium is the second most abundant element in the universe. It is present in all stars. It was, and is still being, formed from alpha-particle decay of radioactive elements in the Earth. Some of the helium formed escapes into the atmosphere, which contains about 5 parts per million by volume.
  • Now, we consider the Helium atom andwill see that due to the attendant 3-bodyproblemforwhichwecannot determineaclosed-form, rst-principles analytic solution, we will have to nd recourse in approximate methods. The Helium atom has 2 electrons with coordinates r1 and r2 as well as a single nucleus with coordinate R. The nucleus carries a Z= +2echarge.

A neutral helium atom is about 0.6 angstroms in diameter, or about 300 times larger. There is nowhere near enough time for electrons to be captured before the helium-5 nucleus splits into helium-4 and a free neutron. In the absence of valence electrons, helium-5 does not undergo any chemical reactions. The helium ground state consists of two identical 1s electrons. The energy required to remove one of them is the highest ionization energyof any atom in the periodic table: 24.6 electron volts. The energy required to remove the second electron is 54.4 eV, as would be expected by modeling it after the hydrogen energy levels.

Helium, the most noble of the noble gases, long thought to be completely inert and thus too standoffish to bond with other atoms, recently surprised chemists by forming chemical compounds after all.

Last year scientists reported producing the compounds—crystals made of sodium and helium atoms—but could not understand how they formed. Now a new team of researchers has offered an explanation: Helium manages to combine with other atoms without making any chemical bonds—that is, without sharing or exchanging any electrons. The element does this by shielding positively charged atoms from each other, acting as a buffer between their repellent charges. “They have proposed an explanation, and I like it,” says Artem Oganov, a chemist at the Skolkovo Institute of Science and Technology in Russia and leader of the group that initially discovered the helium compounds. “This model is predictive and it explains all the observations we have so far.”

Helium electrons

The compounds are stunning because scientists had thought helium extremely unlikely to combine with other atoms. This is because a helium atom is loath to give up its two electrons, which perfectly fill its only electron shell. Every atom has such shells, which hold specific numbers of electrons and structure these negatively charged particles around the atomic nucleus. Atoms prefer their shells to be totally full, and will bond with other atoms that can take or give an extra particle or two to fill out a shell. Elements with shells that are already full and have no electrons to lend are called noble gases—and helium, the smallest of these, is considered the most inert. “And then came this wonderful work last year,” says California State University, Northridge, chemist Maosheng Miao, leader of the team that offered the new explanation. Miao’s graduate student, Zhen Liu, was lead author of the paper, which was published March 5 in Nature Communications. “They found that if you put sodium and helium together and compress it to pressures like at the center of the Earth, sodium can actually react with helium and form stable compounds.” At first some scientists thought helium might be sharing electrons after all. But Miao’s team suggested an alternative explanation: Maybe helium is not giving or receiving any electrons, but is somehow combining with sodium anyway. How to clean out system storage on mac.

High-enough pressure can crush a collection of sodium atoms to the point that the extra electron on each atom gets squeezed out, turning all the atoms into positively charged ions. Each ion then repels all its neighboring ions, because like charges push against each other. Miao and his colleagues reasoned that if helium atoms could come and sit in between sodium ions, the distance between the positive charges would increase—and the repulsive energy would lessen, stabilizing the material. “I think this is the first time ever that there’s no chemical bond involved, and yet you can form a stable compound,” Miao says. “Very clever work,” says Roald Hoffmann, a Cornell University chemist who was not involved in the research.

Based on their hypothesis, Miao’s team performed exhaustive computer calculations using the quantum mechanical laws governing each atom, and found that indeed such compounds should work. “It was exciting that the idea turned out to be correct in the computations,” says Eva Zurek, a chemist at the University at Buffalo, S.U.N.Y., and a member of the team. “We could also predict new compounds that have not been studied previously.” The scientists hope experimentalists will try to create the new compounds, which include combinations of helium with magnesium fluoride and calcium fluoride.

The discovery may also have implications for the composition of elements thought to exist deep inside our planet. Scientists had thought helium, lacking a way to bond with other elements, could not possibly be locked away inside Earth’s rocks. “Now it becomes increasingly clear that this is a gross oversimplification,” Oganov says. “Even helium, the most inert of all, is not actually as inert as we thought. It can actually form stable compounds and be retained in the Earth’s mantle.”

