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This content was accessible as of December 29, 2012, and it was downloaded then by Andy Schmitz in an effort to preserve the availability of this book.
PDF copies of this book were generated using Prince, a great tool for making PDFs out of HTML and CSS. For more information on the source of this book, or why it is available for free, please see the project's home page. DonorsChoose.org helps people like you help teachers fund their classroom projects, from art supplies to books to calculators. One property of waves is that their speed is equal to their wavelength times their frequency. For light, however, speed is actually a universal constant when light is traveling through a vacuum (or, to a very good approximation, air). Because the speed of light is a constant, the wavelength and the frequency of light are related to each other: as one increases, the other decreases and vice versa. Seconds are in the numerator and the denominator, so they cancel, leaving us with joules, the unit of energy. There are two fundamental ways of generating light: either heat an object up so hot it glows or pass an electrical current through a sample of matter (usually a gas). Why does the light emitted from an electrically excited gas have only certain colors, while light given off by hot objects has a continuous spectrum?
The spectrum of hydrogen was particularly simple and could be predicted by a simple mathematical expression. In 1913, the Danish scientist Niels Bohr suggested a reason why the hydrogen atom spectrum looked this way.
This means that only certain frequencies (and thus, certain wavelengths) of light are emitted. Bohra€™s description of the hydrogen atom had specific orbits for the electron, which had quantized energies.
In the quantum-mechanical model of an atom, the state of an electron is described by four quantum numbers, not just the one predicted by Bohr. Within a shell, there may be multiple possible values of the next quantum number, the angular momentum quantum numberAn index that affects the energy and the spatial distribution of an electron in an atom. The next quantum number is called the magnetic quantum numberThe index that determines the orientation of the electrona€™s spatial distribution. The particular value of ma„“ dictates the orientation of an electrona€™s distribution in space.
The a„“ quantum number dictates the general shape of electron distribution in space (Figure 8.6 "Electron Orbitals").
The final quantum number is the spin quantum numberThe index that indicates one of two spin states for an electron. Of the set of quantum numbers {n, a„“, ma„“, ms}, which are possible and which are not allowed? The quantum number n is an integer, but the quantum number a„“ must be less than n, which it is not.
Although we know now that a gas discharge gives off only certain colors of light, without a prism or other component to separate the individual light colors, we see a composite of all the colors emitted. The different colors of these a€?neona€? lights are caused by gases other than neon in the discharge tubes. A continuous spectrum is a range of light frequencies or wavelengths; a line spectrum shows only certain frequencies or wavelengths. Electrons are typically organized around an atom by starting at the lowest possible quantum numbers first, which are the shells-subshells with lower energies. The Pauli exclusion principle has the net effect of limiting the number of electrons that can be assigned a shell-subshell combination of quantum numbers. Now that we see how electrons are partitioned among the shells and subshells, we need a more concise way of communicating this partitioning. The three electrons for Li are arranged in the 1s subshell (two electrons) and the 2s subshell (one electron).
Now that the 2s subshell is filled, electrons in larger atoms must go into the 2p subshell, which can hold a maximum of six electrons.
Now that the 2p subshell is filled (all possible subshells in the n = 2 shell), the next electron for the next-larger atom must go into the n = 3 shell, s subshell. For larger and larger atoms, the order of filling the shells and subshells seems to become even more complicated. Electrons in larger atoms fill shells and subshells in a regular pattern that we can follow. Electron configurations are a shorthand method of indicating what subshells electrons occupy in atoms. Abbreviated electron configurations are a simpler way of representing electron configurations for larger atoms.
Three subshells (1s, 2s, 2p) are completely filled, and one shell (3s) is partially filled.
Determine the expected electron configuration of an element by its place on the periodic table.
In Chapter 3 "Atoms, Molecules, and Ions", we introduced the periodic table as a tool for organizing the known chemical elements.
See the license for more details, but that basically means you can share this book as long as you credit the author (but see below), don't make money from it, and do make it available to everyone else under the same terms.
However, the publisher has asked for the customary Creative Commons attribution to the original publisher, authors, title, and book URI to be removed. Before we can understand the composition of atoms (especially electrons), we need to understand the properties of light. We can use this equation to calculate what one property of light has to be when given the other property. It turns out that for light, the energy of the a€?packagea€? of energy is proportional to its frequency.
