Current understanding of atomic structure had to await the introduction of quantum mechanics by the scientists Werner Heisenberg of Germany and Erwin Schrödinger of Austria in the mid-1920s. Indeed, the structure of the hydrogen atom that is still employed today was developed by Schrödinger in the four papers with which he introduced his version of quantum mechanics—wave mechanics—to the world. The quantum mechanical model of the hydrogen atom has the same numerical agreement with experiment that proved so coincidental with the Bohr model, but it is more fundamentally founded (i.e., the discreteness of the allowed energy states emerges from more general aspects and is not imposed), and the model can be extended (albeit with difficulty) to many-electron atoms. Moreover, unlike Bohr’s theory, it is consistent with the fundamental principles of quantum mechanics—specifically the wave character of the electron and the requirements of the uncertainty principle, which states that the position and momentum (mass times velocity) of a particle cannot be specified simultaneously.
The location of the electron
In the quantum mechanical model of the hydrogen atom, the location of the electron is expressed in terms of a probability distribution, so one speaks of the probability that an electron will be found at a particular location near a nucleus. The probability distribution, in turn, is determined by a mathematical function known as a wave function, denoted ψ. Wave functions for the distribution of particles are a general feature of quantum mechanics, and for electrons in atoms they are known as atomic orbitals. The name orbital is intended to express a distribution that is less precise than the explicit orbits of the Bohr model. The probability of finding an electron at a specified location is proportional to the square of the amplitude of the wave function at that point. Hence, the sign (positive or negative) of the orbital is not relevant to the location of the electron, because taking the square of ψ eliminates any negative sign it may have. However, as explained below in Molecular orbital theory, the sign is of crucial importance in the discussion of bonding between atoms and so cannot be ignored.
Three quantum numbers are needed to specify each orbital in an atom, the most important of these being the principal quantum number, n, the same quantum number that Bohr introduced. The principal quantum number specifies the energy of the electron in the orbital, and, as n increases from its lowest value 1 through its allowed values 2, 3,…, the energies of the corresponding orbitals increase. The ground state, or lowest energy state of the hydrogen atom, is the state in which it is normally found and has n = 1, it consists of a single electron in the orbital closest to the nucleus. As n increases, so does the average distance of the electron from the nucleus, and, as n approaches infinity, the average distance also approaches infinity. The energy required to elevate the electron from the orbital with n = 1 to the orbital with n = ∞ is called the ionization energy of the hydrogen atom; this is the energy required to remove the electron completely from the atom.
The quantum number n labels the shell of the atom. Each shell consists of n2 individual orbitals with the same principal quantum number and hence (in the hydrogen atom) the same energy. Broadly speaking, each shell consists of orbitals that lie at approximately the same distance from the nucleus. The shells resemble the layers of an onion, with successive shells surrounding the inner shells.
The next quantum number needed to specify an orbital is denoted l and called the orbital angular momentum quantum number. This quantum number has no role in determining the energy in a hydrogen atom. It represents the magnitude of the orbital angular momentum of the electron around the nucleus. In classical terms, as l increases, the rate at which the electron circulates around the nucleus increases. The values of l in a shell of principal quantum number n are limited to the n values 0, 1, 2,…, n − 1, and the value of l of an orbital in a given shell determines the subshell to which that orbital belongs. It follows from the allowed values of l that there are n subshells in a shell of principal quantum number n. As will be explained, there are 2l + 1 orbitals in a given subshell.
Although subshells are uniquely specified by the values of n and l, it is conventional to label them in a slightly different manner. A subshell with l = 0 is called an s subshell, one with l = 1 is called a p subshell, and one with l = 2 is called a d subshell. Other subshells are encountered, but these three are the only ones that need to be considered here. The three subshells of the shell with n = 3, for example, are called the 3s, 3p, and 3d subshells.
As noted above, a subshell with quantum number l consists of 2l + 1 individual orbitals. Thus, an s subshell (l = 0) consists of a single orbital, which is called an s orbital; a p subshell (l = 1) consists of three orbitals, called p orbitals; and a d subshell (l = 2) consists of five orbitals, called d orbitals. The individual orbitals are labeled with the magnetic quantum number, ml, which can take the 2l + 1 values l, l − 1,…, −l. The orbital occupied in the lowest energy state of the hydrogen atom is called a 1s orbital, signifying that it belongs to (and is in fact the only member of) the shell with n = 1 and subshell with l = 0.
Metallic And Ionic Bonding Essay
-Good conductors of electricity
-Good conductors of Heat
-Lustrous or reflective when freshly cut or polished
-Malleable ? can be shaped by beating
-Ductile ? can be drawn into a wire
-Exihibit a range of melting and boiling temperatures
-Generally have high densities
Exceptions in metals:
-Mercury ? liquid at room temperature, unusually low melting point.
-Chromium ? brittle rather than malleable.
Structure of Metals
Model of metal in solid state must be one in which:
-Some of particles are charged and free to move
-There are strong forces between particles throughout metal lattice
-Force that exist between charged particles: electrostatic force
Obtaining stability ?
Releasing one or more of outer shell (valence) electrons into a common pool within lattice. Atom is now a positive ion.
Metallic bonding model
-The only particles that are small enough to move through a solid lattice are electrons. If a metal atom loses one or more electrons it forms a positive ion.
-Ions: atoms or groups of atoms that have either gained or lost electrons and thus have a negative or positive charge.
-In ions, total number in protons differ from total number of electrons
-Cations: atoms that have lost electron to form + charge ions. (Metals)
-Anions: Atoms that have gained electrons form - charge ions. (Non-metals)
-Positive ions are arranged in closely packed structure.
oThis structure described as a regular, 3D lattice of positive ions. The ions occupy fixed positions in the lattice.
oThe much smaller electrons are free to move throughout the lattice.
?Called delocalised electrons
?Because they belong to lattice as a whole
?Delocalised electrons come from valence (outer) shell. (fig 3.5)
oElectrons that are not free to move throughout the lattice:
?Localised electrons in inner shell.
-The ions are held in lattice by attraction to delocalised electrons. This attraction extends throughout lattice and is called metallic bonding.
Metallic Bonding can be used to explain some properties of metals:
-Delocalised electrons in metallic lattice are free to move.
oIf source of electricity is supplied across metal, electrons are forced in one end and are able to flow out the other
o? Thus metals are good conductors of electricity.
-Delocalised electrons able to bump into one another and the cations able to transmit heat energy rapidly throughout the lattice
o? Thus metals are good conductors of heat
-Because of delocalised electrons in their lattice
o? metals reflect light and are lustrous
-Even when beaten into sheets or drawn into wires, delocalised electrons move so they still surround cations.
oElectrostatic forces of attraction may change but still operate through lattice
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