Su5c12 By Adel Khamis
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Unit Five
-38-
Chapter Twelve
Wave Particle Duality Overview: Studying physics can be divided into two branches:
Classical physics •
Quantum (Modern) physics •
Explain everything in our daily life and our common experiences.
Explain some phenomena at which the classical physics can’t explain.
•
It deals with atomic and subatomic system.
•
It explains all phenomena involved in electronics.
Light:
•
Light is electromagnetic waves, therefore it reflect, refract, interfere and diffract. •
γ rays
10-12
x rays
10-9
Visible light is a small part of the electromagnetic waves. UV
V L
Infra red
10-6
Microwaves TV radio 10-3
1
103
Wavelength in meter • Summary
Electromagnetic waves propagate in space at a constant speed (3x108 m/sec). 2007/2008
Unit Five
-39•
Chapter Twelve
Electromagnetic waves differ in frequency and wavelength.
Planck’s distribution: • •
Hot bodies emit light and heat.
The light emitted from the hot bodies consists of all wavelengths, but in different intensity.
•
By drawing a graphical relation between the wavelength and the radiation intensity, we found that the radiation intensity increase by increasing the wavelength then it decrease again. •
The wave length at with the
radiation intensity has its maximum value is decrease by increase the temperature of the source of radiation.
Wien’s law: The wavelength at which the peak of the (radiation intensity – wavelength) curve occurs is inversely proportional to temperature.
Example one: • •
Sun surface temperature is 6000ºK.
The wavelength at the peak is 5000 A. (visible range of light)
Summary
2007/2008
Unit Five •
-40-
Chapter Twelve
40% of the total energy emitted by sun is in the radiation visible range, 50% is heat (infra radiation), while the rest of energy is distributed over the remaining spectrum.
Example two: •
Glowing incandescent lamp’s temperature is 3000ºK. •
•
The wavelength at the peak is 10000 A.
20% of the total energy emitted by the lamp is in the radiation visible range, and most of the rest of energy is heat.
Explanation of Planck’s distribution: Disadvantage of classical physics: • • • •
Classical physics can’t explain the distribution.
Where the energy is directly proportional to the frequency.
Therefore by increase the frequency the radiation intensity will increase.
Which mean by decrease the wavelength the radiation intensity will increase. •
That can explain the right part of the curve, but not the left part. Modern physics (Planck’s explanation):
•
Radiation made up of small units (packets) of energy, each called Quantum (Photon). • •
•
Electrons rotate in energy levels each has energy = n h ν
The atom does not radiate as long as it remains in one energy level.
If the atom shifts from a high energy level to a lower energy level, it emits a photon whose energy = h ν •
Therefore, Photons are not equal in energy, but the energy of the photon is directly proportional to its frequency.
Summary
2007/2008
Unit Five •
-41-
Chapter Twelve
At small wavelength of radiation (high frequency) the energy of each photon is high, which lead to decrease the number of emitted photons to keep the energy constant.
•
The intensity of radiation is indicated by the number of photons, therefore, at high frequency the intensity of radiation decrease, due to the decrease of photons number and the curve of radiation intensity – wavelength becomes directly proportional.
•
Since the total number of photons are so huge therefore we can’t see separated photons, but we observe the features of the stream of photons as a whole, which represent the classical properties of radiation
Black body radiation: •
All non glowing bodies (even living
creatures) absorb the radiation and reemit it. •
Bodies of black color absorb all radiation, therefore it consider as perfect absorber. •
The black bodies emit the absorbed
radiation, therefore it consider as perfect emitter. •
An enclosed cavity with a small hole, can considered as black body, because all of the radiation within the cavity remains trapped due to multiple reflection. •
Small part of the radiation leaks out which is called black body radiation.
Application on Black body radiation: • Summary
Earth absorbs the radiation from the sun, and reemits it. 2007/2008
Unit Five •
-42-
Chapter Twelve
The temperature of earth’s surface is low therefore the wavelength of emitted radiation at the peak is high according to wien’s law.
