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Table 1 Electrical charge and relative mass of electrons, protons, and neutrons. Particle Symbol Relative Charge Mass Proton P +1 1.0073 amu Neutron N 0 1.0087 amu Electron - -1 5.468 x 10-4 amu e amu (atomic mass unit): a unit used to express very small masses 1.66054 x 10-24 g Rutherford’s conclusions Most of the mass and all of the positive charge of the atom are contained in a small space called the nucleus. Most of the volume of the atom is empty space occupied by tiny negatively charged electrons. There are as many negatively charged electrons outside the nucleus as units of positive charge inside the nucleus the atom is electrically neutral Rutherford Model Nuclear Page 7 Atomic Theory His research led him to believe that electrons in an atom exist in specific regions at various distances from the nucleus. He visualized the electrons as rotating in orbits around the nucleus like planets rotating around the sun. Bohr's first paper in this field dealt with the hydrogen atom, which he described as a single electron rotating in an orbit about a relatively heavy nucleus. He applied the concept of energy quanta, proposed in 1900 by the German physicist Max Planck (1858-1947) to the observed spectra of hydrogen. Planck stated that energy is never emitted in a continuous stream, but only in small discrete packets called "quanta" (Latin, quantus, how Page 8 Atomic Theory much). Bohr theorized that there are several possible orbits for electrons at different distances from the nucleus. But an electron had to be in one specific orbit or another; it could not exist between orbits. Bohr also stated that when a hydrogen atom absorbed one or more quanta of energy, its electron "jumped" to another orbit a greater distance from the nucleus. When the electron fell back to lower orbits, it emitted quanta of energy as light, giving rise to the spectrum of hydrogen. Each orbit, he said, is at a different energy level. An electron in the orbit closest to the nucleus is in the first energy level; at greater distances it may be in the second, third, or fourth energy level. Page 9 Atomic Theory Niels Bohr's ideas of electron distribution within the atom are useful concepts and laid the foundation for much of the later progress in understanding atomic structure. But, as is the case with many theories, Bohr's assumptions have had to be modified. Difficulty arose in applying the theory to atoms containing many electrons. Bohr's concept of the atom has been replaced by quantum mechanics theory one of the chief difference between these two theories is that in the quantum mechanics theory electrons are not considered to be revolving around the nucleus in orbits, but to occupy "orbitals"—somewhat cloudlike regions surrounding the nucleus and corresponding to energy levels. The concept of electrons being in specific energy levels is still retained in the modern theory. In 1926, the Austrian physicist Erwin Schrodinger (1887-1961) introduced his now-famous wave equation and a new method of calculation— quantum mechanics, or wave mechanics. Schrodinger’s equation, which is a complex mathematical expression, describes an electron as simultaneously having properties of a wave and a particle. Thus, the electron was given dual characteristics—some of its properties are best described in terms of waves (like light) and other properties, like those of a particle, having mass. The solution of the Schrodinger equation is complex. However, the solution leads to the introduction, of four quantum numbers which define the probabilities of location and spatial properties of electrons in atoms. Page 10 Atomic Theory The four quantum numbers—n, l, m, and s. specify the energy and probable location of each electron in an atom. 1. Electrons exist in energy levels at different distances from the nucleus. The principal quantum number, n, indicates the energy levels of the electrons relative to their distance from the nucleus. The number n may have any positive integral value up to infinity (n = 1,2,3,4,... ), but only values of 1 to 7 have been established for atoms of known elements in their ground state (lowest energy slate). Energy level n = 1 is closest to the nucleus and is the lowest principal energy level. 