Energy changes within an atom are the result of an electron changing from a wave pattern with one energy to a wave pattern with a different energy usually accompanied by the absorption or emission of a photon of light. Each electron in an atom is described by four different quantum numbers. The first three n , l , m l specify the particular orbital of interest, and the fourth m s specifies how many electrons can occupy that orbital.
The distribution of electrons among the orbitals of an atom is called the electron configuration. The electrons are filled in according to a scheme known as the Aufbau principle "building-up" , which corresponds for the most part to increasing energy of the subshells:. It is not necessary to memorize this listing, because the order in which the electrons are filled in can be read from the periodic table in the following fashion:. In electron configurations, write in the orbitals that are occupied by electrons, followed by a superscript to indicate how many electrons are in the set of orbitals e.
Another way to indicate the placement of electrons is an orbital diagram , in which each orbital is represented by a square or circle , and the electrons as arrows pointing up or down indicating the electron spin. I just did in kind of the horizontal direction. You can have it in a vertical direction. You could also have it on the in-out direction of this page. And if you were wondering where did these shapes come from and if you keep adding more and more energy, you get these more and more exotic shapes for orbitals, think about standing waves.
That's my best hint I can give you that the quantum level, actually at all levels, but especially at the quantum level, you see things like electrons have both particle and wave-like properties. Imagine something like a standing wave where if I were to just take a rope and if I were to just shake it, I might get standing waves that look like that.
If I were to take a some type of a membrane in two dimensions and if I were to push on one side right here if I were to drum on that, you might get, so this part dips down, and then that part dips up. And so when you get to three dimensions, you end up getting this dumbbell shape when you add more energy and then you get more and more and more exotic shapes, just to imagine what some of the first orbitals look like rendered by a computer, you see it right over here.
So if you have your lowest energy electron, you are in what is called an S-orbital right over here and this one we would call 1s 'cause it is at the first shell, the one closest to the nucleus. If you give even more energy, then that electron might jump into the second energy level or the second shell and the orbital in that second shell which would be the default if it's the lowest energy in the second shell would be the 2s orbital.
Once again, you have this spherical orbital, it's just a little, it's more likely to be found further out than the one, it was just in the one shell. Once again, if you add even more energy, you'll fall, you'll still be in the second shell but you will be into one of these orbitals that have higher energies so you could view this as the 2p orbital that is in the x-dimension.
This could be the 2p orbital that is in the y-dimension as some people call that 2px. Some people would call that 2py. This you could view as the in and out of the page so you could view that as the z-dimension. So that is 2pz and the orbitals keep going. There is a d-orbital once you get to the third shell.
Once you get to the fourth shell, there is an f-orbital. All we've talked about right now is an hydrogen. If you keep giving more energy to that one electron, what happens to it?
What is the shape of the probabilities of where it might be into two-dimensional space? As you can imagine, if you have two electrons, it's not exactly the same but this is pretty good approximation.
You can actually put two electrons in this 1s orbital but after that, you can imagine the electrons are repelling each other. So another electron doesn't wanna go there so the third electron that you add is going to end up in the 2s orbital. It's gonna be at that higher energy level and then that can fit two.
So you can fit up to four electrons between the 1s and the 2s. And then the fifth one is going to have to go into one of these p-orbitals.
In effect, we are dividing the atom into very thin concentric shells, much like the layers of an onion part a in Figure 2. Because the surface area of the spherical shells increases at first more rapidly with increasing r than the electron probability density decreases, the plot of radial probability has a maximum at a particular distance part d in Figure 2.
As important, when r is very small, the surface area of a spherical shell is so small that the total probability of finding an electron close to the nucleus is very low; at the nucleus, the electron probability vanishes because the surface area of the shell is zero part d in Figure 2. The density of the dots is therefore greatest in the innermost shells of the onion.
Because the surface area of each shell increases more rapidly with increasing r than the electron probability density decreases, a plot of electron probability versus r the radial probability shows a peak. This peak corresponds to the most probable radius for the electron, Thus the most probable radius obtained from quantum mechanics is identical to the radius calculated by classical mechanics. The difference between the two models is attributable to the wavelike behavior of the electron and the Heisenberg Uncertainty Principle.
Note that all three are spherically symmetrical. For the 2 s and 3 s orbitals, however and for all other s orbitals as well , the electron probability density does not fall off smoothly with increasing r. Instead, a series of minima and maxima are observed in the radial probability plots part c in Figure 2. The minima correspond to spherical nodes regions of zero electron probability , which alternate with spherical regions of nonzero electron probability.
Note the presence of circular regions, or nodes, where the probability density is zero. The cutaway drawings give partial views of the internal spherical nodes. The orange color corresponds to regions of space where the phase of the wave function is positive, and the blue color corresponds to regions of space where the phase of the wave function is negative. Three things happen to s orbitals as n increases Figure 2.
Fortunately, the positions of the spherical nodes are not important for chemical bonding. This makes sense because bonding is an interaction of electrons from two atoms which will be most sensitive to forces at the edges of the orbitals.
Only s orbitals are spherically symmetrical. As the value of l increases, the number of orbitals in a given subshell increases, and the shapes of the orbitals become more complex.
