Electromagnetic Spectrum

Light as a Wave - Recap Light exhibits several wavelike properties including Refraction Refraction: Light bends upon passing from one substance to another) Dispersion Dispersion: White light can be separated into colors. Diffraction Diffraction: Light sources interact to give both constructive and destructive interference. c = c = = wavelength (m) = frequency (s -1 ) c c = speed of light (3.00  10 8 m/s)

Blackbody Radiation & Max Planck The classical laws of physics do not explain the distribution of light emitted from hot objects. photons Max Planck solved the problem mathematically (in 1900) by assuming that the light can only be released in “chunks” of a discrete size (quantized like currency or the notes on a piano). We can think of these “chunks” as particles of light called photons. E = h E = h E = hc/ E = hc/ = wavelength (m) = frequency (s -1 ) h h = Planck’s constant (6.626  J-s)

Photoelectric Effect In 1905 Albert Einstein explained the photoelectric effect using Planck’s idea of quantized photons of light. He later won the Nobel Prize in physics for this work.

Line Spectrum of Hydrogen In 1885 Johann Balmer, a Swiss schoolteacher noticed that the frequencies of the four lines of the H spectrum obeyed the following relationship: = k [(1/2) 2 – (1/n) 2 ] = k [(1/2) 2 – (1/n) 2 ] Where k is a constant and n = 3, 4, 5 or 6. n=3n=4n=5n=6

Rydberg Equation When you look at the light given off by a H atom outside of the visible region of the spectrum, you can expand Balmer’s equation to a more general one called the Rydberg Equation = (cR H )[(1/n 1 ) 2 – (1/n 2 ) 2 ] = (cR H )[(1/n 1 ) 2 – (1/n 2 ) 2 ] 1/ = R H [(1/n 1 ) 2 – (1/n 2 ) 2 ] E = (hcR H )[(1/n 1 ) 2 – (1/n 2 ) 2 ] Where R H is the Rydberg constant (1.098  10 7 m -1 ), c is the speed of light (3.00  10 8 m/s), h is Planck’s constant (6.626  J-s) and n 1 & n 2 are positive integers (with n 2 > n 1 )

Bohr Model of the Atom In 1914 Niels Bohr proposed that the energy levels for the electrons in an atom are quantized E n = -hcR H (1/n) 2 E n = (-2.18  J)(1/n 2 ) Where n = 1, 2, 3, 4, … n=1 n=2 n=3 n=4

Louis DeBroglie & the Wave- Particle Duality of Matter While working on his PhD thesis (at the Sorbonne in Paris) Louis DeBroglie proposed that matter could also behave simultaneously as an particle and a wave. = h/mv = h/mv = wavelength (m) v v = velocity (m/s) h h = Planck’s constant (6.626  J-s) This is only important for matter that has a very small mass. In particular the electron. We will see later that in some ways electrons behave like waves.

Electron Diffraction Transmission Electron Microscope Electron Diffraction Pattern

Werner Heisenberg & the Uncertainty Principle While working as a postdoctoral assistant with Niels Bohr, Werner Heisenberg formulated the uncertainty principle.  x  p = h/4   x  x = position uncertainty  p  p = momentum uncertainty (p = mv) h h = Planck’s constant We can never precisely know the location and the momentum (or velocity or energy) of an object. This is only important for very small objects. The uncertainty principle means that we can never simultaneously know the position (radius) and momentum (energy) of an electron, as defined in the Bohr model of the atom.

Schrodinger and Electron Wave Functions Erwin Schrodinger, an Austrian physicist, proposed that we think of the electrons more as waves than particles. This led to the field called quantum mechanics. In Schrodinger’s wave mechanics the electron is described by a wave function, . The exact wavefunction for each electron depends upon four variables, called quantum numbers they are n = principle quantum number l = azimuthal quantum number m l = magnetic quantum number m s = spin quantum number

s-orbital Electron Density (where does the electron spend it’s time)  2 = Probability density # of radial nodes = n – l – 1

Velocity is proportional to length of streak, position is uncertain. Position is fairly certain, but velocity is uncertain. Schrodinger’s quantum mechanical picture of the atom 1. The energy levels of the electrons are well known 2. We have some idea of where the electron might be at a given moment 3. We have no information at all about the path or trajectory of the electrons

s & p orbitals

d orbitals # of nodal planes = l

Electrons produce a magnetic field. All electrons produce a magnetic field of the same magnitude Its polarity can either be + or -, like the two ends of a bar magnet Thus the spin of an electron can only take quantized values (m s =+½,-½), giving rise to the 4th quantum number

Single Electron Atom Multi Electron Atom