quantum theory waves behave like particles maxwell’s wave theory (1860) maxwell postulated that...
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Quantum Theory
Waves Behave Like ParticlesMaxwell’s Wave Theory (1860)
Maxwell postulated that changing electric fields produce changing magnetic fields: EMradiation ~ EM waves.Discrepancy:1. The wave theory could not explain the spectrum
of light emitted by a hot body.2. It could not explain the photoelectric effect
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Quantum Theory• Hot body – any body that has a temperature > 0
Kelvin Radiation From Incandescent BodiesLight & infrared radiation are produced by thevibration of the charged particles within theatom of a body that is so hot, it glows.• The higher the temperature, the more radiation at
frequencies of yellow, green, blue and violet is produced, and the “whiter” the body appears.
• The color you see depends on the relative amounts of emission at various frequencies.
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Quantum Theory• (see Blackbody curve
http://cwx.prenhall.com/petrucci/medialib/media_portfolio/text_images/FG09_11.JPG)
• The higher the Kelvin temperature, the more intense the radiation is, and the higher the frequency that can be emitted.
Intensity – amount of energy emitted each second. (power)
The amount of energy emitted each second in EM waves is proportional to absolute temperature
raised to the 4th power (T4)** Maxwell could not explain the shape of a
blackbody curve**
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Quantum TheoryMax Planck (1858-1947) – calculated the
spectrum (curve) – plot of radiation emitted at various frequencies.
Planck assumed the energy of vibration ofatoms could only have specific frequencies:E = n h f n = whole number
h = Planck’s constantf = frequencyE = Energy
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Quantum Theory
This behavior is described as being quantized – energy only comes in packets of specific sizes.
Planck also stated: • Atoms could only emit radiation when their
vibration energy changed• Planck’s constant: h= 6.626 x 10 –34 J/Hz
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The Photoelectric Effect
Maxwell could not explain why UV light discharged a negatively charged plate, but ordinary light could not.1905 – Albert Einstein explained the Photoelectric
Effect: Light & other forms of radiation consist of discrete bundles of energy called PHOTONS (particles of light). Each photon depends on the frequency of light.
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The Photoelectric Effect
Energy of a Photon: E = h f
Dual Nature of Light
• Maxwell & Planck’s work proposed light and hot bodies’ wave nature
• Einstein proposed that light and other energy acted like particles
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The Photoelectric Effect
Threshold frequency
• Electrons are only ejected if the frequency of the radiation is above a certain minimum value ~ threshold frequency (f0)
• This frequency varies with the type of metal (cathode) – only high frequency radiation ejects electrons.
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The Photoelectric EffectEinstein’s Photoelectric EquationKE = h f - h f0 Restatement of the conservation of Energy
A photon with minimum energy (h f0 ) is needed to eject an electron.
Work Function (W0) – energy needed to free an electron from a metal. W0 = h f0
• Radiation with a frequency greater than the threshold frequency (f0 ) has more energy. The excess ( h f - h f0 ) becomes KE.
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The Photoelectric Effect
The Kinetic Energy of the electrons can be determined by measuring the potential difference needed to stop them.
Work = KE = - q V0 V0 = stopping potential
The unit, Joule is too large for atomic systems so we use the electronvolt (eV)
1 eV = (1.6 x 10 -19 C) (1V) = 1.6 x 10 -19 CV
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The Photoelectric Effect
Kinetic Energy vs. Frequency
KEmax slope = Planck’s constant
Frequency
The rate of photoemission (emitted e-) depends on
the intensity (power) of the incident light.
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The Photoelectric Effect
Doubling the illumination (or intensity)
doubles the number of electrons emitted:
Photoelectric
Current
Intensity
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The Photoelectric Effect
The maximum KE depends only on the
frequency of the incident radiation
(KE = hf – hf0).
KEmax
Intensity
KEmax is independent of the intensity of the light source.
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The Compton Effect
Einstein predicted that a photon (even with no mass) has kinetic energy as a particle does, and Momentum, another particle property.