In the future chemists would like to find more general rules to predict when such unusual molecules could arise, because under high pressure many of the normal laws of chemistry do not apply. “This is a weird kind of chemical bonding,” says Richard Dronskowski of RWTH Aachen University in Germany, a collaborator on the team that discovered the sodium–helium combination. “If you think about it for a while, everything’s perfectly reasonable but you don’t expect it at the beginning. It’s fascinating.”

Quantum Numbers: H to Ne

There are four quantum numbers: n, ℓ, m, and ms. Each one is a particular factor in an equation describing a property of the electron. At this introductory level, the equations are not needed. The value of each quantum number is assigned to each electron in an atom by a 'building up' process. Niels Bohr called this process the 'Aufbau' principle: aufbau means 'building up.'

n is ALWAYS the starting point for building up a series of quantum numbers. Each quantum number is then assigned according to a set of rules, each of which took years of study to finally determine. The rules ARE NOT just any old arbitrary ones; they have been determined from a study of nature. Remember the rules:

(1) n = 1, 2, 3, and so on.
(2) ℓ = 0, 1, 2, . . . , n - 1
(3) m starts at negative ℓ, runs by whole numbers to zero and then goes to positive ℓ.
(4) after the n, ℓ and m to be used have been determined, assign the ms value +½ to one electron, then assign the ms value of -½ to the next electron, while using the same n, ℓ and m values.

Also, keep in mind that we use only one n, ℓ, m, and ms value each to make a set of four quantum numbers for each electron. It is this set of four quantum numbers that uniquely identifies each electron.

Helium

Last point: the last column in each table below is called 'Orbital Name.' As you are reading this tutorial, you may not yet know what an orbital is. That's OK, but please understand the concept called 'orbital' is an important one. Here's a real simple description that ignores lots of details: each orbital is a region of space around the nucleus which contains a MAXIMUM of two electrons. Realize that it's more complex than that, but the above description is good enough for now. I hope!!

Hydrogen - one electron

First Electron

n = 1
ℓ = 0
m = 0

In each case, note that we start with the smallest value of n, ℓ, or m possible. Make sure you look over the rules to see how each value was arrived at. ℓ starts at zero and goes to n - 1, which is zero since we get 1 - 1 = 0, when using n = 1. When ℓ = 0, there is only one possible choice for m, which must be zero.

ms = +½

This completes the four quantum numbers for the single electron possessed by hydrogen. I shall build up a table like this:

Atomic
Number
ElementnmmsOrbital
Name
1Hydrogen1001s

Helium Electrons Count

Helium - two electrons

First Electron

Helium Atomic Structure

n = 1
ℓ = 0
m = 0
ms = +½

The first electron in helium has exactly the same four quantum number of the first electron in hydrogen. However, helium has TWO electrons. So we 'build up' from the previous electrons by adding one more.

Second Electron

n = 1
ℓ = 0
m = 0
ms = -½

Notice the same n, ℓ, and m values, but ms has shifted from positive ½ to negative ½. This was the problem Pauli saw in 1925. Three quantum numbers was insufficient to UNIQUELY identify each electron, but a fourth one (the one called ms) did the trick.

Atomic
Number
ElementnmmsOrbital
Name
2Helium1001s
100

Lithium - three electrons

The first two electrons quantum numbers' are EXACTLY the same as the two in helium:

Helium
1, 0, 0, +½ and 1, 0, 0, -½

Third Electron: here's where we 'build up' by adding one more electron.

However, we are now presented with a problem. All the values with n = 1 have been used up, but we have only accounted for two of lithium's three electrons. What to do about the third?

Answer: start with the NEXT n value; n = 2. However, there is a problem with ℓ; do we use ℓ = 0 or ℓ = 1, since both are possible with n = 2?

Helium electrons protons

Answer: start with the lowest value first, so that means using ℓ = 0. (Don't worry, we will use ℓ = 1 soon enough.)

Figuring out m should be easy; when ℓ = 0, m can only equal 0. So n, ℓ, m for the third electron is 2, 0, 0. I'll add in ms in the table below.

Atomic
Number
ElementnmmsOrbital
Name
3Lithium1001s
100
2002s

Beryllium - four electrons

In the building up process, we go one electron at a time. Therefore, we will use the three from lithium and add one more.

Fourth Electron

n = 2
ℓ = 0
m = 0
ms = -½

Notice the same n, ℓ, and m values as the third electron, but ms for the fourth electron has shifted from positive ½ to negative ½.

