1. General Physics (PHY 2140) Lecture 27 Modern Physics Quantum Physics
Blackbody radiation
Plank’s hypothesis
Chapter 27
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2. If you want to know your progress so far, please send me an request at
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3. Lightning Review Last lecture: Modern physics
Relativistic energy, momentum
Relativistic addition of velocities
Review Problem: You are packing for a trip to another star, to which you will be traveling at 0.99c. Should you buy smaller sizes of your clothing, because you will be skinnier on the trip? Can you sleep in a smaller cabin than usual, because you will be shorter when you lie down?
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4. Reminder (for those who don’t read syllabus)
Reading Quizzes (bonus 5%):
It is important for you to come to class prepared, i.e. be familiar with the
material to be presented. To test your preparedness, a simple five-minute
quiz, testing your qualitative familiarity with the material to be discussed in
class, will be given at the beginning of some of the classes. No make-up
reading quizzes will be given.
There could be one today…
… but then again…
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5. 26.9 Relativistic Energy
The definition of kinetic energy requires modification in relativistic mechanics
KE = mc2 – mc2
The term mc2 is called the rest energy of the object and is independent of its speed
The term mc2 is the total energy, E, of the object and depends on its speed and its rest energy
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6. Relativistic Energy – Consequences
A particle has energy by virtue of its mass alone
A stationary particle with zero kinetic energy has an energy proportional to its inertial mass
E = mc2
The mass of a particle may be completely convertible to energy and pure energy may be converted to particles
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7. Energy and Relativistic Momentum
It is useful to have an expression relating total energy, E, to the relativistic momentum, p
E2 = p2c2 + (mc2)2
When the particle is at rest, p = 0 and E = mc2
Massless particles (m = 0) have E = pc
This is also used to express masses in energy units
mass of an electron = 9.11 x kg = MeV
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8. Problem: relativistic proton
A proton in a high-energy accelerator is given a kinetic energy of 50.0 GeV. Determine
the momentum and
the speed of the proton.
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9. Recall that E2 = p2c2 + (mc2)2. This can be used to solve for p:
A proton in a high-energy accelerator is given a kinetic energy of 50.0 GeV. Determine (a) the momentum and (b) the speed of the proton.
Recall that E2 = p2c2 + (mc2)2. This can be used to solve for p:
Given:
E = 50.0 GeV
Find:
p = ?
v =?
Thus,
Similarly with velocity:
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10. QUICK QUIZ
A photon is reflected from a mirror. True or false: (a) Because a photon has a zero mass, it does not exert a force on the mirror. (b) Although the photon has energy, it cannot transfer any energy to the surface because it has zero mass. (c) The photon carries momentum, and when it reflects off the mirror, it undergoes a change in momentum and exerts a force on the mirror. (d) Although the photon carries momentum, its change in momentum is zero when it reflects from the mirror, so it cannot exert a force on the mirror.
False
True
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11. Example 1: Pair Production
An electron and a positron are produced and the photon disappears
A positron is the antiparticle of the electron, same mass but opposite charge
Energy, momentum, and charge must be conserved during the process
The minimum energy required is 2me = 1.04 MeV
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12. Example 2: Pair Annihilation
In pair annihilation, an electron-positron pair produces two photons
The inverse of pair production
It is impossible to create a single photon
Momentum must be conserved
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13. Quantum Physics
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14. Introduction: Need for Quantum Physics
Problems remained from classical mechanics that relativity didn’t explain:
Blackbody Radiation
The electromagnetic radiation emitted by a heated object
Photoelectric Effect
Emission of electrons by an illuminated metal
Spectral Lines
Emission of sharp spectral lines by gas atoms in an electric discharge tube
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15. Development of Quantum Physics
Development of ideas of quantum mechanics
Also called wave mechanics
Highly successful in explaining the behavior of atoms, molecules, and nuclei
Quantum Mechanics reduces to classical mechanics when applied to macroscopic systems
Involved a large number of physicists
Planck introduced basic ideas
Mathematical developments and interpretations involved such people as Einstein, Bohr, Schrödinger, de Broglie, Heisenberg, Born and Dirac
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16. 26.1 Blackbody Radiation
An object at any temperature is known to emit electromagnetic radiation
Sometimes called thermal radiation
Stefan’s Law describes the total power radiated
The spectrum of the radiation depends on the temperature and properties of the object
Stefan’s constant
emissivity
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17. Blackbody
Blackbody is an idealized system that absorbs incident radiation of all wavelengths
If it is heated to a certain temperature, it starts radiate electromagnetic waves of all wavelengths
Cavity is a good real-life approximation to a blackbody
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18. Blackbody Radiation Graph
Experimental data for distribution of energy in blackbody radiation
As the temperature increases, the total amount of energy increases
Shown by the area under the curve
As the temperature increases, the peak of the distribution shifts to shorter wavelengths
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19. Wien’s Displacement Law
The wavelength of the peak of the blackbody distribution was found to follow Wein’s Displacement Law
λmax T = x 10-2 m • K
λmax is the wavelength at the curve’s peak
T is the absolute temperature of the object emitting the radiation
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20. The Ultraviolet Catastrophe
Classical theory did not match the experimental data
At long wavelengths, the match is good
Rayleigh-Jeans law
At short wavelengths, classical theory predicted infinite energy
At short wavelengths, experiment showed no energy
This contradiction is called the ultraviolet catastrophe
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21. Planck’s Resolution En = n h ƒ
Planck hypothesized that the blackbody radiation was produced by resonators
Resonators were submicroscopic charged oscillators
The resonators could only have discrete energies
En = n h ƒ
n is called the quantum number
ƒ is the frequency of vibration
h is Planck’s constant, h=6.626 x J s
Key point is quantized energy states
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