Its value is 6.626 A— 10a?’34 JA·sa€”a very small number that is another fundamental constant of our universe, like the speed of light. We are mostly familiar with visible light, which is light having a wavelength range between about 400 nm and 700 nm.
Incandescent lights and fluorescent lights generate light via these two methods, respectively.
He suggested that the electron in a hydrogen atom could not have any random energy, having only certain fixed values of energy that were indexed by the number n (the same n in the equation above and now called a quantum numberAn index that corresponds to a property of an electron, like its energy.). Figure 8.5 "Bohra€™s Model of the Hydrogen Atom" shows a model of the hydrogen atom based on Bohra€™s ideas.
However, later researchers generalized Bohra€™s ideas into a new theory called quantum mechanicsThe theory of electrons that treats them as a wave., which explains the behavior of electrons as if they were acting as a wave, not as particles. The first quantum number is called the principal quantum numberThe index that largely determines the energy of an electron in an atom. Any s orbital is spherically symmetric (part (a) in Figure 8.6 "Electron Orbitals"), and there is only one orbital in any s subshell. Electricity excites electrons in the gas atoms, which then give off light as the electrons go back into a lower energy state. The second electron can also go into the 1s shell-subshell combination but only if its spin quantum number is different from the first electrona€™s spin quantum number. However, now the Pauli exclusion principle implies that we cannot put that electron in the 1s shell-subshell because no matter how we try, this third electron would have the same set of four quantum numbers as one of the first two electrons.


For example, in any s subshell, no matter what the shell number, there can be a maximum of only two electrons.
Two additional electrons can go into the 2s shell-subshell, but now this subshell is filled with the maximum number of electrons. Chemists use an electron configurationThe representation of the organization of electrons in shells and subshells in an atom. This is because after the 3p subshell is filled, filling the 4s subshell first actually leads to a lesser overall energy than filling the 3d subshell. There are some useful ways to remember the order, like that shown in Figure 8.7 "Electron Shell Filling Order". The subshells you reach along each arrow give the ordering of filling of subshells in larger atoms.
An abbreviated electron configurationAn electron configuration that uses one of the noble gases to represent the core of electrons up to that element. So for larger elements, the abbreviated electron configuration can be a very useful shorthand. In many cases, an electron goes from a higher-numbered shell to a lower-numbered but later-filled subshell to fill the later-filled subshell. At this point, you do not need to memorize the exceptions; but if you come across one, understand that it is an exception to the normal rules of filling subshells with electrons, which can happen. The valence electrons, electrons in the outermost shell, are the determining factor for the unique chemistry of the element. You may also download a PDF copy of this book (40 MB) or just this chapter (3 MB), suitable for printing or most e-readers, or a .zip file containing this book's HTML files (for use in a web browser offline).
The units on Plancka€™s constant may look unusual, but these units are required so that the algebra works out.
Light can have much longer and much shorter wavelengths than this, with corresponding variations in frequency and energy.
Quantities that have certain specific values are called quantizedWhen a quantity is restricted to having only certain values.
Quantum mechanics predicts two major things: quantized energies for electrons of all atoms (not just hydrogen) and an organization of electrons within atoms. True neon lights, with neon gas in them, have a reddish-orange light due to the large amount of red-, orange-, and yellow-colored light emitted.
Under normal conditions, the single electron would go into the n = 1 shell, which has only a single s subshell with one orbital (because ma„“ can equal only 0).
Once the s subshell is filled up, any additional electrons must go to another subshell in the shell (if it exists) or to higher-numbered shell. The n = 2 shell also has a p subshell, so the remaining two electrons can go into the 2p subshell. Recall that while the principal quantum number largely dictates the energy of an electron, the angular momentum quantum number also has an impact on energy; by the time we get to the 3d and 4s subshells, we see overlap in the filling of the shells. If you follow the arrows in order, they pass through the subshells in the order that they are filled with electrons in larger atoms. The n = 5 and higher shells have more subshells, but only those subshells that are needed to accommodate the electrons of the known elements are given.
The elements are listed by atomic number (the number of protons in the nucleus), and elements with similar chemical properties are grouped together in columns. The wavelength of visible light, which is detected by the eyes, varies from about 700 nm to about 400 nm. Figure 8.2 "The Electromagnetic Spectrum" shows the entire electromagnetic spectrum and how certain regions of the spectrum are labeled.