•
The peak wavelength is about 10 Micron, which is within the infrared region.
•
Satellites, airborne and terrestrial equipment are mapping the earth surface by using of all radiation regions including the visible region and the microwave region in addition to the infrared radiation.
•
Scientists analyze such images to determine possible natural earth resources.
•
In military purposes, the same technique is also used as night vision system. •
•
In medicine, it is used to tumor detection.
In criminology, where the heat radiation from a person lingers for a while even after the person has left, which called remote sensing.
Photoelectric effect: Surface potential barrier: •
A metal contains positive ions and free
electrons which can move around inside the metal but cannot leave it, due to the attractive forces of the surface which known as surface potential barrier. •
Light energy or heat energy can overcome the surface potential barrier. Photoelectric effect: It is the emission of electrons when light falls on metal’s surface. Disadvantage of classical physics:
•
The emission of electrons (the electric current intensity) should be directly proportional to the intensity of light, but it does not.
Summary
2007/2008
Unit Five
-43-
•
Chapter Twelve
The energy of emitted electrons (its velocity) should be directly proportional to the light intensity, but it does not.
•
In case of low light intensity, giving sufficient time should give some electrons enough energy to be freed, but it does not •
The frequency of light has no effect on the emission of electrons, but it has. Properties of photoelectric effect:
•
The emission of electrons depends primarily on the frequency of the incident light not on its intensity.
•
No electrons emit if the frequency of light less than a certain frequency νc, no matter the intensity of light was. •
The emission of electrons occurs instantly as long as ν > νc, which means that the electrons do not need time to collect energy if the light intensity is low. Modern physics (Einstein’s explanation):
•
Releasing of electron required a certain amount of energy called work function (Ew). •
Since energy of photon can be calculated according to the relation E = hν, therefore the photon who is able to release electron must has energy equal Ew=hνc.
•
If the energy of the photon is greater than Ew, then the difference of energy is gained by the electron as kinetic energy which increase the velocity of that electron.
Summary
2007/2008
Unit Five
-44•
Chapter Twelve
Work function (Ew) is a specific property of the metal. Factor affects the emission:
•
The emission of electrons depends on work function, which mean depends on the kind of metal only. •
It does not depend on the light intensity. •
•
It does not depend on exposure time.
It does not depend on the voltage difference between the anode and the cathode.
Application on Black body radiation: Cathode ray tube (CRT):
• It consists of evacuated tube has narrow end called electronic gun (Egun) and wide end panted with fluorescent material called screen. •
The E-gun contains cathode and anode connected to high potential difference •
The cathode is heated by filament heater, to estimate it to emit electrons in form of electron beam.
•
The intensity of electron beam can be controlled by negative grid in its way.
Summary
2007/2008
Unit Five •
-45-
Chapter Twelve
The direction of electron beam can be controlled by electric or magnetic field in its way to sweep the screen point by point which called raster.. •
When the electron beam fall on the screen it forms an illuminated point, and by raster the screen images can be formed.
Interpretation of the photoelectric effect: • •
When the cathode of discharge tube affected by light, it emits electrons.
By connecting negative potential difference between the anode and cathode, therefore the velocity of electrons will decrease, and at a certain potential difference (Stopping voltage Vs). The flow of electrons will stop and no electron arrive to the anode.
•
At the stopping voltage, the electric energy equals to the kinetic energy of the electron
W = KEmax Vs e = KEmax 1 Vs = KE max e Sine the electrons emits by the effect of photon’s energy, therefore: •
Photons energy = work function + kinetic energy
hν = Ew + KEmax KEmax = hν - Ew •
Which mean that the kinetic energy depends on the frequency of photon, what ever the intensity of light was.
N.B.: By drawing a graphical relation between the stopping potential for different kind of metals as x-axis, and the kinetic energy of electrons as y-axis, then: Summary
2007/2008
Unit Five
-46•
Chapter Twelve
The mathematical relation: Vs e = KEmax •
The slope means: electron charge.
