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Electromagnetic Radiation

• Matter waves involve material movement– Water ripples in a pond, ocean waves– Sound waves carried by air, metal. Wood, water– Earthquakes (s & p waves)

• Electromagnetic waves don’t require a carrier– A source of early confusion due to bad analogies – EM spans enormous range of frequencies

• Radio, TV, Cell Phone, microwave, x-ray …– Can be Ionizing (interact with matter to make ions)

• X-rays, gamma radiation, ultraviolet light– Mostly non-ionizing (no ions, but energy transferred)

• Useful because energy (e.g. information) IS transferred• Infrared heating, microwave, radio, GPS, TV, internet

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Water Wavesrequire material movement

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Electromagnetic WavesPass through vacuum or matter

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Electromagnetic Spectrum

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“starlight scope” or “night vision”allows one to see in darkness by converting

infrared to visible light

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Frequency

• How quickly the wave repeats– A time domain measure (cycles/second)

• Cycles/second now considered “slow”– Power line is 60 cycles/sec (60 Hertz or Hz)

• NY subway once 25 cps, Europe power at 50cps• Energy transfer per cycle is limited by frequency

• Modern devices run much faster– Laptop CPU now >3 GHz (3*10E9 Hz)– Microwave at 2.5 GHz, Cell Phone 1.9 GHz– More information or energy transfer per unit of time

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Electromagnetic Spectrum

• Wavelength– Expressed in length instead of time domain

• Completely EQUIVALENT to frequency– A measured length versus oscillation rate

• Wavelength inversely related to Frequency– C (meter/sec) = freq (cycle/sec) * wavelength (meter/cycle)– Higher frequency has smaller wavelength, and vice versa

– Common way of defining radiation frequency• “VHF” includes 2-meter wavelength applications

» Aircraft and Marine radio, TV channels >7, “2M ham band”

• Light usually specified in nanometers (per wavelength)– Violet at 440nm to Red at 650 nm

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Wavelength and Frequencymeters/sec (c) = cycles/sec (ע) * meters/cycle (λ)

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Atomic Spectra

Scientists troubled about light <1900• Similar to Mendeleev situation

– A jumble of disconnected but related information • Why lines of light at precise frequencies?

– Both Astronomical and Laboratory observations• Some frequencies interact with matter, others do not

– X-rays penetrate objects, – visible light absorbed or reflected– Radio waves “collected” by wire antenna (but not light or X-ray)

– Classical mechanics failed to provide explanations• Newton’s laws don’t work at atomic distances

– “ultraviolet catastrophe” does not happen

– When analogies are failing … need to create a new model• “out of the box” thinking required• Something seems to be going on with discrete numbers

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Splitting light with a prism“white” light comprised of many colorsSingle light source has limited colors

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Kirchoff and Bunsen

Flame Color Viewing

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Hydrogen Spectral Lines

HYDROGEN spectra, produced by gas discharge tube operating at 5000 VoltsSpectra seen through 600 line/mm diffraction grating.

Wavelength Relative

(nm) Intensity Transition Color

383.538 5 9-->2 Violet

388.905 6 8-->2 Violet

397.007 8 7-->2 Violet

410.174 15 6-->2 Violet

434.047 30 5-->2 Blue-Violet

486.133 60 4-->2 Blue-Green

656.285 120 3-->2 Red

656.2852 180 3-->2 Red

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Discrete Helium emission colorsHELIUM spectra, produced by gas discharge tube operating at 5000 voltsSpectra seen through 600 line/mm diffraction grating.

wavelength

Nanometers Intensity Intensity Color

396.4 50 Violet

402.6 70 Violet

438.793 w Blue-Violet

443.755 w Blue-Violet

447.148 s 100 Blue-Violet

471.314 m 40 Blue-Green

492.193 m 50 Dark Green

501.567 s 100 light Green

504.774 w

587.562 s 1000 Yellow

667.815 m 100 Red

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Atomic Spectra

• Johann Balmer– Developed a numerical formula which worked

• Formalized and predicted relationships of spectra colors

• He had no idea why it succeeded

• His model later validated by quantum mechanics– M’s and N’s turned out to be principal quantum numbers

– Differences between values correspond to light energy

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Original Balmer Equation

The formula discovered by Johann Balmer could be used to find the wavelength of the absorption/emission lines and was originally presented as follows:

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Spectral series

• “m” and “n” have simple integer values• Some color ranges named for individuals

– Lyman series, m=1 (Ultra Violet)– Balmer series, m=2 (visible light)– Paschen series, m=3 (infrared)

• The formulas worked … but why ?– Initially a “numerology” experiment– We gain deeper understanding via Q.M.

