Periodic Table of the Elements
The periodic table of the elements may be constructed with Bohr’s atomic model by applying the Pauli exclusion principle. This principle states that no two electrons in any atom may have the same set of four quantum numbers. Hydrogen, the first element, has a nuclear charge of +1 and therefore has only one electron. Since the principal quantum number of this electron must be 1,landmmust be 0 and the spin quantum number s may be either plus or minus 1/2. If now we go to the second element, helium, we must have two orbital electrons since helium has a nuclear charge of+2. The first electron in the helium atom may have the same set of quantum numbers as the electron in the hydrogen atom. The second electron, however, must differ. This difference can be only in the spin since we may have two different spins for the set of quantum numbersn=1,l=0, andm=0. This second electron exhausts all the possibilities forn=1. If now a third electron is added when we go to atomic number 3, lithium, it must have the principal quantum number 2.
In this principal energy level, the orbit may be either circular or elliptical, that is, the azimuthal quantum numberl may be either 0 or 1. In the case ofl=0, the magnetic quantum numbermcan only be equal to 0; whenl =1,mmay be either
−1, 0, or+1. Each of these quantum states may contain two electrons, one with spin +1/2 and the other with spin−1/2. Eight different electrons, each with its own unique set of quantum numbers, are therefore possible in the second principal energy level. These eight different possibilities are utilized by the elements Li, Be, B, C, N, O, F, and Ne (atomic numbers 3–10 inclusive). The additional electron for sodium (atomic number 11) must have the principal quantum number n=3. By assigning all the possible combinations of the four quantum numbers to the electrons in the third principal energy level, it is found that 18 electrons are possible. These
energy levels are not filled successively, as were those in the K and Lshells. (The principal quantum levels corresponding ton=1, 2, 3, 4, 5, 6, and 7 are called the K,L,M,N,O,P, andQ shells, respectively.) No outermost electron shell contains more than eight electrons. After theMshell contains eight electrons, as in the case of argon, the next element in the periodic table, potassium (atomic number 20), starts another principal energy level with one electron in the N shell. Subsequent elements then may add electrons either in the M or in the N shells, until the M shell contains its full complement of 18 electrons. No electrons appear in the O shell until the Nshell has eight electrons. The maximum number of electrons that may exist in any principal energy level is given by the product 2n2, wherenis the principal quantum number. Thus, theO shell may have a maximum of 2×52=50 electrons.
The fact that no outermost electron shell contains more than eight electrons is responsible for the periodicity of the chemical properties of many elements and is the physical basis for the periodic table. Since chemical reactions involve the outer electrons, it is not surprising that atoms with similar outer electronic structures should have similar chemical properties. For example, Li, Na, K, Rb, and Cs behave chemically in a similar manner because each of these elements has only one electron in its outermost orbit. The gases He, Ne, Ar, Kr, Xe, and Rn are chemically inert because their outermost electron shells are filled. Therefore, these elements do not undergo chemical reactions. The elements are thought to have the electronic configurations given in Table 3-1.
Examination of Table 3-1 reveals certain interesting points. The first 20 elements successively add electrons to their outermost shells. The next 8 elements, Sc to Ni, have four shells but add successive electrons to the third shell until it is filled with the maximum number of 18. These elements are calledtransition elements. The same thing happens with elements 39–46 inclusive. Electrons are added to the fourth shell until they number 18, then the fifth shell increases until it contains 8 electrons. In element number 55, Cs, the sixth principal electron orbit, the P shell, starts to fill. Instead of continuing, however, theNlevel starts to fill. Beginning with Ce, and continuing through Lu, electrons are successively added to the fourth electron shell while the two outermost shells remain about the same. This group of elements is usually called the rare earthsand sometimes thelanthanidesbecause these elements begin immediately after La. The rare earth elements differ from the transition elements in the depth of the electronic orbit that is filling. While the transition elements fill the second outer orbit, the rare earths fill the third electron shell, which is deeper in the atom.
Since, in the case of the rare earths, the two outermost electron shells are alike, it is extremely difficult to separate them by chemical means. They are of importance to the health physicist because they include a great number of the fission products. The concern of the health physicist with the rare earths is aggravated by the fact that the analytical chemistry of the rare earths is very difficult and also by the relative dearth of knowledge regarding their metabolic pathways and toxicological properties. Despite their name, the rare earths are not rare; they are found to be widely distributed in nature, albeit in small concentrations. Another group of rare earths is found in the elements starting with Th and continuing to where the O shell fills while the P and Q shells remain about the same. These rare earths are usually called theactinideelements. They are of importance to the health physicist because they are all naturally radioactive and include the fuel used in nuclear reactors.
