We now realize that the phenomena of chemical interactions, and, ultimately life itself, are to be understood in terms of electromagnetism". -Richard Feynman
Quantum H Atom Review Radia Wave Function (1s): Radial Probability Density: Most Probable value: 1 ψ1s () r = e π a 3 0 r/ a P(r) = 4πr 2 ψ 2 dp solve dr = 0 0 Average value: rave = r = rp() r dr 0 Probability in (0-r): P r = P() r dr 0
The Electromagnetic Spectrum c = λ f Increasing Energy
If you pass white light through a prism, it separates into its component colors. long wavelengths R.O.Y. G. B.I.V spectrum short wavelengths
The Sun s Spectrum
Fraunhofer Lines: 1814 The English chemist William Hyde Wollaston was in 1802 the first person to note the appearance of a number of dark features in the solar spectrum. In 1814, Fraunhofer independently rediscovered the lines and began a systematic study and careful measurement of the wavelength of these features. In all, he mapped over 570 lines, and designated the principal features with the letters A through K, and weaker lines with other letters.
Atomic Emission of Light Each chemical element produces its own unique set of spectral lines when it burns
Incandescent Light Bulb Continuous Spectrum
Hydrogen Spectra
Helium Spectra
Mercury Spectra
Neon Spectrum
Oxygen Spectrum
Argon Spectrum
Kirkoff s Rules for Spectra: 1859 German physicist who developed the spectroscope and the science of emission spectroscopy with Bunsen. Kirkoff Bunsen * Rule 1 : A hot and opaque solid, liquid or highly compressed gas emits a continuous spectrum. * Rule 2 : A hot, transparent gas produces an emission spectrum with bright lines. * Rule 3 : If a continuous spectrum passes through a gas at a lower temperature, the transparent cooler gas generates dark absorption lines.
Kirkoff s Rules
Absorption Spectrum of Hydrogen Gas
Compare absorption lines in a source with emission lines found in the laboratory! Kirchhoff deduced that elements were present in the atmosphere of the Sun and were absorbing their characteristic wavelengths, producing the absorption lines in the solar spectrum. He published in 1861 the first atlas of the solar spectrum, obtained with a prism ; however, these wavelengths were not very precise : the dispersion of the prism was not linear at all.
Anders Jonas Ångström 1869 Ångström measured the wavelengths on the four visible lines of the hydrogen spectrum, obtained with a diffraction grating, whose dispersion is linear, and replaced Kirchhoff's arbitrary scale by the wavelengths, expressed in the metric system, using a small unit (10-10 m) with which his name was to be associated. Line color red blue-green violet violet Wavelength 6562.852 Å 4861.33 Å 4340.47 Å 4101.74 Å
Dispersion: Diffraction Gratings How does dispersion with a grating compare with a prism? Longer wavelength light is bent more with a grating. Shorter wavelength light is bent more with a prism. d sin θ = m λ
Balmer Series: 1885 Johann Balmer found an empirical equation that correctly predicted the four visible emission lines of hydrogen Johannes Robert Rydberg generalized it in 1888 for all transitions: 1 = R 1 1 λ 2 n H 2 2 R H is the Rydberg constant R H = 1.097 373 2 x 10 7 m -1 n is an integer, n = 3, 4, 5, The spectral lines correspond to different values of n H α is red, λ = 656.3 nm H β is green, λ = 486.1 nm H γ is blue, λ = 434.1 nm H δ is violet, λ = 410.2 nm
Oscillating Charges Produce Radio Waves: 1887 Heinrich Hertz I do not think that the wireless waves I have discovered will have any practical application." Frequency of EM wave is the same as the frequency of oscillation.
1896: Zeeman Effect The Zeeman Effect is the splitting of spectral lines when a magnetic field is applied. photo Zeeman took of the effect named for him Einstein visiting Pieter Zeeman in Amsterdam, with his friend Ehrenfest. (around 1920)
Everything we know about the Universe is based on SPECTRA! Cosmological Redshift: Expanding Universe Stellar Motions: Rotations and Radial Motions Solar Physics: Surface Studies and Rotations Gravitational Redshift: Black Holes & Lensing Exosolar Planets via Doppler Wobbler
Doppler Shift for Light Spectral lines shift due to the relative motion between the source and the observer
Red Shift: Moving Away Blue Shift: Moving Toward
The Universe is Expanding V = H o d Ho = 77 km/s/mpc 1 Megaparsec = 3.26 million light years
Where does light actually come from? What causes the discrete spectra?
Atomic Energy is quantized. It comes in chunks of Planck s constant, h. E = nhf, n= 0,1,2,3,... 34 h= 6.626x10 Js
Joseph John Thomson Plum Pudding Model 1904 Received Nobel Prize in 1906 Usually considered the discoverer of the electron Worked with the deflection of cathode rays in an electric field His model of the atom A volume of positive charge Electrons embedded throughout the volume
1911: Rutherford s Planetary Model of the Atom A beam of positively charged alpha particles hit and are scattered from a thin foil target. Large deflections could not be explained by Thomson s model. (Couldn t explain the stability or spectra of atoms.)