By drawing a graphical relation between the square velocity of electrons as y-axis, and the potential difference of the cathode tube as xaxis, then: • •
e 2 The mathematical relation: v = 2 VS m
The slope means: double the specific charge of electrons. By drawing a graphical relation between the kinetic energy of emitted electron as y-axis, and the frequency of fallen photon as x-axis, then: •
The mathematical relation: K.E = h ν - h υc •
• •
The slope means: Planck’s constant.
Intersection with Y-axis means: work function.
Intersection with X-axis means: critical frequency.
Compton Effect: When photon of high frequency (x ray or γ ray) collides with free electron then: • •
For photon: frequency decreases, and direction changes.
For electron: velocity increase, and direction changes. This can’t explain by classical
physics, while the quantum physics can explain that by using of the conservation law of energy and conservation law of momentum. Summary
2007/2008
Unit Five •
-47-
Chapter Twelve
(Energy of photon + Energy of electron) before collision = (Energy of photon + Energy of electron) after collision. •
(Momentum of photon + Momentum of electron) before collision = (Momentum of photon + Momentum of electron) after collision.
Photon: •
It is a packet of energy which has mass, velocity and linear momentum.
Photon Properties: • • •
According to Planck equation E = h ν According to Einstein equation E = mc2
Therefore the mass of photon (m) can be calculated from the relation m=
•
hυ c2
And the momentum of photon (p) can be calculated from the relation PL = •
hυ c
Also, the momentum can be calculated from rate of energy
PW = rate of energy = energy of photon x ϕ L PW = h υ Φ L Where: • •
ϕL: Rate of emitted photon
If a beam of photons is incident on a certain surface at the rate of ϕL photons/sec, therefore, the rate of change of momentum (force) can be calculated from the relation:
Summary
2007/2008
Unit Five
-48-
Chapter Twelve
F = 2mc Φ L hυ F = 2 Φ L c F= •
2PW c
This force is so small, since the velocity of light is so large, therefore the
effect of that force, will not unless if affects small mass such as electron, and that can explain Compton effect.
N.B.: By drawing a graphical relation between the mass of photon as y-axis, and its frequency as y-axis, then: •
The mathematical relation: m = •
hν c2 h c2
The slope means:
By drawing a graphical relation between the mass of photon as y-axis, and reciprocal of its wavelength as y-axis, then: •
The mathematical relation: m = •
h cλ
The slope means:
h c
By drawing a graphical relation between the momentum of photon as y-axis, and its frequency as y-axis, then: •
The mathematical relation: PL = •
hν c
The slope means:
h c
By drawing a graphical relation between the momentum of photon as y-axis, and reciprocal of its wavelength as y-axis, then: Summary
2007/2008
Unit Five
-49-
Chapter Twelve h λ
•
The mathematical relation: PL =
•
The slope means: Planck’s constant.
Application of Einstein equation: The atomic bomb is an application of Einstein equation where the nuclear fission is associated with a small loss of mass which is converted to large amount of energy due to the equation of Einstein:
E = mc2 Coincident between microscopic and macroscopic models: Microscopic model: •
Photon can be considered as a sphere of radius λ, vibrates with frequency ν. •
The stream of photons collectively has a magnetic field and electric field. •
The two fields are perpendicular to each other and to the direction of propagation. •
•
The photon stream (flux) carries the energy of the wave.
The wave intensity measured by measuring the magnitude of the electric or magnetic field associated with the light wave. •
•
That means that the intensity of wave indicates the number of photons.
N.B.: This model used when deal with very small objects such as atoms or electrons. Macroscopic model: •
•
The wave motion accompanies the photon stream.
N.B.: This model used when deal with larger object than the wavelength of light.