However, when electricity is passed through a gas and light is emitted and this light is passed though a prism, we see only certain lines of light in the image (part (b) in Figure 8.3 "Prisms and Light"). Electrons are no longer thought of as being randomly distributed around a nucleus or restricted to certain orbits (in that regard, Bohr was wrong). The a„“ quantum number has a minor effect on the energy of the electron but also affects the spatial distribution of the electron in three-dimensional spacea€”that is, the shape of an electrona€™s distribution in space. Electrons and other subatomic particles behave as if they are spinning (we cannot tell if they really are, but they behave as if they are). However, if you use krypton instead of neon, you get a whitish light, while using argon yields a blue-purple light.
The convention is to label the shell-subshell combination with the number of the shell and the letter that represents the subshell. Notice that the overall set is different for the two electrons, as required by the Pauli exclusion principle. However, the n = 1 shell doesna€™t have another subshell; it is restricted to having just a„“ = 0, or an s subshell. An electron configuration simply lists the shell and subshell labels, with a right superscript giving the number of electrons in that subshell.
Initially, the order is the same as the expected shell-subshell order, but for larger atoms, there is some shifting around of the principal quantum numbers.
Every element on the Periodic Table consists of atoms, which are composed of protons, neutrons, and electrons.
You may already be familiar with some of these regions; they are all lighta€”with different frequencies, wavelengths, and energies.
Bohr suggested that the energy of the electron in hydrogen was quantized because it was in a specific orbit.
Instead, electrons are collected into groups and subgroups that explain much about the chemical behavior of the atom. This goes on and on for other values of a„“, but we need not consider any higher values of a„“ here. When there is more than one possible value of ma„“, each orbital is labeled with one of the possible values. Therefore, this third electron has to be assigned to the n = 2 shell, which has an s (a„“ = 0) subshell and a p (a„“ = 1) subshell.
A d subshell can hold a maximum of 10 electrons, while an f subshell can have a maximum of 14 electrons.
However, Figure 8.7 "Electron Shell Filling Order" gives a valid ordering of filling subshells with electrons for most atoms.
Because the energies of the electron can have only certain values, the changes in energies can have only certain values (somewhat similar to a staircase: not only are the stair steps set at specific heights but the height between steps is fixed). Electrons in the same atom that have the same principal quantum number are said to occupy an electron shellA term used to describe electrons with the same principal quantum number.
Each value of ma„“ designates a certain orbitalThe specific set of principal, angular momentum, and magnetic quantum numbers for an electron..
It should be noted that the diagrams in Figure 8.6 "Electron Orbitals" are estimates of the electron distribution in space, not surfaces electrons are fixed on. Again, we usually start with the lowest quantum number, so this third electron is assigned to the 2s shell-subshell combination of quantum numbers. By limiting subshells to these maxima, we can distribute the available electrons to their shells and subshells. Wavelength is typically represented by I», the lowercase Greek letter lambda, while frequency is represented by I?, the lowercase Greek letter nu (although it looks like a Roman a€?vee,a€? it is actually the Greek equivalent of the letter a€?ena€?).
Thus, there is only one orbital when a„“ is zero, three orbitals when a„“ is 1, five orbitals when a„“ is 2, and so forth.
Ironically, despite its importance in the development of modern electronic theory, hydrogen lamps emit little visible light and are rarely used for illumination purposes.


Wavelength has units of length (meters, centimeters, etc.), while frequency has units of per second, written as sa?’1 and sometimes called a hertz (Hz).
The ma„“ quantum number has no effect on the energy of an electron unless the electrons are subjected to a magnetic fielda€”hence its name.
As stated, the electron configuration of each element is unique to its position on the periodic table. Figure 8.1 "Characteristics of Light Waves" shows how these two characteristics are defined. The energy level is determined by the period and the number of electrons is given by the atomic number of the element. Orbitals on different energy levels are similar to each other, but they occupy different areas in space.
The 1s orbital and 2s orbital both have the characteristics of an s orbital (radial nodes, spherical volume probabilities, can only hold two electrons, etc.) but, as they are found in different energy levels, they occupy different spaces around the nucleus. For more information on how electron configurations and the periodic table are linked, visit the Connecting Electrons to the Periodic Table module. Rules for Assigning Electron Orbitals Occupation of Orbitals Electrons fill orbitals in a way to minimize the energy of the atom. Therefore, the electrons in an atom fill the principal energy levels in order of increasing energy (the electrons are getting farther from the nucleus). The first three (n, l, and ml) may be the same, but the fourth quantum number must be different.
