ELECTRON CLOUD MODELElectron Density and Orbital ShapesAtomic orbitals are mathematicaldescriptions of where the electrons in anatom (or molecule) are most likely to befound. These descriptions are obtained bysolving an equation known as theSchrödinger equation, which expressesour knowledge of the atomic world. As theangular momentum and energy of anelectron increases, it tends to reside indifferently shaped orbitals. The orbitalscorresponding to the three lowest energystates are s, p, and d, respectively. Theillustration shows the spatial distribution of electrons within these orbitals. Thefundamental nature of electrons prevents more than two from ever being in thesame orbital. The overall distribution of electrons in an atom is the sum of many suchpictures. This description has been confirmed by many experiments in chemistry andphysics, including an actual picture of a p-orbital made by a Scanning TunnelingMicroscope.Electron CloudMost of the physical and chemical properties of atoms, and hence of all matter, aredetermined by the nature of the electron cloud enclosing the nucleus.The nucleus of an atom, with its positive electric charge, attracts negatively chargedelectrons. This attraction is largely responsible for holding the atom together. Therevolution of electrons about a nucleus is determined by the force with which theyare attracted to the nucleus. The electrons move very rapidly, and determination ofexactly where any particular one is at a given time is theoretically impossible (seeUncertainty Principle). If the atom were visible, the electrons might appear as acloud, or fog, that is dense in some spots, thin in others. The shape of this cloud andthe probability of finding an electron at any point in the cloud can be calculated fromthe equations of wave mechanics (see Quantum Theory). The solutions of theseequations are called orbitals. Each orbital is associated with a definite energy, and
each may be occupied by no more than two electrons. If an orbital contains twoelectrons, the electrons must have opposite spins, a property related to the angularmomentum of the electrons. The electrons occupy the orbitals of lowest energy first,then the orbitals next in energy, and so on, building out until the atom is complete(see Atom).The orbitals tend to form groups known as shells (so-called because they areanalogous to the layers, or shells, around an onion). Each shell is associated with adifferent level of energy. Starting from the nucleus and counting outward, the shells,or principal energy levels, are numbered 1, 2, 3, … , n. The outer shells have morespace than the inner ones and can accommodate more orbitals and therefore moreelectrons. The nth shell consists of 2n-1 orbitals, and each orbital can hold amaximum of 2 electrons. For example, the third shell contains five orbitals and holdsa maximum of 10 electrons; the fourth shell contains seven orbitals and holds amaximum of 14 electrons. Among the known elements, only the first seven shells ofan atom contain electrons, and only the first four shells are ever filled.Each shell (designated as n) contains different types of orbitals, numbered from 0 ton-1. The first four types of orbitals are known by their letter designations as s, p, d,and f. There is one s-orbital in each shell, and this orbital contains the most firmlybound electrons of the shell. The s-orbital is followed by the p-orbitals (which alwaysoccur in groups of three), the d-orbitals (which always occur in groups of five), andfinally the f-orbitals (which always occur in groups of seven). The s-orbitals arealways spherically shaped around the nucleus; each p-orbital has two lobesresembling two balls touching; each d-orbital has four lobes; and each f-orbital haseight lobes. The p-, d-, and f-orbitals have a directional orientation in space, but thespherical s-orbitals do not. The three p-orbitals are oriented perpendicular to oneanother along the axis of an imaginary three-dimensional Cartesian (x, y, z)coordinate system. The three p-orbitals are designated px, py, and pz, respectively.The d- and f-orbitals are similarly arranged about the nucleus at fixed angles to oneanother.When elements are listed in order of increasing atomic number, an atom of oneelement contains one more electron than an atom of the preceding element (seeChemical Elements). The added electrons fill orbitals in order of the increasingenergy of the orbitals. The first shell contains the 1s orbital; the second shell containsthe 2s orbital and the 2p orbitals; the third shell contains the 3s orbital, the 3porbitals, and the 3d orbitals; the fourth shell contains the 4s orbital, the 4p orbitals,the 4d orbitals, and the 4f orbitals.After the two innermost shells, certain orbitals of outer shells have lower energiesthan the last orbitals of preceding shells. For this reason, some orbitals of the outershells fill before the previous shells are complete. For example, the s-orbital of the
fourth shell (4s) fills before the d-orbitals of the third shell (3d). Orbitals generally fillin this order: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s.In a notation frequently used to describe the electron configuration of an element, asuperscript after the orbital letter gives the number of electrons in that orbital. Thus,1s22s22p5 means that the atom has two electrons in the 1s orbital, two electrons inthe 2s orbital, and five electrons in the 2p orbitals.Neutral atoms with exactly eight electrons in the outer shell (meaning the s- and p-orbitals of the outer shell are filled) are exceptionally stable. These neutral atoms areatoms of the noble gases, which are so stable that getting them to chemically reactwith other elements is very difficult. The unusual stability of the noble-gas electronstructures is of great importance in chemical bonding and reactivity. All otherelements tend to combine with each other in such a way as to imitate this stablestructure. The structure of helium is 1s2; neon adds another stable shell, 2s22p6, tothis; argon adds the orbitals 3s23p6; krypton adds the orbitals 4s23d104p6; and