Atomic Structure & Periodicity

Atomic Structure & Periodicity • What is the nature of the atom? • How can atomic structure account for the periodic properties observed? • What is quantum mechanics?

Electromagnetic Radiation • Electromagnetic Radiation • a way that energy travels through space • exhibits wavelike behavior • travels at the speed of light

Waves • Three primary characteristics of waves • wavelength • frequency • speed

Waves • Wavelength • l = lamda • distance between two consecutive peaks • units could be meters, nm, Angstroms, cm, etc.

Waves • Frequency • n = nu • number of waves or cycles that pass a certain point per second • units may be cycles/second or Hertz (Hz) or just sec-1

Waves • Speed • all types of EM (electromagnetic) radiation travel at the speed of light • Speed = c = 3.00 x 108 m/sec

Waves • There is an inverse relationship between wavelength and frequency. • l a 1/n • in other words • ln = c • The shorter the wavelength, the higher the frequency. • Low frequency, long wavelength

Electromagnetic Radiation • An important means of energy transfer • Electromagnetic Spectrum:

Electromagnetic Radiation • Calculate the frequency of red light of wavelength 6.50 x 102 nm. • (Answer: n = 4.61 x 1014 Hz)

The Nature of Matter • Classical Physics…pre-1900’s • could predict the motion of planets • could explain the dispersion of light by a prism • the assumption was that physicists at that time knew all that there was to know about physics

The Nature of Matter • Pre-1900’s • Matter and Energy are distinct • Matter is particulate • has mass • position in space could be specified • Energy is wavelike • no mass • delocalized

The Nature of Matter • 1900 • Max Planck (1858 - 1947) • Studied the radiation profiles emitted by solid bodies heated to incandescence (I.e., heated so hot that the objects gave off light) • These profiles could not be explained with classical physics

The Nature of Matter • Classical Physics - matter could absorb or emit any quantity of energy • Planck observed that energy could be gained or lost only in whole number multiples of a quantity, hn • h = Planck’s constant h = 6.626 x 10-34 J.sec • n = the frequency of the energy absorbed or emitted

The Nature of Matter • Max Planck’s equation for the change in energy for a system: • DE = nhn ( where n = 1, 2, 3, …) • From Planck’s work, we learn that energy is quantized • energy occurs in discrete packets called quanta; one packet of energy is called a quantum • THUS, Energy seems to have particulate properties!

The Nature of Matter • The blue color in fireworks is often achieved by heating copper (I) chloride to about 1200oC. Then the compound emits blue light with a wavelength of 450 nm. What is the quantum that is emitted at 4.50 x 102 nm by CuCl? • (Answer: DE = 4.41 x 10-19 J)

The Nature of Matter • Albert Einstein • proposed that electromagnetic radiation is quantized • EMR can be viewed as a stream of “particles” known as photons • The energy of the photon then is: • Ephoton = hn = hc l

The Nature of Matter • Albert Einstein (cont.) • E = mc2 • energy has mass • m = E c2 • use this equation to calculate the mass associated with a given quantity of energy

The Nature of Matter • Mass of a photon: • Ephoton = hc and m = E l c2 • so m = hc/l c2 • m = h ( so the mass of a photon depends on its wavelength) cl • Arthur Compton’s work (1922) with X rays and electrons showed that photons have the mass calculated

The Nature of Matter • Conclusions: • Energy is quantized • Energy can occur is discrete units called quanta • EMR can show characteristics of particulate matter (photons) as well as wavelike characteristics • This phenomenon is known as the dual nature of light

The Nature of Matter • So light can be particulate as well as wavelike • Can matter then be wavelike as well as particulate?

The Nature of Matter • Louis de Broglie (1892 - 1987) • for EMR: m = h/lc • for a particle: m = h/lv • v = velocity …because matter does not travel at the speed of light • so rearrange to solve for the wavelength of a particle: • l = h (de Broglie’s equation) mv

The Nature of Matter • Compare the wavelength for an electron ( a particle with m = 9.11 x 10-31 kg) traveling at a speed of 1.0 x 107m/s with that for a ball ( a particle with m = 0.10 kg) traveling at 35 m/s • (Answer: le = 7.27 x 10-11 m; lb = 1.9 x 10-34 m)

The Nature of Matter • How can de Broglie’s equation be tested? • The wavelength of an electron is the same length as the distance between the atoms in a typical crystal • A crystal diffracts electrons just as it diffracts EMR (in the form of X-rays) • Therefore, electrons do have an associated wavelength

The Nature of Matter • EMR was found to possess particulate properties • Particles, like electrons, were found to have an associated wavelength • Matter and Energy are not distinct! • Energy is really a form of matter!

The Nature of Matter • Large pieces of matter - predominately particulate • Very small pieces of matter (e.g. photons) are predominately wavelike (but can exhibit particulate properties) • Intermediate pieces of matter (e.g. electrons) are wavelike as well as particulate

The Atomic Spectrum Of Hydrogen • Add energy (in the form of a spark) to H2(g) • H2 molecules absorb energy, some H-H bonds are broken, and the H atoms get excited • this excess energy is released in the form of light • an emission spectrum (the pattern of light emitted) is always the same for a particular element (like a fingerprint for an element) • passing H’s emission spectrum through a prism results in a few characteristic lines…hence the term line spectrum

The Atomic Spectrum of Hydrogen • H’s line spectrum shows that hydrogen’s electrons are quantized • I.e., only certain energies are allowed for the electron • if not, then the spectrum would be continuous, like the rainbow observed when light passes through a prism • fits in with Max Planck’s postulates • DE = hn = hc l