Atomic
Number
ElementnmmsOrbital
Name
4Beryllium1001s
100
2002s
200

Pretty easy, eh? It stays easy, if you follow the rules. With beryllium, we have exhausted the possibilities for the n = 2; ℓ = 0 combination. However, when n = 2, ℓ can take on another value, namely ℓ = 1. This has consequences for the m value as well and, after we finish, there will be six electrons that have a combination of n = 2 and ℓ = 1.

Here's the rule for m again: start at negative ℓ, run by whole numbers to zero and then go to positive ℓ. Since ℓ = 1, we start with -1, go to zero and end up at +1. This gives us three values for m when ℓ = 1. Hopefully you can see that, since ms takes on +½ and -½, we will wind up with six sets of quantum numbers.

Warning: there's going to be a new rule introduced after boron. So prepare yourself because, just as you thought it was getting easy, there gets added some new stuff. By the way, us mean old teachers didn't make all this stuff up to torture poor chemistry students. Nature really does do what I will explain below. Here's boron:

Boron - five electrons

Following the usual pattern, I've repeated the previous four electrons. As we go on to the ℓ = 1 values, keep in mind that we will start with the lowest value of m, namely negative one.

Atomic
Number
ElementnmmsOrbital
Name
5Boron1001s
100
2002s
200
21-12px

Eventually, I will wind up with three orbital names. 2px is just the first, x meaning the x-axis. Next will be 2py, for the y-axis and the last name used will be 2pz, for the z-axis. These three orbitals are oriented at 90° to each other.

Hund's Rule (named for Fredrich Hund) is the name of the new rule. This rule concerns the relationship between the ℓ and m quantum numbers. When ℓ = 0, m can only equal zero and Hund's Rule does not show up. However, now that we have reached ℓ = 1, m can take on multiple values. Hund's Rule concerns the order in which we assign the ℓ and m values.

Helium

By the way, I'm going to avoid a technical statement of Hund's Rule for the moment. I'll discuss how it works first.

Hund's Rule means that we will use each possible ℓ, m combination ONCE before going back and using it a second time. Here are the three possible ℓ, m combos when ℓ = 1:

m
1-1
10
1+1

For boron, we have used the ℓ, m combination of 1, -1. The key is to see that Hund's Rule requires we go on to the NEXT ℓ, m combination for the next element: carbon.

Carbon - six electrons

Following the usual pattern, I've repeated the previous five electrons. As we continue on with the ℓ = 1 values, keep in mind that Hund's Rule will affect how we assign the next m value.

Atomic
Number
ElementnmmsOrbital
Name
6Carbon1001s
100
2002s
200
21-12px
2102py

Nitrogen - seven electrons

Since we still have not first used all possible ℓ, m values ONCE, we go on to the next ℓ, m combination.

Atomic
Number
ElementnmmsOrbital
Name
7Nitrogen1001s
100
2002s
200
21-12px
2102py
21+12pz

2px, 2py and 2pz are three different orbitals, each one capable of holding two electrons. Notice how, in nitrogen, each of the three orbitals is filled up HALF-WAY (that is, with one electron) before we go back and fill up each orbital with the second electron.

This 'half-filled orbital' has definite chemical consequences. Remember it well. Also, using 2px first, then going to y and then z is purely convention. The x, y, z order is not of consequence in the above examples. However keep in mind the using each letter ONCE first being using it for the second electron is important.

Oxygen - eight electrons

Now that we have used each ℓ, m combination once, we proceed to go back and use each combo the second time. For oxygen to neon, I've marked which electron is the one added.

Atomic
Number
ElementnmmsOrbital
Name
8Oxygen1001s
100
2002s
200
21-12px
this one
added
--->21-1
2102py
21+12pz

Fluorine - nine electrons

Atomic
Number
ElementnmmsOrbital
Name
9Fluorine1001s
100
2002s
200
21-12px
21-1
2102py
this one
added
--->210
21+12pz

Neon - ten electrons

Atomic
Number
ElementnmmsOrbital
Name
10Neon1001s
100
2002s
200
21-12px
21-1
2102py
210
21+12pz
this one
added
--->21+1

We have now completed all possible values for n = 1 AND n = 2. Starting with element 11, sodium, we will proceed on to n = 3. When we finish, we will have used ℓ = 0, ℓ = 1 (and applied Hund's Rule again) and then, before going on to ℓ = 3, we will hit another interesting twist that nature has handed us. We will wind up going on to n = 4 and then coming back to finish n = 3. It will be fun!