TABLE 3-1. Electronic Structure of the Elements
K L M N O P Q
ATOMIC SHELL SHELL SHELL SHELL SHELL SHELL SHELL
PERIOD SYMBOL ELEMENT NO. 1 2 3 4 5 6 7
1 H Hydrogen 1 1
He Helium 2 2
2 Li Lithium 3 2 1
Be Beryllium 4 2 2
B Boron 5 2 3
C Carbon 6 2 4
N Nitrogen 7 2 5
O Oxygen 8 2 6
F Fluorine 9 2 7
3 Ne Neon 10 2 8
Na Sodium 11 2 8 1
Mg Magnesium 12 2 8 2
AI Aluminum 13 2 8 3
Si Silicon 14 2 8 4
P Phosphorus 15 2 8 5
S Sulfur 16 2 8 6
Cl Chlorine 17 2 8 7
4 Ar Argon 18 2 8 8
K Potassium 19 2 8 8 1
Ca Calcium 20 2 8 8 2
Sc Scandium 21 2 8 9 2
Ti Titanium 22 2 8 10 2
V Vanadium 23 2 8 11 2
Cr Chromium 24 2 8 13 1
Mn Manganese 25 2 8 13 2
Fe Iron 26 2 8 14 2
Co Cobalt 27 2 8 15 2
Ni Nickel 28 2 8 16 2
Cu Copper 29 2 8 18 1
Zn Zinc 30 2 8 18 2
Ga Gallium 31 2 8 18 3
Ge Germanium 32 2 8 18 4
As Arsenic 33 2 8 18 5
Se Selenium 34 2 8 18 6
Br Bromine 35 2 8 18 7
5 Kr Krypton 36 2 8 18 8
Rb Rubidium 37 2 8 18 8 1
Sr Strontium 38 2 8 18 8 2
Y Yttrium 39 2 8 18 9 2
Zr Zirconium 40 2 8 18 10 2
Nb Niobium 41 2 8 18 12 1
Mo Molybdenum 42 2 8 18 13 1
Tc Technetium 43 2 8 18 14 1
Ru Ruthenium 44 2 8 18 15 1
Rh Rhodium 45 2 8 18 16 1
Pd Palladium 46 2 8 18 18 0
Ag Silver 47 2 8 18 18 1
Cd Cadmium 48 2 8 18 18 2
In Indium 49 2 8 18 18 3
Sn Tin 50 2 8 18 18 4
Sb Antimony 51 2 8 18 18 5
Te Tellurium 52 2 8 18 18 6
(continued)
TABLE 3-1. Electronic Structure of the Elements (Continued)
K L M N O P Q
ATOMIC SHELL SHELL SHELL SHELL SHELL SHELL SHELL
PERIOD SYMBOL ELEMENT NO. 1 2 3 4 5 6 7
I Iodine 53 2 8 18 18 7
6 Xe Xenon 54 2 8 18 18 8
Cs Cesium 55 2 8 18 18 8 1
Ba Barium 56 2 8 18 18 8 2
La Lanthanum 57 2 8 18 18 9 2
Ce Cerium 58 2 8 18 19 9 2
Pr Praseodymium 59 2 8 18 20 9 2
Nd Neodymium 60 2 8 18 22 8 2
Pm Promethium 61 2 8 18 23 8 2
Sm Samarium 62 2 8 18 24 8 2
Eu Europium 63 2 8 18 25 8 2
Gd Gadolinium 64 2 8 18 25 9 2
Tb Terbium 65 2 8 18 26 9 2
Dy Dysprosium 66 2 8 18 28 8 2
Ho Holmium 67 2 8 18 29 8 2
Er Erbium 68 2 8 18 30 8 2
Tm Thulium 69 2 8 18 31 8 2
Yb Ytterbium 70 2 8 18 32 8 2
Lu Lutetium 71 2 8 18 32 9 2
Hf Hafnium 72 2 8 18 32 10 2
Ta Tantalum 73 2 8 18 32 11 2
W Tungsten 74 2 8 18 32 12 2
Re Rhenium 75 2 8 18 32 13 2
Os Osmium 76 2 8 18 32 14 2
Ir Iridium 77 2 8 18 32 15 2
Pt Platinum 78 2 8 18 32 17 1
Au Gold 79 2 8 18 32 18 1
Hg Mercury 80 2 8 18 32 18 2
Tl Thallium 81 2 8 18 32 18 3
Pb Lead 82 2 8 18 32 18 4
Bi Bismuth 83 2 8 18 32 18 5
Po Polonium 84 2 8 18 32 18 6
At Astatine 85 2 8 18 32 18 7
7 Rn Radon 86 2 8 18 32 18 8
Fr Francium 87 2 8 18 32 18 8 1
Ra Radium 88 2 8 18 32 18 8 2
Ac Actinium 89 2 8 18 32 18 9 2
Th Thorium 90 2 8 18 32 19 9 2
Pa Protactinium 91 2 8 18 32 20 9 2
U Uranium 92 2 8 18 32 21 9 2
Np Neptunium 93 2 8 18 32 22 9 2
Pu Plutonium 94 2 8 18 32 24 8 2
Am Americium 95 2 8 18 32 25 8 2
Cm Curium 96 2 8 18 32 25 9 2
Bk Berkelium 97 2 8 18 32 27 8 2
Cf Californium 98 2 8 18 32 28 8 2
Es Einsteinium 99 2 8 18 32 29 8 2
Fm Fermium 100 2 8 18 32 30 8 2
Md Mendelevium 101 2 8 18 32 31 8 2
No Nobelium 102 2 8 18 32 32 8 2
Lr Lawrencium 103 2 8 18 32 32 9 2
Rf Rutherfordium 104 2 8 18 32 32 10 2
Characteristic X-rays
There are certain virtues of the solar system type of atomic model, in which electrons rotate about the nucleus in certain radii corresponding to unique energy levels.