Summary
2007/2008
Unit Five
-50-
Chapter Twelve
Tomography Scan: X Rays: •
X rays are used to detect tumors, where the body placed on a movable bed, while the source and the detector of x rays surrounding the body by different angles.
•
By changing the angle of both x rays and the detector together, many images can be produced. •
By using of computer, the images can be collected to produce tomography picture for the body, which can indicates the tumors. MRI:
•
Magnetic resonance imaging is preferred to x ray in producing tomography scan, where the x ray has possibly harmful side effects.
•
A body placed on a movable bed, where a strong (superconductive) magnet and source of radio waves (RF) surrounded it. • •
The strong magnet used to orients the spins of the nuclei of hydrogen.
RF used to disturb the spin motion of the nuclei of hydrogen then the RF stopped.
•
The hydrogen nuclei relaxing to their original state, producing RF waves which can be received by a detector, and by using of the computer that can produce tomography picture for the body, which can indicates the tumors.
Relation between photon wavelength and its linear momentum: C = λυ
λ= •
Summary
C ν
Multiply the fraction by h (Planck’s constant)
2007/2008
Unit Five
-51-
Chapter Twelve
λ=
hC hν
λ=
h hν C •
λ=
Linear momentum (PL) = mc =
hν C
h PL N.B.:
•
When photons fall on a surface, a comparison is made between the wavelength and the inter-atomic distance of the surface:
•
If λ is greater than the inter-atomic distance, these photons sense the surface as a continuous surface, and refract from it •
If λ is smaller than the inter-atomic distance, photons penetrate through the surface, such as what happens in case of X-Rays.
Wave properties of a particle: •
When electron moves with velocity (v), it accompanied with wave, and wavelength can be determined by using of De Broglie equation: λ=
h PL
The electron wave: •
Electron wave is similar to photon wave where both refract, reflect, interfere and diffract. •
Electron wave differ than photon wave, where it is not an electromagnetic wave, while it has probabilistic nature.
Summary
2007/2008
Unit Five
-52-
•
Chapter Twelve
According to Heisenberg the probability of electron waves denoted by ψ,
where the location of electron can’t determined precisely, but the probability ψ 2
•
indicates its distance from the nucleus.
The probability of being at distance zero is zero, or the electron will fall in the nucleus. •
The probability of being at distance infinity from the nuclei is zero, or the electron will escape and the atom ionized. • •
Atom has lower energy than its ion by the ionization energy
Electron circulates the nuclei in a path which has integer number of wavelength.
Summary
2007/2008
Unit Five
-53-
Chapter Twelve
Electron Microscope: •
Electron microscope has higher resolving power that optical microscope.
•
Electron microscope use electron waves, and magnetic lenses. •
Due to the short wavelength of electron waves, so it can detect very small objects.
Quantum Mechanics: Schrodinger stat the assumptions of quantum mechanics which used instead of the classical mechanics if the object is tightly bounded in a limited size: •
Electron energy has a certain value called energy levels, and the atoms does not emit any energy unless it falls from a high level to a lower level. •
Relaxation: The emission of atom is in form of photon whose energy (hυ) equals to the difference between the two energy levels.
•
Excitation: Absorption of photon does not occur unless the photon has energy exactly equal to the difference between two energy levels. •
Ionization: If the photon has energy greater than ionization energy, then the electron totally freed from the atom, and the atom becomes ionized. •
•
Relaxation and excitation are simultaneous processes.
There is a function which is always positive that describes the electron in the atom.
Summary
2007/2008
-38-
Chapter Twelve
Wave Particle Duality Overview: Studying physics can be divided into two branches:
Classical physics •
Quantum (Modern) physics •
Explain everything in our daily life and our common experiences.
Explain some phenomena at which the classical physics can’t explain.
•
It deals with atomic and subatomic system.
•
It explains all phenomena involved in electronics.