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Bohr Atom

• Classical mechanics says “any orbit is OK”– No apparent limitation for observable objects

• Stars, planets, moons, satellites, ball on a string

– Infinitely variable orbits fail for very small things

• Bohr’s contribution is model with fixed orbits– Electrons must occupy “allowed” orbits– No electron permitted between defined orbits– Electrons must “jump” between allowed orbits

• It’s that “jump” which emits or absorbs light• Energy difference between orbits = energy of light

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Bohr Atom• Quantized behavior not an obvious concept

– Violates Newton’s laws, which worked well >200 yrs

• Bohr “digitized” atomic behavior– Electron orbits became “quantized” in specific radii– Orbit closest to nucleus designated as n=1

• Closest orbit has least energy, called “ground state”

– Orbits with increasing radii designated n=2, 3, 4 …• Orbits with greater radii have higher energy• Moving into higher orbit = “excited state”• Energy difference between excited & ground = energy of light

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IC1848 RGB Tricolor

Image courtesy: Dr. Robert Gendler

www.robgendlerastropics.com

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IC1848 Tricolor Emission Line

In the light of sulfur, hydrogen and oxygen

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Analog versus DigitalAnalog world allows any possible positionDigital world has only discrete possibilities

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Energy content of Light• Einstein’s photoelectric experiment

– Alkalai metal photocell results baffling• Cesium cathode selectively releases electrons • Red light released no electrons

– No matter how intense the source of light

• Blue light did release electrons from surface– Electron quantity varied with light intensity

– Blue light therefore had to have more energy• Capable of moving electrons between orbits• Enough energy to move electron away from atom• Ionization = complete removal

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Particles of Light Energy

• Orbit energy rises & falls by discrete amounts– Unit of discrete step is Planck’s constant = h

• h = 6.62*E-34 Joule-sec (fundamental natural constant)

• Relates energy of orbit transition to color of light

• Famous result is Energy = h*frequency– Explains the emission and absorption of light

• Reason why Balmer’s formula worked

• Digital values were related to electron orbit numbers

– Explains why red light failed in photocell• Insufficient energy to “excite” electron to higher level

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Energy content of Light• Light is therefore little “bundles of energy”

– Energy content depends on color– Color related to frequency (or wavelength)– Δ energy between orbits = energy of light– Packet or bundle of energy called “Photon”

– E=h*ע is a fundamental formula

• Meets the “½ inch to be famous” rule (e.g. E=mC2)– We also know c = ע*λ (freq *wavelength0

• Therefore E=h*c/λ• Einstein awarded Nobel Prize for this discovery

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Quantum Mechanics

• Newton’s laws didn’t work on nanometer-scale– Non arbitrary energy levels were a new concept

– Dual nature of light as a particle also a new idea

– Need a new model to account for microscope behavior

• Niels Bohr Atom– Used a planetary model to describe the atom

• Electrons circling the nucleus (earth and sun analogy)

• New twist was that only certain orbits are allowed

• This effectively “quantizes” the levels of energy permitted

• Still a “mechanical analogy”, in a world of particles = waves

• Needed another update to deal with wave behavior

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Key Points• Mechanical models didn’t work at atomic scale

– Wave based models gave better predictions

• Equivalence of particles and waves– Electrons found in both domains– Baseballs have wavelength, light has mass

• Uncertainty idea “baked into” QM– Cannot know everything to infinite level of detail

• Certainty exchanged for statistics– cannot know exactly where electrons are– Know only of High & Low Probability regions

• Electron distribution around polar molecule• Locations of charges within chemical bonds

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Quantum Numbers(the “nitty-gritty” part)

• “game of numbers” modeling the atom– A mathematical representation

• Set of rules developed to model what we see• “Rules” are empirical• Names are arbitrary, sometimes differing

– Started with 3 numbers, evolved to 4• Spectral line splitting required the fourth

– Consider baseball• Could have been defined differently• What is optimum number of bases, players?• How and why are rules established• Sometimes changes improve the game

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Quantum NumbersDigital values, no fractions allowed

• Atomic structure defined by electron levels– Principal Quantum Number is “n”

• Small integer numbers

• n defines effective size (radius) of the electron orbit

• The radius determines the energy – Larger radius = more energy

– Electron escapes as n∞, the “ionization energy”

• n also defines electron groups having same “n”– Also called “shells”

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HP Pavilion in San JoseEach seat is unique, no 2 seats have same set of location numbers

Seat assignment includes row, section, & seat numberSame idea used for N, L, & M electron “seats” in the atom

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“Quantum Stadium” Analogy

• Must add energy to climb into higher rows– Potential energy is greater the higher you go

• Lose energy descending to lower row– Potential energy reduced with lower altitude– Can “Jump” more than one row at a time

• Larger energy change doing this

• Lowest energy is “ground state”– Cannot descend lower than floor of stadium

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Nice QM analogy, the Amphitheater

• To use the analogy of an amphitheater, quantum numbers describe how many rows and seats are available. Individual electrons may be described by the combination of quantum numbers, like a spectator in an amphitheater assigned to a particular row and seat.

