7.1 Electromagnetic Radiation

• ****It is one of the ways that energy travels through space

• Waves have three primary characteristics: wavelength, frequency, and speed

• Wavelength: The distance between two consecutive peaks or troughs in a wave

• Frequency: The number of waves per second that pass a given point in space

• The wave with the shortest wavelength has the highest frequency and the wave with the longest wavelength has the lowest frequency

• Wavelength and frequency are inversely related

• Radiation provides an important means of energy transfer.

7.2 The Nature of Matter

• Studying the radiation profiles emitted by solid bodies heated to incandescence, Planck found that the results could not be explained in terms of the physics of his day

  • Planck could account for these observations only by postulating that energy can be gained or lost only in whole-number multiples of the quantity, where h is a constant called Planck’s constant

  • Planck’s constant= 6.626 x 10^-34 J  x  s

• Energy can be gained or lost only in integer multiples of h

• The photoelectric effect refers to the phenomenon in which electrons are emitted from the surface of a metal when light strikes it.

  • The observations of the photoelectric effect can be explained by assuming that electromagnetic radiation is quantized (consists of photons), and that the threshold frequency represents the minimum energy required to remove the electron from the metal’s surface.

• The apparent mass of a photon depends on its wavelength. The mass of a photon at rest is thought to be zero, although we never observe it at rest.

• Diffraction results when light is scattered from a regular array of points or lines.

• A diffraction pattern can only be explained in terms of waves.

• All matter exhibits both particle and wave properties.

• Pieces of matter with intermediate-mass, such as electrons, show clearly both the particulate and wave properties of matter.

7.3 The Atomic Spectrum of Hydrogen

• An important experiment is the study of the emission of light by excited hydrogen atoms

• When a sample of hydrogen gas receives a high-energy spark, the H2 molecules absorb energy, and some of the HOH bonds are broken

• The resulting hydrogen atoms are excited; that is, they contain excess energy, which they release by emitting light of various wavelengths to produce what is called the emission spectrum of the hydrogen atom.

• The line spectrum of hydrogen indicates that only certain energies are allowed for the electron in the hydrogen atom.

• Changes in energy between discrete energy levels in hydrogen will produce only certain wavelengths of emitted light,

• If any energy level were allowed, the emission spectrum would be continuous.

7.4 The Bohr Model

• Danish physicist named 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 certain allowed circular orbits.

• He also knew that the correct model had to account for the experimental spectrum of hydrogen, which showed that only certain electron energies were allowed.

• Bohr’s model gave hydrogen atom energy levels consistent with the hydrogen emission spectrum

  • Although Bohr’s model fits the energy levels for hydrogen, it is a fundamentally incorrect model for the hydrogen atom.

  • When Bohr’s model was applied to atoms other than hydrogen, it did not work at all

  • The model is, however, very important historically, because it showed that the observed quantization of energy in atoms could be explained by making rather simple assumptions.

7.5 The Quantum Mechanical Model of the Atom

• Broglie originated the idea that the electron, previously considered to be a particle, also shows wave properties.

• Schrödinger, an Austrian physicist, decided to attack the problem of atomic structure by giving emphasis to the wave properties of the electron

• To Schrödinger and de Broglie, the electron bound to the nucleus seemed similar to a standing wave, and they began research on a wave mechanical description of the atom

• The physical principles for describing standing waves were well known in 1925 when Schrödinger decided to treat the electron in this way

• Wave function: a function of the coordinates (x, y, and z) of the electron’s position in three-dimensional space

• The first point of interest is to explore the meaning of the word orbital

• There is a fundamental limitation to just how precisely we can know both the position and momentum of a particle at a given time.

• Probability is the likelihood, or odds, that something will occur.

  • The square of the function indicates the probability of finding an electron near a particular point in space.

• The square of the wave function is most conveniently represented as a probability distribution, in which the intensity of the color is used to indicate the probability value near a given point in space.