Light:
•
Light is electromagnetic waves, therefore it reflect, refract, interfere and diffract. •
γ rays
10-12
x rays
10-9
Visible light is a small part of the electromagnetic waves. UV
V L
Infra red
10-6
Microwaves TV radio 10-3
1
103
Wavelength in meter • Summary
Electromagnetic waves propagate in space at a constant speed (3x108 m/sec). 2007/2008
Unit Five
-39•
Chapter Twelve
Electromagnetic waves differ in frequency and wavelength.
Planck’s distribution: • •
Hot bodies emit light and heat.
The light emitted from the hot bodies consists of all wavelengths, but in different intensity.
•
By drawing a graphical relation between the wavelength and the radiation intensity, we found that the radiation intensity increase by increasing the wavelength then it decrease again. •
The wave length at with the
radiation intensity has its maximum value is decrease by increase the temperature of the source of radiation.
Wien’s law: The wavelength at which the peak of the (radiation intensity – wavelength) curve occurs is inversely proportional to temperature.
Example one: • •
Sun surface temperature is 6000ºK.
The wavelength at the peak is 5000 A. (visible range of light)
Summary
2007/2008
Unit Five •
-40-
Chapter Twelve
40% of the total energy emitted by sun is in the radiation visible range, 50% is heat (infra radiation), while the rest of energy is distributed over the remaining spectrum.
Example two: •
Glowing incandescent lamp’s temperature is 3000ºK. •
•
The wavelength at the peak is 10000 A.
20% of the total energy emitted by the lamp is in the radiation visible range, and most of the rest of energy is heat.
Explanation of Planck’s distribution: Disadvantage of classical physics: • • • •
Classical physics can’t explain the distribution.
Where the energy is directly proportional to the frequency.
Therefore by increase the frequency the radiation intensity will increase.
Which mean by decrease the wavelength the radiation intensity will increase. •
That can explain the right part of the curve, but not the left part. Modern physics (Planck’s explanation):
•
Radiation made up of small units (packets) of energy, each called Quantum (Photon). • •
•
Electrons rotate in energy levels each has energy = n h ν
The atom does not radiate as long as it remains in one energy level.
If the atom shifts from a high energy level to a lower energy level, it emits a photon whose energy = h ν •
Therefore, Photons are not equal in energy, but the energy of the photon is directly proportional to its frequency.
Summary
2007/2008
Unit Five •
-41-
Chapter Twelve
At small wavelength of radiation (high frequency) the energy of each photon is high, which lead to decrease the number of emitted photons to keep the energy constant.
•
The intensity of radiation is indicated by the number of photons, therefore, at high frequency the intensity of radiation decrease, due to the decrease of photons number and the curve of radiation intensity – wavelength becomes directly proportional.
•
Since the total number of photons are so huge therefore we can’t see separated photons, but we observe the features of the stream of photons as a whole, which represent the classical properties of radiation
Black body radiation: •
All non glowing bodies (even living
creatures) absorb the radiation and reemit it. •
Bodies of black color absorb all radiation, therefore it consider as perfect absorber. •
The black bodies emit the absorbed
radiation, therefore it consider as perfect emitter. •
An enclosed cavity with a small hole, can considered as black body, because all of the radiation within the cavity remains trapped due to multiple reflection. •
Small part of the radiation leaks out which is called black body radiation.
Application on Black body radiation: • Summary
Earth absorbs the radiation from the sun, and reemits it. 2007/2008
Unit Five •
-42-
Chapter Twelve
The temperature of earth’s surface is low therefore the wavelength of emitted radiation at the peak is high according to wien’s law.
•
The peak wavelength is about 10 Micron, which is within the infrared region.
•
Satellites, airborne and terrestrial equipment are mapping the earth surface by using of all radiation regions including the visible region and the microwave region in addition to the infrared radiation.
•
Scientists analyze such images to determine possible natural earth resources.
•
In military purposes, the same technique is also used as night vision system. •
•
In medicine, it is used to tumor detection.
In criminology, where the heat radiation from a person lingers for a while even after the person has left, which called remote sensing.
