Atomic Structure Zumdahl Chemistry Chapter 7 Energy travels through space as electromagnetic radiation. All forms of e.m.r. exhibit the same type of wavelike behavior and travel at the speed of light in a vacuum. Waves have three primary characteristics: wavelength, frequency and speed. Wavelength (symbolized buy the lower case Greek letter lambda ( )) is the distance between two consecutive peaks or troughs in a wave. Frequency ( symbolized by a lower case Greek letter nu ( ) is defined as the number of waves (cycles) per second that pass a given point in space. There is an inverse relationship between wavelength and frequency where the wavelength is in meters, the c frequency is in cycles per second, and c is the speed of light (2.9979 x 10 8 m/s). In the SI system, cycles is understood and the unit per second becomes 1/s, or s –1, which is called the hertz ( abbreviated Hz) Nature of matter: Energy can be gained or lost only in whole number multiples of the quantity h where h is a constant called Planck’s constant which has been determined by experiment to have the value 6.626 x 10 –34 J*s. This means that energy is in fact quantized and can only occur in discrete units of size. Each of these small packets of energy is called a quantum. A system can transfer energy only in whole quanta. Electromagnetic radiation, as a type of energy, is quantized. Einstein suggested that electromagnetic radiation can be viewed as a stream of particles called photons. Ephoton = h = hc It turns out that not only does light act both as a wave (emr) and a particle (photon), but that all matter can be described as both a particle and a wave. The wavelength for any matter can be calculated by de Broglie’s equation h mv Electromagnetic radiation, which at the turn of the twentieth century was thought to be a pure waveform, was found to possess particulate properties. Conversely, electrons, which were thought to be particles, were found to have a wavelength associated with them. The significance of these results is that matter and energy are not distinct. Energy is really a form of matter, and all matter shows the same types of properties. That is all matter exhibited both particulate and wave properties. Large pieces of matter, exhibit predominantly particulate properties. Very small bits of matter, such as photons exhibit predominantly wave properties. The atomic spectrum of hydrogen: A continuous spectrum that results when white light is passed through a prism contains all the wavelengths of visible light. When the hydrogen emission spectrum in the visible region is passed through a prism, we see only a few lines, each of which corresponds to a discrete wavelength. The hydrogen emission spectrum is called a line spectrum. It indicates that only certain energies are allowed for the electron in the hydrogen atom. Energy of the electron in the hydrogen atom is quantized. The Bohr model: Niels Bohr developed a quantum model for the hydrogen atom. Bohr proposed that the electron in a hydrogen atom moves around the nucleus only in a certain allowed circular orbits. Energy levels available for the electron in the hydrogen atom: E= -2.178 x 10 -18 ( Z2 n2 ) In which n is an integer Z is the nuclear charge We must emphasize two important points about the Bohr model: 1. The model correctly fits the quantized energy levels of the hydrogen atom and postulates only certain allowed circular orbits for the electron. 2. As the electron becomes more tightly bound, its energy becomes more negative relative to the zero energy reference stat (corresponding to the electron being at infinite distance form the nucleus). As the electron brought closer to the nucleus energy is released from the system. The quantum mechanical model of the atom: Heisenberg’s uncertainty principle states that there is a limit to how w ell we can know either the position of momentum of a particle. The more accurately we know one, the less accurately we can know the other . There is a fundamental limitation to just how precisely we can know both the position and momentum of a particle at a given time. This limitation is so small for large particles that it is unnoticed. However for a small particle such as the electron the limitation becomes quite important. x * (mv) where h 4 x is the uncertainty in a particles position, ( mv) is the uncertainty in a particles momentum and h is Planck’s constant. In the quantum mechanical model then, the specific electron motions are unknown and we look at the most probable distance at which the electron is found from the nucleus. Schrodinger’s equations are beyond this class, but describe the probability of finding an electron at a given position around the nucleus. When graphed it gives us the shapes and positions of our electron orbitals. An orbital as a three-dimensional electron density map. Quantum numbers: Describe the likeliest place to find an electron within an atom. The principle quantum number (n) has integral values: 1,2,3 and corresponds to the energy level. The principle quantum number is related to the size and energy of the orbital. As n increases the orbital becomes larger and the electron spends more time further from the nucleus. An increase in n also means higher energy, because the electron is less tightly bound to the nucleus, and the energy is less negative. The angular momentum quantum number ( ) corresponds to the sublevel and has integral values from 0 to n-1 for each value of n. This is related to the shape of atomic orbital. The value of ( ) for a particular orbital is commonly assigned a letter: = 0 is called s; = 1 is called p; = 2 is called d; and =3 is called f . The magnetic quantum number ( m )corresponds to the three dimensional orientation of the particular orbital an electron is in and has integral values between and - ,including zero. The magnetic spin number ( ms ) corresponds to the direction of the electrons magnetic moment and can have two values +1/2 and –1/2. Wolfgang Pauli (1900-1958)discovered that in a given atom no two electrons can have the same set of four quantum numbers Since electrons in the same orbital have the same value of the first three, this postulate says that they must have different values of spin. An orbital can only hold two electrons and they must have opposite spins. In an unexcited atom (ground state) the electrons are found to fill orbitals in the following order: 1s,2s,2p,3s,3p,4s,3d,4p,5s,4d,5p,6s,4f,5d,6p,7s,5f,6d,7p, which can be read off a periodic chart. Many exceptions are found, most, dealing with the increased stability of filled and half filled sublevels. For sublevels which possess more then one degenerate (equal energy) orbitals, Hund’s rule states that the lowest energy configuration (and therefore the most favored) is the one having the greatest number of unpaired electrons. Unpaired electrons are shown spinning upward. Valence electrons are electrons located in the outermost principle quantum level. Others are known as core electrons. The “A” Group numbers indicate the number of valence electrons in each of the elements in these columns. The columns are known as the representative elements. (The 1-18 method counts the number of s, d, and p electrons added since the last noble gas.) Periodic trends and Table The present form of the perodic table was conceived by Dimitri Ivanovich Mendeleev. The nuclear charge can be shielded by core electrons (not very well by electrons in the same sublevel) and so a valence electron will feel an effective nuclear charge ( Zeff) Ionization Energy * n z eff 1310kj / mol where the ionization energy is the energy required to remove the outer most electron from an atom. The first I. E. is to remove the first electron, the second I.E. removes the second and so on. The first is always the easiest. Half filled and filled subshells have especially difficult electrons to remove. --As you go across a period I.E. increases because Z goes up, but shielding does not, so Zeff goes up. As you go down a group, I.E. decreases because shielding increases and the distance of the electron from the nucleus increases dramatically and so Zeff goes down. --As you go down a family, density tends to increase. As you go across a period elements radii become smaller. As you go down a family, radii become larger. As ions become more negative their radii become larger. As ions become more positive, their radii become smaller. --The essence of the periodic table is that groups of representative elements exhibit similar chemical properties, because they have similar electron (and especially valence electron) structures. --You should know the names of the different groups of elements on the periodic table --Metals (left side of the table) tend to give up valence electrons (act as reducing agents) to form positive ions and have low ionization energies. The most reactive are the Alkali metals. --Non-metals (right hand side of the table) tend to gain electrons (act as oxidizing agents), form negative ions, and have high ionization energies. The most reactive non-metals are the halogens. --The Noble gases are mostly inert.