Recall: The photoelectric effect showed that photons have KE.
p = hf = h
c λ
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The Compton Effect
Arthur Compton (1922) tested Einstein’s theory:
Compton Effect – the increase in λ when X-rays are scattered off of electrons
Result: A shift in energy
The Experiment: He directed X-rays at a graphite target and measured the λ’s of the scattered X-rays
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The Compton Effect
E = hc E = hf where f = c/λ λ**increased wavelength meant that both energy &
momentum were lost by the photon**-the incoming photon suffers an elastic collision with
an atomic electronEnergy & momentum are transferred to the electron
**this is another proof of light’s particle behavior**
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The Compton Effect
Incoming photon e-
e-
outgoing photon
increased λ
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Particles Behave like Waves
• Photoelectric Effect
• Compton Scattering
1923 Louis Victor de Broglie
• Suggested particles have wave properties
Showed particle nature
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Matter Waves
Recall: p = mv and momentum of a photon:p = h/λ
So… p = mv = h/λRewrite the equation:λ = h/p = h/mv de Broglie wavelength• de Broglie suggested that all matter has wave
properties • The de Broglie wavelength for ordinary matter
(macroscopic) is far too small to produce observable effects
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Matter Waves
Particles & Waves
EM waves show particle-like properties:
Photoelectric Effect & Compton Effect
Particles show wave-like properties:
Diffraction & Interference
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The Atom
Rutherford & the Nuclear Model(previously, J.J.Thompson discovered the
electron & he believed a massive, positively
charged substance was also in the
atom~arranged like raisins in a muffin)
Ernest Rutherford proved otherwise…
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Rutherford’s Experiment• He directed a beam of alpha particles at a thin
sheet of gold foil (only a few atoms thick)• (an alpha particle is a helium nucleus consisting of
2 protons & 2 neutrons)• He noticed the following: ALPHA PARTICLE
SCATTERING…
The Atom
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Alpha particle scattering:
1. Most passed through undeflected
2. Some(small percentage) are scattered through angles ranging up to 180°. They are hyperbolic paths because of electric forces (Coulomb forces) between the particles and the positive nuclei
3. Some completely rebounded
The Atom
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• Rutherford explained these results by using Coulomb’s law and Newton’s laws of motion:– All positive charge of the atom is concentrated
at the nucleus– All mass is in the nucleus (99%)– Electrons are outside and far away from the
nucleus
NUCLEAR MODEL
The Atom
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Nuclear Model Limitations:
1. It did not account for the lack of emission of radiation as electrons move around the nucleus
2. It did not account for the spectrum of each element
The Atom
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The Bohr Model of the Atom
Many physicists tried to explain the atomic
spectra of various elements.
Niels Bohr (Danish Physicist)
• Tried to unite Rutherford’s model with Einstein’s theory of light (photons with discrete energy) PLANETARY MODEL
The Atom
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Bohr Model:1. The electron can only travel around the nucleus
in certain select orbits and no others.2. An electron may exist only in these orbits where
its angular momentum (mvr) is an integral multiple of Planck’s constant divided by 2
3. When an electron changes from one energy state to another, a quantum of energy equal to the difference between the energies of two states is emitted or absorbed.
The Atom
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The change in energy is given by:
hf = Ei – Ef Ei = energy of the initial
state
Ef = energy of the final
state
The photon must be exactly large enough (quantized) to raise
or lower the electron to another allowable orbit. Otherwise
the atom cannot absorb or emit it.
The Atom
n = 3
n = 2
n = 1
Photon emittedhf = E3 – E2
f = E3 – E2
h
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Atomic Spectra
• The arrangement of electrons around the nucleus can be predicted by the EMISSION SPECTRA.
EMISSION SPECTRA – set of visible wavelengths emitted by an atom
• The properties of individual atoms only becomes apparent when they are not combined with other elements.
(recall: an incandescent blackbody’s spectrum does not depend on the type of atom that makes its up)
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You can see an emission spectrum of a type of atom by looking through a diffraction grating or by putting the grating in front of a lens.
Spectrascope – light passes through a slit, then is dispersed by passing through a prism- each forms an image on the slit(dispersion)
Atomic Spectra
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Spectrum tubes (gas discharge tubes) – the gas glows when HIGH VOLTAGE is applied. The electrons collide and transfer energy to the atoms ~ the atoms give up this energy in the form of EM radiation
Incandescent solids – show a continuous spectrumGases – show a series of lines of different colors,
each a Analysis of line Spectra• Can tell us what elements are present• The relative amounts of the elements
Atomic Spectra
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• By comparing intensities of lines, percentages of compositions can be determined
ABSORPTION SPECTRA
• Gases will absorb light at characteristic wavelengths when they are cooled (reverse of emission)
Atomic Spectra
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• White light is sent through a sample of gas and through a spectrascope
• What normally would be a continuous spectrum now has dark lines in it.
• Bright lines of an emission spectra and dark lines of an absorption spectra occur at the same .
Analysis of spectra allows for the identification of the elements that make up a mixture
Fraunhofer – noticed some dark lines while examining the sun – Fraunhofer lines.
Atomic Spectra