Photoelectric effect: Surface potential barrier: •
A metal contains positive ions and free
electrons which can move around inside the metal but cannot leave it, due to the attractive forces of the surface which known as surface potential barrier. •
Light energy or heat energy can overcome the surface potential barrier. Photoelectric effect: It is the emission of electrons when light falls on metal’s surface. Disadvantage of classical physics:
•
The emission of electrons (the electric current intensity) should be directly proportional to the intensity of light, but it does not.
Summary
2007/2008
Unit Five
-43-
•
Chapter Twelve
The energy of emitted electrons (its velocity) should be directly proportional to the light intensity, but it does not.
•
In case of low light intensity, giving sufficient time should give some electrons enough energy to be freed, but it does not •
The frequency of light has no effect on the emission of electrons, but it has. Properties of photoelectric effect:
•
The emission of electrons depends primarily on the frequency of the incident light not on its intensity.
•
No electrons emit if the frequency of light less than a certain frequency νc, no matter the intensity of light was. •
The emission of electrons occurs instantly as long as ν > νc, which means that the electrons do not need time to collect energy if the light intensity is low. Modern physics (Einstein’s explanation):
•
Releasing of electron required a certain amount of energy called work function (Ew). •
Since energy of photon can be calculated according to the relation E = hν, therefore the photon who is able to release electron must has energy equal Ew=hνc.
•
If the energy of the photon is greater than Ew, then the difference of energy is gained by the electron as kinetic energy which increase the velocity of that electron.
Summary
2007/2008
Unit Five
-44•
Chapter Twelve
Work function (Ew) is a specific property of the metal. Factor affects the emission:
•
The emission of electrons depends on work function, which mean depends on the kind of metal only. •
It does not depend on the light intensity. •
•
It does not depend on exposure time.
It does not depend on the voltage difference between the anode and the cathode.
Application on Black body radiation: Cathode ray tube (CRT):
• It consists of evacuated tube has narrow end called electronic gun (Egun) and wide end panted with fluorescent material called screen. •
The E-gun contains cathode and anode connected to high potential difference •
The cathode is heated by filament heater, to estimate it to emit electrons in form of electron beam.
•
The intensity of electron beam can be controlled by negative grid in its way.
Summary
2007/2008
Unit Five •
-45-
Chapter Twelve
The direction of electron beam can be controlled by electric or magnetic field in its way to sweep the screen point by point which called raster.. •
When the electron beam fall on the screen it forms an illuminated point, and by raster the screen images can be formed.
Interpretation of the photoelectric effect: • •
When the cathode of discharge tube affected by light, it emits electrons.
By connecting negative potential difference between the anode and cathode, therefore the velocity of electrons will decrease, and at a certain potential difference (Stopping voltage Vs). The flow of electrons will stop and no electron arrive to the anode.
•
At the stopping voltage, the electric energy equals to the kinetic energy of the electron
W = KEmax Vs e = KEmax 1 Vs = KE max e Sine the electrons emits by the effect of photon’s energy, therefore: •
Photons energy = work function + kinetic energy
hν = Ew + KEmax KEmax = hν - Ew •
Which mean that the kinetic energy depends on the frequency of photon, what ever the intensity of light was.
N.B.: By drawing a graphical relation between the stopping potential for different kind of metals as x-axis, and the kinetic energy of electrons as y-axis, then: Summary
2007/2008
Unit Five
-46•
Chapter Twelve
The mathematical relation: Vs e = KEmax •
The slope means: electron charge.
By drawing a graphical relation between the square velocity of electrons as y-axis, and the potential difference of the cathode tube as xaxis, then: • •
e 2 The mathematical relation: v = 2 VS m
The slope means: double the specific charge of electrons. By drawing a graphical relation between the kinetic energy of emitted electron as y-axis, and the frequency of fallen photon as x-axis, then: •
The mathematical relation: K.E = h ν - h υc •
• •
The slope means: Planck’s constant.