2. Electrons exist in orbitals having specific shapes. The principal energy levels (except the first) contain sublevels closely grouped together. These sublevels consist of orbitals of specific shape. In quantum mechanics the term orbital (not orbit) is used and refers to the region around the nucleus in which we may expect to find a particular electron. The orbital quantum number l (ell) specifics the shape of the electron "cloud" about the nucleus. The four common sublevels (orbitals) normally encountered are designated here by the lower-case italicized letters s, p, d and f 3. Electron orbitals have specific orientation in space. The magnetic quantum number, m, designates this orientation. This quantum number accounts for the number of s, p, d, and f orbitals that can be present in the principal energy levels. There can be at most one s orbital, three p Page 11 Atomic Theory orbitals, five d orbitals; and seven f orbitals in any given principal energy level. 4. An electron spins about its own axis in either a clockwise or counterclockwise direction. The spin quantum number, s, relates to the direction of spin of an electron. Because there are only two possible directions of spin, each orbital, no matter what its designation, can contain a maximum of two electrons. Perspective representation of the s, px, pv and pz atomic orbitals. Page 12 Atomic Theory When two electrons occupy the same orbital, they must have opposite spins. When an orbital contains two electrons, the electrons are said to be "paired." Thus, the quantum numbers tell us relatively how far the electrons are located from the nucleus, the shapes of the electron orbitals, and the orientation of the orbitals in space. The basic rules and limitations regarding the state of electrons in atoms follow. 1. In the ground state (lowest energy state) of an atom, electrons occupy orbitals of the lowest possible energy. Thus, an electron will occupy an s orbital in the n = 1 level before it occupies an s orbital in the n = 2 level. An electron will occupy an s orbital in any principal energy level before it occupies a p orbital in that same energy level. 2. Each orbital may contain a maximum of two electrons (with opposite spins). 3. No two electrons in an atom can have the same four quantum numbers. This is a statement of the Pauli Exclusion Principle. All the electrons in an atom are not located the same distance from the nucleus. As pointed out by both the Bohr Theory and quantum mechanics, the probability of finding the electrons is greatest at certain specified distances, called energy levels, from the nucleus. Energy levels are also referred to as electron shell and may contain only a limited number of electrons. Energy levels are numbered starting with n = 1 as the shell nearest Page 13 Atomic Theory the nucleus and going to n = 7. They are also identified by the letters K. L. M. N, 0, P. Q with K equivalent to the first energy level, L to the second level, etc., as follows: Table 2 Energy Level 1st 2nd 3rd 4th 5th 6th 7th n 1 2 3 4 5 6 7 Letter Designation K L M N O P Q Each succeeding energy level is located farther away from the nucleus. The maximum number of electrons that can occupy a specific energy level can be calculated from the formula 2n2, where n is the number of the principal energy level. For example, shell K, or energy level 1, can have a maximum of two electrons (2 x 12 = 2); shell L, or energy level 2, can have a maximum of eight electrons (2 x 22 = 8) etc. Table 3 shows the maximum number of electrons that can exist in each of the first five energy levels. Table 3 Maximum number of electrons that can occupy each principal energy level: Energy Level n 1 2 3 4 5 Letter Designation K L M N O Maximum number 2n 2 2 2x1 =2 2 2x2 =4 2 2x 3 = 18 2 2x 4 = 32 2 2x 5 = 50 The theoretical value of 50 electrons in energy level 5 has never been attained in any clement known to date. Page 14 Atomic Theory The principal energy levels contain sublevels, designated by the letters s, p, d, f. The s sublevel consists of one orbital; the p sublevel consists of three orbitals; the d sublevel consists of five orbitals; and the f sublevel consists of seven orbitals. The maximum number of electrons that can exist in these sublevels is 2 electrons in the s sublevel, 6 in the p sublevel, 10 in the d sublevel, and 14 in the f sublevel. Since each orbital can contain two electrons the 6 electrons in the p sublevel are distributed in 3 p orbitals; the 10 d electrons are determination, we need to know the maximum number of electrons possible in an energy level and to use two of the rules: (I) No more than two electrons can occupy one orbital, and (2) An electron will occupy the lowest possible sublevel. The maximum number of electrons in the first energy level is two (see Table 3); both of these must then be s electrons. These are designated as Is2 indicating two s electrons in the first energy level. The s orbital in the second energy level is written as 2s, in the third energy level as 3s, etc- The second energy level, with a maximum of eight electrons, will contain only s and p electrons; namely, a maximum of two s and six p electrons. They are designated as 2s22p6. Page 15 Atomic Theory