quantum theory
TRANSCRIPT
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Chapter 27: Quantum Theory
PHYSICS Principles and
Problems
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BIG IDEA
Waves can behave like particles, and particles can behave like waves.
CHAPTER
27 Quantum Theory
MAIN IDEALight can behave as massless particles called photons.
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• James Maxwell’s electromagnetic wave theory was proven to be correct by the experiments of Heinrich Hertz in 1889.
• Light is an electromagnetic wave: able to explain all of optics, including interference, diffraction, and polarization,.
• Problem: absorption or emission of electromagnetic radiation.
A New Model Based on Packets of Energy
SECTION27.1
A Particle Model of Waves
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Emission Spectrum
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A Particle Model of Waves
Use of diffraction grating:
all of the colors of the rainbow would be visible.
The bulb also emits infrared radiation that our eyes cannot see.
emission spectrum. A plot of the intensity of the light emitted from a hot body over a range of frequencies
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• curve’s maximum height = temperature and frequency (energy emitted) increases,
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A Particle Model of Waves
Emission spectra of the incandescent body
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• a dense ball of gases heated to incandescence by the energy produced within it.
• surface temperature: 5800 K, radiates 4×1026 W
• On average, each square meter of Earth’s surface receives about 1000 J of energy per second (1000 W), enough to power ten 100-W lightbulbs.
SECTION27.1
A Particle Model of Waves
The Sun (common example of a hot body)
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• The problem with Maxwell’s electromagnetic theory: unable to explain the shape of the spectrum
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A Particle Model of Waves
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• Between 1887 and 1900, many physicists used existing classical physics theories to try to explain the shape. They all failed.
• In 1900, German physicist Max Planck found that he could calculate the spectrum if he introduced a revolutionary hypothesis: that atoms are not able to continuously change their energy.
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A Particle Model of Waves
Max Planck
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• Planck assumed that the vibrational energy of the atoms in a solid could have only specific frequencies, as shown by the following equation.
Energy of Vibration E = nhfUsed to measure the energy of vibrating atomPlanck’s constant = 6.63 × 10-34 J/Hz while n is an integer such as 0, 1, 2, 3 . . .
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A Particle Model of Waves
n = 0: E = (0)hf = 0n = 1: E = (1)hf = hfn = 2: E = (2)hf = 2hfn = 3: E = (3)hf = 3hf and so on but can never be
a fraction. Thus, energy is quantized (exist only in bundles of specific amount)
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• atoms do not always radiate electromagnetic waves when they are vibrating, as predicted by Maxwell.
• atoms emit radiation only when their vibrational energy changes. For example, if the energy of an atom changes from 3hf to 2hf, the atom emits radiation.
• The energy radiated is equal to the change in energy of the atom, in this case hf.
• Since h, has an extremely small value - the energy-changing steps are too small to be noticeable in ordinary bodies.
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A Particle Model of Waves
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The Photoelectric Effect
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A Particle Model of Waves
The two factors that are important in making light waves behave as a particle. When the frequency is increased the more current or energy is released.
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• 1905, Albert Einstein published a research that explained the photoelectric effect.
• light and other forms of electromagnetic radiation consist of discrete, quantized bundles of energy, each of which was later called a photon.
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A Particle Model of Waves
• The energy of a photon depends on its frequency.
Energy of a Photon E = hf
• Because the unit Hz = 1/s or s−1, the J/Hz unit of Planck’s constant is also equivalent to J·s.
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1 eV = (1.60 × 10−19 C)(1 V)
= 1.60 × 10−19 CV
= 1.60 × 10−19 J
• Because the joule is too large a unit of energy to use with atomic-sized systems, the more convenient energy unit of the electron volt (eV) is usually used.
• One electron volt is the energy of an electron accelerated across a potential difference of 1 V.
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A Particle Model of Waves
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• Using the definition of an electron volt allows the photon energy equation to be rewritten in a simplified form, as shown below.
• The energy of a photon is equal to the constant 1240 eV·nm divided by the wavelength of the photon.
Energy of a Photon
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The Photoelectric Effect (cont.)
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• Einstein’s photoelectric-effect theory is able to explain the existence of a threshold frequency (minimum frequency of incident light which can cause photo electric emission).
• minimum frequency and energy, hf0, is needed by a photon to eject an electron from metal.
• frequency below f0, the photon will not have the energy needed to eject an electron.
• A photon must have enough energy to be ejected.
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A Particle Model of Waves
The Photoelectric Effect (cont.)
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• radiation with a frequency greater than f0 has more than enough energy to eject an electron.
• In fact, the excess energy, hf − hf0, becomes the kinetic energy of the ejected electron.
Kinetic Energy of an Electron Ejected Due to the Photoelectric Effect
KE = hf − hf0
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A Particle Model of Waves
The Photoelectric Effect (cont.)
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• Note that hf0 is the minimum energy needed to free the most loosely held electron in an atom.
• some will require more than the minimum Because not all electrons in an atom have the same energy,
• As a result, the ejected electrons have differing kinetic energies. Some of the ejected electrons will have less kinetic energy.
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A Particle Model of Waves
The Photoelectric Effect (cont.)
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• At the stopping potential, the kinetic energy of the electrons at the cathode equals the work done by the electric field to stop them.
• This is represented in equation form as KE = −eV0.
• In this equation, V0 is the magnitude of the stopping potential in volts (J/C), and e is the charge of the electron (−1.60×10−19 C).
• Note that the negative sign in the equation along with the negative value of q yield a positive value for KE.
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A Particle Model of Waves
Planck and Einstein (cont.)
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Problem Solving
• Solve problem # 2 to 4 on page 734 and # 6 to 8 on page 736