Electrons exist in quantized orbitals with energies given by multiples of Planck s constant. Light is emitted or absorbed when an electron makes a transition between energy levels. The energy of the photon is equal to the difference in the energy levels: E = nhf, n= 0,1,2,3,... = 34 h 6.626x10 Js E E E hf γ = i f =
Light Absorption & Emission E E E hf = = γ i f
Bohr s Assumptions 1. Electrons in an atom can occupy only certain discrete quantized states or orbits. 2. Electrons are in stationary states: they don t accelerate and they don t radiate. 3. Electrons radiate only when making a transition from one orbital to another, either emitting or absorbing a photon. Postulate: The angular momentum of an electron is always quantized and cannot be zero: L = n 2 h π ( n = 1,2,3,...)
Bohr s Derivation of the Energy for Hydrogen: Conservation of E: E = K + U F is centripetal: (1) Sub back into E: From Angular Momentum: (2) h L= n = mvr ( n= 1, 2,3,...) 2π Sub r back into (1): Sub into (2): Why is it negative?
Bohr Orbital Binding Energy for Single Electron Atoms E n Z = 13.6eV n 2 2 Ground State: n = 1 First Excited: n = 2 2 nd Excited: n = 3 1. -13.6eV is the energy of the H ground state. 2. Negative because it is the Binding Energy and work must be done on the atom (by a photon) to ionize it. 3. A 13.6eV photon must be absorbed to ionize the ground state 4. Bohr model only works for single electron atoms since it doesn t take into account electron-electron interaction forces.
Bohr: Allowed Orbital Radii n 2 11 rn = (5.9x10 m) Z n = 1, 2, 3 Bohr Radius (ground state): 5.9x10-11 m
The frequency of the photon emitted when the electron makes a transition from an outer orbit to an inner orbit is E E k e 1 1 2 i f e ƒ = = 2 2 h 2aoh nf ni It is convenient to look at the wavelength instead The wavelengths are found by 2 1 ƒ ke e 1 1 1 1 = = = R 2 2 H 2 2 λ c 2aohc nf ni nf ni
Bohr Line Spectra of Hydrogen Bohr s Theory derived the spectra equations that Balmer, Lyman and Paschen had previously found experimentally! 1 1 1 = ( ) λ 2 RZ n 2 2 f n i 7 1 R= 1.097x10 m Balmer: Visible Lyman: UV Paschen: IR
Problem A hydrogen atom is in the third (n = 4) excited state. It can make a jump to a different state by transition A, B, or C as shown, and a photon is either emitted or absorbed. a) Which transition, A, B, or C, emits a photon with the greatest energy? Calculate the wavelength in m and the energy in ev. b) What is the energy of a photon needed to ionize the atom when the electron is initially in the third excited state? Calculate in ev. A transition emits a photon with greatest energy. 1 1 1 = ( ) λ 2 RZ n 2 2 f n i = 10284375m 1 1 1 = 1 4 7 1 2 (1.097x10 m )1 ( ) 2 2 λ = 9.72x10 8 m E = 13.6eV Z 3 3 2 2 2 1 = 13.6eV 2 γ = 1.51eV 3
IMPORTANT NOTE!! Free electrons have continuous energy states! Only bound electrons have quantized energy states! This is because they are not forced to fit in a confined space like a wave in a box!!! Continuous or Discrete? Bound-Bound Transitions: Atoms, boxes D Bound-Free Transitions: Ionization C Free-Bound Transitions: Ion captures an electron C Free-Free Transitions: Collisions, electron absorption C
Spontaneous Emission Transition Probabilities Fermi s Golden Rule Transition probabilities correspond to the intensity of light emission.
Stimulated Emission 1 photon in, 2 out "When you come right down to it, there is really no such thing as truly spontaneous emission; its all stimulated emission. The only distinction to be made is whether the field that does the stimulating is one that you put there or one that God put there..." David Griffths, Introduction to Quantum Mechanics
Lasers Light Amplification by Simulated Emission of Radiation "A splendid light has dawned on me about the absorption and emission of radiation..." Albert Einstein, 1916
Stimulated Emission
Sample Problem What average wavelength of visible light can pump neodymium into levels above its metastable state? From the figure it takes 2.1eV to pump neodymium into levels above its metastable state. Thus, hc λ = = E 6 124. 10 ev m 2.10 ev 7 = 590. 10 m = 590 nm
Laser Applications
UV in, vibrant color out. Fluorescence
Phosphorescence Time Delayed Fluorescence Glow in the Dark: Day Glow
BTW: Iridescence: Diffraction
Phaser?