As in Figure 2. The electron probability distribution for one of the hydrogen 2 p orbitals is shown in Figure 2. Because this orbital has two lobes of electron density arranged along the z axis, with an electron density of zero in the xy plane i. As shown in Figure 2. Note that each p orbital has just one nodal plane. In each case, the phase of the wave function for each of the 2 p orbitals is positive for the lobe that points along the positive axis and negative for the lobe that points along the negative axis.
It is important to emphasize that these signs correspond to the phase of the wave that describes the electron motion, not to positive or negative charges. In the next section when we consider the electron configuration of multielectron atoms, the geometric shapes provide an important clue about which orbitals will be occupied by different electrons.
Because electrons in different p orbitals are geometrically distant from each other, there is less repulsion between them than would be found if two electrons were in the same p orbital. Thus, when the p orbitals are filled, it will be energetically favorable to place one electron into each p orbital, rather than two into one orbital.
Each orbital is oriented along the axis indicated by the subscript and a nodal plane that is perpendicular to that axis bisects each 2 p orbital. The phase of the wave function is positive orange in the region of space where x , y , or z is positive and negative blue where x , y , or z is negative. Just as with the s orbitals, the size and complexity of the p orbitals for any atom increase as the principal quantum number n increases. Four of the five 3 d orbitals consist of four lobes arranged in a plane that is intersected by two perpendicular nodal planes.
These four orbitals have the same shape but different orientations. The phase of the wave function for the different lobes is indicated by color: orange for positive and blue for negative. The hydrogen 3 d orbitals, shown in Figure 2.
All five 3 d orbitals contain two nodal surfaces, as compared to one for each p orbital and zero for each s orbital. In three of the d orbitals, the lobes of electron density are oriented between the x and y , x and z , and y and z planes; these orbitals are referred to as the 3 d xy , 3 d xz , and 3 d yz orbitals, respectively. In contrast to p orbitals, the phase of the wave function for d orbitals is the same for opposite pairs of lobes.
Like the s and p orbitals, as n increases, the size of the d orbitals increases, but the overall shapes remain similar to those depicted in Figure 2. These subshells consist of seven f orbitals. Each f orbital has three nodal surfaces, so their shapes are complex. Because f orbitals are not particularly important for our purposes, we do not discuss them further, and orbitals with higher values of l are not discussed at all.
Equivalent illustrations of the shapes of the f orbitals are available. Although we have discussed the shapes of orbitals, we have said little about their comparative energies.
We begin our discussion of orbital energies A particular energy associated with a given set of quantum numbers. This is the simplest case. Consequently, the energies of the 2 s and 2 p orbitals of hydrogen are the same; the energies of the 3 s , 3 p , and 3 d orbitals are the same; and so forth. The orbital energies obtained for hydrogen using quantum mechanics are exactly the same as the allowed energies calculated by Bohr. The different values of l and m l for the individual orbitals within a given principal shell are not important for understanding the emission or absorption spectra of the hydrogen atom under most conditions, but they do explain the splittings of the main lines that are observed when hydrogen atoms are placed in a magnetic field.
As we have just seen, however, quantum mechanics also predicts that in the hydrogen atom, all orbitals with the same value of n e. Note that the difference in energy between orbitals decreases rapidly with increasing values of n.
In general, both energy and radius decrease as the nuclear charge increases. As a result of the Z 2 dependence of energy in Equation 2. The most stable and tightly bound electrons are in orbitals those with the lowest energy closest to the nucleus. In ions with only a single electron, the energy of a given orbital depends on only n , and all subshells within a principal shell, such as the p x , p y , and p z orbitals, are degenerate.
For an atom or an ion with only a single electron, we can calculate the potential energy by considering only the electrostatic attraction between the positively charged nucleus and the negatively charged electron. When more than one electron is present, however, the total energy of the atom or the ion depends not only on attractive electron-nucleus interactions but also on repulsive electron-electron interactions.
When there are two electrons, the repulsive interactions depend on the positions of both electrons at a given instant, but because we cannot specify the exact positions of the electrons, it is impossible to exactly calculate the repulsive interactions. Consequently, we must use approximate methods to deal with the effect of electron-electron repulsions on orbital energies. If an electron is far from the nucleus i. Hence the electrons will cancel a portion of the positive charge of the nucleus and thereby decrease the attractive interaction between it and the electron farther away.
As a result, the electron farther away experiences an effective nuclear charge Z eff The nuclear charge an electron actually experiences because of shielding from other electrons closer to the nucleus. This effect is called electron shielding The effect by which electrons closer to the nucleus neutralize a portion of the positive charge of the nucleus and thereby decrease the attractive interaction between the nucleus and an electron father away.
If, on the other hand, an electron is very close to the nucleus, then at any given moment most of the other electrons are farther from the nucleus and do not shield the nuclear charge. Thus the actual Z eff experienced by an electron in a given orbital depends not only on the spatial distribution of the electron in that orbital but also on the distribution of all the other electrons present.
This leads to large differences in Z eff for different elements, as shown in Figure 2. The trend that you see in Figure 2.
0コメント