xenonadds the orbitals 5s24d105p6 (the s-orbital fills before the d-orbital of the previousshell).A.Electron Orbitals Electron Density and Orbital Shapes Atomic orbitals are mathematical descriptions of where the electrons in an atom (or molecule) are most likely to be found. These descriptions are obtained by solving an equation known as the Schrödinger equation, which expresses our knowledge of the atomic world. As the angular momentum and energy of an electron increases, it tends to reside in differently shaped orbitals. The orbitals corresponding to the three lowest energy states are s, p, and d, respectively. The illustration shows the spatial distribution of electrons within these orbitals. The fundamental nature of electrons prevents more than two from ever being in the same orbital. The overall distribution of electrons in an atom is the sum of many such pictures. This description has been confirmed by many experiments in chemistry and physics, including an actual picture of a p-orbital made by a Scanning Tunneling Microscope. Atomic Orbital Shapes Atomic orbitals are mathematical descriptions of where the electrons in an atom (or molecule) are most likely to be found. These descriptions are obtained by solving an equation known as the Schrödinger equation, which expresses our
knowledge of the atomic world. As the angular momentum and energy of an electron increases, it tends to reside in differently shaped orbitals. This description has been confirmed by many experiments in chemistry and physics, including an actual picture of a p-orbital made by a scanning tunneling microscope.Quantum Description of ElectronsScientists describe the properties of an electron in an atom with a set of numberscalled quantum numbers. Electrons are a type of particle known as a fermion,and according to a rule of physics, no two fermions can be exactly alike. Eachelectron in an atom therefore has different properties and a different set ofquantum numbers. Electrons that share the same principal quantum numberform a shell in an atom. This chart shows the first three shells. The two electronsthat share the principal quantum number 1 form the first shell. One of theseelectrons has the quantum numbers 1, s, 0, 1/2, and the other electron has thequantum numbers 1, s, 0, -1/2.Scientists cannot simultaneously measure both the exact location of an electron andits precise speed and direction, so they cannot measure the path a specific electrontakes as it orbits the nucleus. The law of physics governing this phenomenon is calledthe uncertainty principle. Scientists can, however, determine the area an electronwill probably occupy, and the probability of finding the electron at some place insidethis area. A map of this area and its probabilities forms a cloudlike pattern known asan orbital. Each orbital can contain two electrons, but these electrons can not haveidentical properties, so they must spin in opposite directions. Orbitals are groupedinto shells, like the layers of an onion, around the nucleus. Each shell can contain alimited number of orbitals, which means that each shell can contain a limitednumber of electrons. Each shell corresponds to a certain level of energy, and all theelectrons in the shell have this same level of energy. As the shells get farther fromthe nucleus, they can contain more electrons, and the electrons in the shells havehigher energy. See also Chemistry: Electron Cloud.Light Absorption and EmissionWhen a photon, or packet of light energy, is absorbed by an atom, the atomgains the energy of the photon, and one of the atom’s electrons may jump to ahigher energy level. The atom is then said to be excited. When an electron ofan excited atom falls to a lower energy level, the atom may emit the electron’sexcess energy in the form of a photon. The energy levels, or orbitals, of the
atoms shown here have been greatly simplified to illustrate these absorptionand emission processes. For a more accurate depiction of electron orbitals,When an atom’s energy is at its minimum, it is said to be in a ground state. In thisground state, the atom’s electrons occupy the innermost available shells, thoseclosest to the nucleus. When atoms are excited by heat, by an electric current, or bylight or some other form of radiation, the atoms’ electrons can acquire energy andjump from an inner to an outer shell, leaving a vacancy in the inner shell. The atomseeks to shed this surplus energy, leading the electron in the outer orbit to fall backdown to an inner vacancy. As it falls, the electron releases energy in the form of aphoton, a tiny flash of light. The color of the light depends on the amount of energyemitted. Spectral Lines of Atomic Hydrogen When an electron makes a transition from one energy level to another, the electron emits a photon with a particular energy. These photons are then observed as emission lines using a spectroscope. The Lyman series involves transitions to the lowest or ground state energy level. Transitions to the second energy level are called the Balmer series. These transitions involve frequencies in the visible part of the spectrum. In this frequency range each transition is characterized by a different color.When an electron moves to a different shell, it does not gradually go from one shellto another, but instead jumps directly to the other shell. These jumps are like stepson a staircase (and are different from a smooth incline, or hill). The electron alsoabsorbs or emits the energy to make jumps in steps. It cannot gradually build up orlose energy, but must instantly absorb the exact amount of energy needed to make acertain jump, or instantly emit the exact amount needed to fall to a lower shell. Eachelement has a different pattern of allowed jumps within its electronic structure, sothe element’s atoms can only absorb or emit a distinct set of energies, or spectrumof colors. In this way, a scientist can tell which elements are present in a sample bylooking at the colors absorbed or emitted when the sample is excited by heat,electricity, or light. See also Spectroscopy.