The Bohr Model of the Hydrogen Atom • Niels Bohr (1885 - 1962) • 1913 developed a quantum model for the hydrogen atom • the electron in a hydrogen atom moves around the nucleus in certain allowed orbits • used classical physics and made some new assumptions to calculate these orbits

The Bohr Model of the Hydrogen Atom • Bohr’s model had to account for the line spectrum of hydrogen • the hydrogen atom has energy levels • E = -2.178 x 10-18 J (Z2/n2) • Z = the nuclear charge (in Hydrogen, Z = 1) • n = (1, 2, 3, …) the energy level ...the larger the value for n, the larger the orbit radius… • negative sign indicates that an electron bound to a nucleus has lower energy than an electron infinitely far away from the nucleus

The Bohr Model of the Hydrogen Atom • n = 1 …the ground state for hydrogen…the electron is closest to the nucleus • When energy is added to the H atom, the electron jumps up to a higher energy level • When giving off energy, the electron falls back to the ground state, or the lowest energy state

The Bohr Model of the Hydrogen Atom • Calculate the energy required to excite the hydrogen electron from n = 1 to n = 2. Also, calculate the wavelength of light that must be absorbed by a hydrogen atom in its ground state to reach this excited state. • (Answer: DE = 1.633 x 10-18J; l = 1.216 x 10-7m)

The Bohr Model of the Hydrogen Atom • The energy levels calculated agree with the line spectrum for hydrogen • Cannot be applied to atoms other than hydrogen • Still a good model because it introduced the quantization of energy in atoms

The Quantum Mechanical Model of the Atom • So the Bohr model did not work for other atoms • Needed a new approach • Three physicists to the rescue: • Heisenberg (1901 - 1976) • de Broglie (1892 - 1987) • Schrodinger (1887 - 1961)

The Quantum Mechanical Model of the Atom • Quantum Mechanics = Wave Mechanics • Emphasized the wave nature of the electron • The electron behaves like a “standing wave” • similar to the stationary waves of string instruments like the guitar and violin • existance of nodes • only whole number of half wavelengths are allowed

The Quantum Mechanical Model of the Atom • Schrodinger’s equation • a mathematical treatment of the electron • too complicated for this course! • Electron’s position in space is described by a wave function • a specific wave function is an orbital

The Quantum Mechanical Model of the Atom • An orbital • not a Bohr model orbit • not a circular path • actually, when we describe an orbital, we do not know exactly how the electron is moving

The Quantum Mechanical Model of the Atom • Heisenberg Uncertainty Principle • we cannot know accurately both the position and the momentum of a particle (such as the electron) at any given time • I.e., the more accurately we know the position, the less accurately we know the momentum…and vice versa

The Quantum Mechanical Model of the Atom • So what does the wave function tell us? • Nothing we can visualize • The square of the wave function gives us the probability of finding an electron in a particular location in space • electron density = electron probability = atomic orbital

The Quantum Mechanical Model of the Atom • Atomic Orbital • a volume that encloses 90% of the total electron probability… • a volume where the electron can be found 90% of the time

The Quantum Mechanical Model of the Atom • Quantum numbers • Schrodinger’s equation has many solutions • I.e., there are many orbitals described by the wave functions • each orbital can be described by a set of quantum numbers

The Quantum Mechanical Model of the Atom • Principal quantum number • n • n = 1, 2, 3, … • related to the size and energy of the orbital • as n increases, the orbital becomes larger, so the electron is farther from the nucleus, and has higher energy

The Quantum Mechanical Model of the Atom • Angular momentum quantum number • l • l = 0 …n - 1 • related to the shape of the atomic orbital • l = 0 (s orbital) • l = 1 ( p orbital) • l = 2 (d orbital) • l =3 ( f orbital)

The Quantum Mechanical Model of the Atom • Magnetic Quantum Number • ml • ml = -l…0…l • related to the orbital’s orientation in space

The Quantum Mechanical Model of the Atom • Electron Spin Quantum Number • ms • ms= + 1/2 • an electron can spin in one of two opposite directions

The Quantum Mechanical Model of the Atom • Orbital Shape and Energies • Nodal Surfaces = nodes • areas of zero probability of finding an electron • as n increases, the number of nodal surfaces increases

The Quantum Mechanical Model of the Atom • Degenerate orbitals (in hydrogen) • have the same value of n • have the same energy • Add energy to an atom • electron becomes excited • electron is transferred to a higher energy orbital

Electron Spin and the Pauli Principle • Electrons spin in two directions • a spinning charge produces a magnetic field • Pauli Exclusion Principle • Wolfgang Pauli (1900 - 1958) • in an atom, no two electrons can have the same set of quantum numbers…I.e., e-’s in the same orbital have opposite spin

Polyelectronic Atoms • When there are many electrons in an atom, what is happening to these electrons? • Electrons • have kinetic energy as they move around • feel attractive forces from the nucleus • are repelled by other electrons

Polyelectronic Atoms • Because of the Heisenberg Uncertainty Principle, the repulsions between e-’s cannot be calculated exactly • Approximate forces on electrons • Approximate which has greater effect, attraction from nucleus or repulsion from other electrons

Polyelectronic Atoms • Example: Na atom • 11 protons, 11 electrons • look at the outermost 3s electron • it is attracted to the 11 protons in the nucleus • however, it doesn’t feel all 11 protons because it is shielded by (repulsions of) the inner electrons

Atomic Structure & Periodicity