Virtues of the model include the simple explanations that it allows for transfer of energy to matter by excitation and ionization, for the photoelectric effect, and for the origin of certain X-rays calledcharacteristic X-rays.It was pointed out that optical and ultraviolet spectra of elements are due to excitation of outer electrons to levels up to several electron volts and that spectral lines represent energy differences between excited states. As more and more electron shells are added, the energy differences between the principal levels increase greatly. In elements with high atomic numbers, these energy levels reach tens of thousands of electron volts. In the case of Pb, for example, the energy difference between the K and Lshells is 72,000 eV. If thisK electron is struck by a photon whose energy exceeds 87.95 keV (the binding energy of theKelectron) the electron is ejected from the atom and leaves an empty slot in the K shell, as shown schematically in Figure 3-4. Instantaneously, one of the outer electrons falls down into the vacant slot left by the photoelectron. When this happens, a photon is emitted whose energy is equal to the difference between the initial and final energy levels, in accordance with Eq. (3.4a). For the Pb atom, when an electron falls from theLto theKlevels, the emitted photon has a quantum energy of 72,000 eV. A photon of such high energy is an X-ray. When produced in this manner, the photon is called a characteristic X-ray because the energy differences between electron orbits are unique for the different atoms and the X-rays representing these differences are “characteristic” of the elements in which they originate. This process is repeated until all the inner electron orbits are refilled. It is possible, of course, that the first transition is from the Mlevel or even from the outermost electronic orbit.
The most likely origin of the first electronic transition, however, is theLshell. When this happens, the resulting X-ray is called aKαphoton; if an electron falls from the Mlevel to theKlevel, we have aKβphoton. When the vacancy in theLorbit is filled by an electron that falls from the Mlevel, we have an Lα X-ray; if the Lvacancy is filled by an electron originally in the Nlevel, then anLβX-ray results, and so on.
These characteristic X-rays are sometimes called fluorescent radiationsince they are emitted when matter is irradiated with X-rays. Characteristic radiation is useful as a tool to the analytical chemist for identifying unknown elements. Characteristic radiation is of importance to the health physicist who must consider the fluorescent
Figure 3-4. Schematic representation of the ori-gin of characteristic X-rays.
radiation that may be produced in radiation absorbers and in certain other cases where inner electrons are ejected from high-atomic-numbered elements.
A characteristic X-ray photon may interact with another electron in the atom where the characteristic photon originated and eject that electron. This second ejected electron is called anAuger(pronouncedozhay)electron.The Auger electron can come from the same orbit as the original photoelectron or it may come from an outer orbit. The kinetic energy of an Auger electron (EkA) is given by
EkA=φi−2φo, (3.15)
where
φi=binding energy of the inner orbit and φo=binding energy of the outer orbit.