The s subshell has 1 orbital that can hold up to 2 electrons, the p subshell has 3 orbitals that can hold up to 6 electrons, the d subshell has 5 orbitals that hold up to 10 electrons, and the f subshell has 7 orbitals with 14 electrons. As we already know from our studies of quantum numbers and electron orbitals, we can conclude that these four quantum numbers refer to the 1s subshell.
Visually, this is be represented as: As shown, the 1s subshell can hold only two electrons and, when filled, the electrons have opposite spins. When visualizing this processes, think about how electrons are exhibiting the same behavior as the same poles on a magnet would if they came into contact; as the negatively charged electrons fill orbitals they first try to get as far as possible from each other before having to pair up.
This is because Hund's Rule states that the three electrons in the 2p subshell will fill all the empty orbitals first before filling orbitals with electrons in them.
If we look at the element after Nitrogen in the same period, Oxygen (Z = 8) its electron configuration is: 1s2 2s2 2p4 (for an atom). The rules above allow one to write the electron configurations for all the elements in the periodic table. Three methods are used to write electron configurations: orbital diagrams spdf notation noble gas notation Each method has its own purpose and each has its own drawbacks.
This is done by first determining the subshell (s,p,d, or f) then drawing in each electron according to the stated rules above.
Also another way of thinking about it is that as you move from each orbital block, the subshells become filled as you complete each section of the orbital in the period. The block that the atom is in (in the case for aluminum: 3p) is where we will count to get the number of electrons in the last subshell (for aluminum this would be one electron because its the first element in the period 3 p-block). This gives the following: Note that in the orbital diagram, the two opposing spins of the electron can be visualized.
This is why it is sometimes useful to think about electron configuration in terms of the diagram.
However, because it is the most time consuming method, it is more common to write or see electron configurations in spdf notation and noble gas notation.
Another example is the electron configuration of iridium: The electron configuration of iridium is much longer than aluminum. Although drawing out each orbital may prove to be helpful in determining unpaired electrons, it is very time consuming and often not as practical as the spdf notation, especially for atoms with much longer configurations.
Hund's rule is also followed, as each electron fills up each 5d orbital before being forced to pair with another electron.
The element yttrium (symbolized Y) is a transition metal, found in the fifth period and in Group 3. A logical way of thinking about it is that all that is required is to fill orbitals across a period and through orbital blocks.
The number of elements in each block is the same as in the energy level it corresponds. Most students who first learn electron configurations often have trouble with configurations that must pass through the f-block because they often overlook this break in the table and skip that energy level. Its important to remember that when passing the 5d and 6d energy levels that one must pass through the f-block lanthanoid and actinoid series. Another method (but less commonly used) of writing the spdf notation is the expanded notation format. This is the same concept as before, except that each individual orbital is represented with a subscript. When representing the configuration of an atom with half filled orbitals, indicate the two half filled orbitals.
The noble gases have the most stable electron configurations, and are known for being relatively inert. All noble gases have their subshells filled and can be used them as a shorthand way of writing electron configurations for subsequent atoms.
This method of writing configurations is called the noble gas notation, in which the noble gas in the period above the element that is being analyzed is used to denote the subshells that element has filled and after which the valence electrons (electrons filling orbitals in the outer most shells) are written. This looks slightly different from spdf notation, as the reference noble gas must be indicated. On recent discussion concerning quantum justification of the periodic table of the elements. Configuration irregularities: deviations from the madelung rule and inversion of orbital energy levels. Without using a periodic table or any other references, fill in the correct box in the periodic table with the letter of each question. Scenario: You are currently studying the element iodine and wish to use its electron distributions to aid you in your work.
Using the Hund's rule and Pauli exclusion principals we can make a diagram like the following: The answer is one.
Because each individual's knowledge of chemistry differs, there are many answers to this question. The important aspect is that we realize that knowing electron configurations helps us determine the valence electrons on an atom. This is important because valence electrons contribute to the unique chemistry of each atom. Orbitals are occupied in a specific order, thus we have to follow this order when assigning electrons.
This means that in one orbital there can only be two electrons and they mus have opposite spins. This is important when describing an electron configuration in terms of the orbital diagrams. Hund's rule states that electrons first occupy the similar energy orbitals that are empty before occupying those that are half full.



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