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Chapter 27Chapter 27
Quantum Physics
General Physics
Quantum Physics I
Sections 1–3
General Physics
Need for Quantum Physics
Other problems remained in classical physics which relativity did not explain
Blackbody Radiation– The electromagnetic radiation emitted by a heated object
Photoelectric Effect– Emission of electrons by an illuminated metal
Compton Effect– A beam of x-rays directed toward a block of graphite
scattered at a slightly longer wavelength Spectral Lines
– Emission of sharp spectral lines by gas atoms in an electric discharge tube
General Physics
Development of Quantum Physics
Beginning in 1900– Development of ideas of quantum physics
• Also called wave mechanics• Highly successful in explaining the behavior of atoms,
molecules, and nuclei
Involved a large number of physicists
General Physics
Particles vs. WavesPARTICLE properties
individual motion position(time) – localized velocity v = x / t mass energy, momentum dynamics: F=ma interaction – collisions
quantum states spin
WAVE properties
collective motion wavelength (freq) – periodic velocity v = f dispersion energy, momentum dynamics: wave equation interference – superposition reflection, refraction, trans. diffraction – Huygens standing waves – modes polarization
General Physics
Blackbody Radiation
An object at any temperature emits 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
4TPower
General Physics
General Physics
General Physics
IR heat lamp Red hot Night vision
Silver heat shield Space blanket
General Physics
General Physics
General Physics
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
The wavelength of the peak of the blackbody distribution was found to follow Wein’s Displacement Law– λmax T = 0.2898 x 10-2 m • K
• λmax is the wavelength at which the curve’s peak
• T is the absolute temperature of the object emitting the radiation
Active Figure: Blackbody Radiation
General Physics
The Ultraviolet Catastrophe
Classical theory did not match the experimental data
At long wavelengths, the match is good
At short wavelengths, classical theory predicted infinite energy
At short wavelengths, experiment showed no energy
This contradiction is called the ultraviolet catastrophe
General Physics
Max Planck
1858 – 1947 Introduced a “quantum
of action” now known as Planck’s constant
Awarded Nobel Prize in 1918 for discovering the quantized nature of energy
General Physics
Planck’s Resolution
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 10-34 J s
Key Point: quantized energy states Few high energy resonators populated
Active Figure: Planck's Quantized Energy States
General Physics
Photoelectric Effect
When light is incident on certain metallic surfaces, electrons are emitted from the surface– This is called the photoelectric effect– The emitted electrons are called photoelectrons
The effect was first discovered by Hertz The successful explanation of the effect was
given by Einstein in 1905– Received Nobel Prize in 1921 for paper on
electromagnetic radiation, of which the photoelectric effect was a part
General Physics
Photoelectric Effect Schematic When light strikes E, photoelectrons
are emitted Electrons collected at C and passing
through the ammeter are a current in the circuit
C is maintained at a positive potential by the power supply
The current increases with intensity, until reaching a saturation level
No current flows for voltages less than or equal to –ΔVs, the stopping potential
The maximum kinetic energy of the photoelectrons is related to the stopping potential: KEmax = eVs
Active Figure: The Photoelectric Effect
General Physics
Features Not Explained by Classical Physics/Wave Theory
The stopping potential Vs (maximum kinetic energy KEmax) is independent of the radiation intensity
Instead, the maximum kinetic energy KEmax of the photoelectrons depends on the light frequency
No electrons are emitted if the incident light frequency is below some cutoff frequency that is characteristic of the material being illuminated
Electrons are emitted from the surface almost instantaneously, even at very low intensities
General Physics
Einstein’s Explanation A tiny wave packet of light energy, called a photon,
would be emitted when a quantized oscillator jumped from one energy level to the next lower one– Extended Planck’s idea of quantization to E.M. radiation
The photon’s energy would be E = hƒ
Each photon can give all its energy to an electron in the metal
The maximum kinetic energy of the liberated photoelectron is KEmax = hƒ –
is called the work function of the metal – it is the energy needed by the electron to escape the metal
General Physics
Explains Classical “Problems”
KEmax = hƒ – – The effect is not observed below a certain cutoff
frequency since the photon energy must be greater than or equal to the work function – without enough energy, electrons are not emitted, regardless of the intensity of the light
– The maximum KE depends only on the frequency and the work function, not on the intensity
– The maximum KE increases with increasing frequency
– The effect is instantaneous since there is a one-to-one interaction between the photon and the electron
General Physics
Verification of Einstein’s Theory
Experimental observations of a linear relationship between KEmax and frequency ƒ confirm Einstein’s theory
The x-intercept is the cutoff frequency– KEmax = 0 →
KEmax = hƒ –
hfc
General Physics
Cutoff Wavelength
The cutoff wavelength is related to the work function
Wavelengths greater than C incident on a material with a work function don’t result in the emission of photoelectrons
c
hc
General Physics
Photocells
Photocells are an application of the photoelectric effect
When light of sufficiently high frequency falls on the cell, a current is produced
Examples– Streetlights, garage door openers, elevators
General Physics
X-Rays
Electromagnetic radiation with short wavelengths– Wavelengths less than for ultraviolet– Wavelengths are typically about 0.1 nm– X-rays have the ability to penetrate most materials
with relative ease– High energy photons which can break chemical
bonds – danger to tissue
Discovered and named by Roentgen in 1895
General Physics
Production by an X-Ray Tube
X-rays are produced when high-speed electrons are suddenly slowed down
– Can be caused by the electron striking a metal target
A current in the filament causes electrons to be emitted
These freed electrons are accelerated toward a dense metal target
The target is held at a higher potential than the filament
General Physics
X-ray Tube Spectrum
The x-ray spectrum has two distinct components
Continuous broad spectrum– Depends on voltage applied to
the tube– Cutoff wavelength– Called bremsstrahlung
(“braking”) radiation The sharp, intense lines
depend on the nature of the target material
General Physics
An electron passes near a target nucleus
The electron is deflected from its path by its attraction to the nucleus– This produces an
acceleration It will emit
electromagnetic radiation when it is accelerated
Production of X-rays, 2
General Physics
Wavelengths Produced If the electron loses all of its energy in the
collision, the initial energy of the electron is completely transformed into a photon
The wavelength can be found from
Not all radiation produced is at this wavelength– Many electrons undergo more than one collision
before being stopped– This results in the continuous spectrum produced
maxmin
ƒhc
e V h
General Physics
Tumors usually have an irregular shape
Three-dimensional conformal radiation therapy (3D-CRT) uses sophisticated computers and CT scans and/or MRI scans to create detailed 3-D representations of the tumor and surrounding organs
Radiation beams are then shaped exactly to the size and shape of the tumor
Because the radiation beams are very precisely directed, nearby normal tissue receives less radiation exposure
X-ray Applications, X-ray Applications, Three-Dimensional Three-Dimensional Conformal Radiation Therapy (3D-Conformal Radiation Therapy (3D-
CRT)CRT)
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