• Another way of representing the electron probability distribution for the 1s wave function is to calculate the probability at points along a line drawn outward in any direction from the nucleus.

• The probability of finding the electron at a particular position is the greatest close to the nucleus and drops off rapidly as the distance from the nucleus increase

• The angstrom is most often used as the unit for atomic radius because of its convenient size. Another convenient unit is the picometer: 1 pm = 10^-12 m

• An electron “in” a particular atomic orbital is assumed to exhibit the electron probability indicated by the orbital map

7.6 Quantum Numbers

• The principal quantum number has integral values: 1, 2, 3. The principal quantum number is related to the size and energy of the orbital.

• As it increases, the orbital becomes larger and the electron spends more time farther from the nucleus.

• The angular momentum quantum number has integral values from 0 to 1 for each value of n.

• This quantum number is related to the shape of atomic orbitals.

7.7 Orbital Shapes and Energies

• Each orbital in the hydrogen atom has a unique probability distribution

• The p orbitals are not spherical like s orbitals but have two lobes separated by a node at the nucleus

  • The p orbitals are labeled according to the axis of the xyz coordinate system along which the lobes lie.

  • The p orbital functions have different signs in different regions of space.

• When the s orbital function is evaluated at any point in space, it results in a positive number

• For the hydrogen atom, the energy of a particular orbital is determined by its value of n.

• All orbitals with the same value of n have the same energy—they are said to be degenerate

• The hydrogen atom has many types of orbitals. In the ground state, the single electron resides in the 1s orbital. The electron can be excited to higher-energy orbitals if energy is put into the atom

7.8 Electron Spin and the Pauli Principle

• ****The concept of electron spin was developed by Samuel Goudsmit and George Uhlenbeck while they were graduate students at the University of Leyden in the Netherlands

• The spectral data indicate that the electron has a magnetic moment with two possible orientations when the atom is placed in an external magnetic field

• It seemed reasonable to assume that the electron could have two spin states, thus producing the two oppositely directed magnetic moments

• Electron spin quantum number: The electron can spin in one of two opposite directions,

• Pauli exclusion principle: In a given atom no two electrons can have the same set of four quantum numbers

• Since only two values of m are allowed, an orbital can hold only two electrons, and they must have opposite spins

7.9 Poly electronic Atoms

• Each orbital can hold a maximum of two electrons

• Three energy contributions must be considered of the helium atom: the kinetic energy of the electrons as they move around the nucleus

  • The potential energy of attraction between the nucleus and the electrons

  • The potential energy of repulsion between the two electrons.

• The approximation used is to treat each electron as if it were moving in a field of charge that is the net result of the nuclear attraction and the average repulsions of all the other electrons.

• One important difference between poly electronic atoms and the hydrogen atom is that for hydrogen all the orbitals in a given principal quantum level have the same energy

• The more effectively an orbital allows its electron to penetrate the shielding electrons to be close to the nuclear charge, the lower is the energy of that orbital

7.10 The History of the Periodic Table

• As chemistry progressed during the eighteenth and nineteenth centuries, it became evident that the earth is composed of a great many elements with very different properties.

• The first chemist to recognize patterns was Johann Dobereiner, who found several groups of three elements that have similar properties, for example, chlorine, bromine, and iodine

  • As Dobereiner attempted to expand this model of triads (as he called them) to the rest of the known elements, it became clear that it was severely limited.

• Mendeleev correctly predicted the existence and properties of these elements from gaps in his periodic table.

  • Using his table, Mendeleev also was able to correct several values for atomic masses

  • He assumed the atomic mass was probably incorrect and proposed that the formula of indium oxide was really In2O3

  • Based on this correct formula, indium has an atomic mass of approximately 113, placing the element among the metals

  • Mendeleev’s periodic table was almost universally adopted, and it remains one of the most valuable tools at the chemist’s disposal

7.11 The Aufbau Principle and the Periodic Table

• Aufbau principle: As protons are added one by one to the nucleus to build up the elements, electrons are similarly added to this hydrogen-like orbitals