• Like spectators in an amphitheater moving between seats and rows, electrons may change their statuses, given the presence of available spaces for them to fit, and available energy. Since shell level is closely related to the amount of energy that an electron possesses, “leaps” between shell (and even subshell) levels requires transfers of energy. If an electron is to move into a higher-order shell, it requires that additional energy be given to the electron from an external source. Using the amphitheater analogy, it takes an increase in energy for a person to move into a higher row of seats, because that person must climb to a greater height against the force of gravity. Conversely, an electron “leaping” into a lower shell gives up some of its energy, like a person jumping down into a lower row of seats, the expended energy manifesting as heat and sound.

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Our Experiment• Exciting an element’s electrons with heat• Electrons fall to ground state emitting light

– Energy of light is difference between QN’s– Color of light defines its wavelength

• Colors used to estimate wavelengths

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Typical colors

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Details

• 8 known materials, use color charts to estimate emission wavelength

• Select 3 unknowns, determine identity by matching flame colors with knowns.

• Look through spectroscope for wavelength values of Hydrogen and one other gas – Grating also separates colors, not calibrated

• Answer questions in text of experiment– Includes energy calculation.

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Color Wheel

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Spectrum Colors

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Energy Calculation• Choose color using flame and color wheel• Estimate wavelength for that color

– Red is 650nm = 650E-9 m or 6.50E-7 m

• Utilize Planck’s constant in E=hc/λ– E = energy in Joules– h = 6.626E-34 Joule-sec, a constant in nature– c = 3.00E8 meters/sec, speed of light is a constant– λ = wavelength of light (650 nm for example)

• E = 6.626E-34*3.00E6 / 6.50E-7– 6.626*3.00/6.50 x (10-34*108*107 1019)– 3.06E-19 Joules, energy of red light quanta– You will make a plot for different colors

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Dip end of wire in acid and then in flame to burn off residues, then dip wire in experiment solution and

into hot part of flame (inner blue cone).

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Colors will be representative of elements

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There is a short burst of color (due to small amount of material). Green color on left is Cu (Copper)

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Something you can do on the kitchen stove

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We’ll look at many of these elements

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Flame colors are basis of fireworks

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Fun Stuff !Colored candles, Haloween pumpkin

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Additive colors apply to lightSubtractive colors apply to ink, paint

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Can also get information from what’s missing

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Emission vs AbsorptionObserving “missing” lines, we determine what elements

absorbed light and therefore composition of the universe.

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Visible Spectrum, all colors from mix of elementsEmission Spectrum, from a single element

Absorption Spectrum, single element absorbs light

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Basic SpectroscopeYou will look at emission of a gas

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Press the button and calibration scale will appear. Note the nanometer value of 3-4

prominent wavelengths for your report

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Sample Calculation• λ = Wavelength = 650 nanometers (for red light)

– 650 nm /109 nm per meter = 6.5*10-7 meters• h = 6.62*10-34 Joule-sec

– Planck’s constant of proportionality– Einstein only said energy and frequency were

proportional, this constant is derived from that.• C= 3*108 meters/second

– Experimentally determined, a universal constant

• Energy E=h*c/λ– E = (6.62*10-34 J-sec)*(3.00*108 m/sec)/ (6.5*10-7 meters)

– E = (6.62 x 3.00 / 6.5) * (10-34 x 108 x 107)– E = 3.055 x 10-19 joules

Simplified Calculation method• Wavelength is the only thing changing

• simplify: constant1 * constant2 = constant3

• E = h * c / λ (red is 650nm)

• E = (6.62*10E-34 J-s)*(3.00*E8 m/s) / λ– Numerator is 19.86E-26, never changes

• Move numerator decimal for easy division– E red = 1986E-28 / 650E-9 = 3.06E-19 J– E yellow = 1986E-28 / 580E-9 = 3.42E-19 J– E blue = 1986E-28 / 450E-9 = 4.41E-19 J

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Let’s do it

• Be sure to wear goggles; we’re working with flames, acids, chemicals.

• Lights off at one end of room to better see the spectra

• Experiment report due next week

• Have fun !