Intersection with Y-axis means: work function.
Intersection with X-axis means: critical frequency.
Compton Effect: When photon of high frequency (x ray or γ ray) collides with free electron then: • •
For photon: frequency decreases, and direction changes.
For electron: velocity increase, and direction changes. This can’t explain by classical
physics, while the quantum physics can explain that by using of the conservation law of energy and conservation law of momentum. Summary
2007/2008
Unit Five •
-47-
Chapter Twelve
(Energy of photon + Energy of electron) before collision = (Energy of photon + Energy of electron) after collision. •
(Momentum of photon + Momentum of electron) before collision = (Momentum of photon + Momentum of electron) after collision.
Photon: •
It is a packet of energy which has mass, velocity and linear momentum.
Photon Properties: • • •
According to Planck equation E = h ν According to Einstein equation E = mc2
Therefore the mass of photon (m) can be calculated from the relation m=
•
hυ c2
And the momentum of photon (p) can be calculated from the relation PL = •
hυ c
Also, the momentum can be calculated from rate of energy
PW = rate of energy = energy of photon x ϕ L PW = h υ Φ L Where: • •
ϕL: Rate of emitted photon
If a beam of photons is incident on a certain surface at the rate of ϕL photons/sec, therefore, the rate of change of momentum (force) can be calculated from the relation:
Summary
2007/2008
Unit Five
-48-
Chapter Twelve
F = 2mc Φ L hυ F = 2 Φ L c F= •
2PW c
This force is so small, since the velocity of light is so large, therefore the
effect of that force, will not unless if affects small mass such as electron, and that can explain Compton effect.
N.B.: By drawing a graphical relation between the mass of photon as y-axis, and its frequency as y-axis, then: •
The mathematical relation: m = •
hν c2 h c2
The slope means:
By drawing a graphical relation between the mass of photon as y-axis, and reciprocal of its wavelength as y-axis, then: •
The mathematical relation: m = •
h cλ
The slope means:
h c
By drawing a graphical relation between the momentum of photon as y-axis, and its frequency as y-axis, then: •
The mathematical relation: PL = •
hν c
The slope means:
h c
By drawing a graphical relation between the momentum of photon as y-axis, and reciprocal of its wavelength as y-axis, then: Summary
2007/2008
Unit Five
-49-
Chapter Twelve h λ
•
The mathematical relation: PL =
•
The slope means: Planck’s constant.
Application of Einstein equation: The atomic bomb is an application of Einstein equation where the nuclear fission is associated with a small loss of mass which is converted to large amount of energy due to the equation of Einstein:
E = mc2 Coincident between microscopic and macroscopic models: Microscopic model: •
Photon can be considered as a sphere of radius λ, vibrates with frequency ν. •
The stream of photons collectively has a magnetic field and electric field. •
The two fields are perpendicular to each other and to the direction of propagation. •
•
The photon stream (flux) carries the energy of the wave.
The wave intensity measured by measuring the magnitude of the electric or magnetic field associated with the light wave. •
•
That means that the intensity of wave indicates the number of photons.
N.B.: This model used when deal with very small objects such as atoms or electrons. Macroscopic model: •
•
The wave motion accompanies the photon stream.
N.B.: This model used when deal with larger object than the wavelength of light.
Summary
2007/2008
Unit Five
-50-
Chapter Twelve
Tomography Scan: X Rays: •
X rays are used to detect tumors, where the body placed on a movable bed, while the source and the detector of x rays surrounding the body by different angles.
•
By changing the angle of both x rays and the detector together, many images can be produced. •
By using of computer, the images can be collected to produce tomography picture for the body, which can indicates the tumors. MRI:
•
Magnetic resonance imaging is preferred to x ray in producing tomography scan, where the x ray has possibly harmful side effects.
•
A body placed on a movable bed, where a strong (superconductive) magnet and source of radio waves (RF) surrounded it. • •
The strong magnet used to orients the spins of the nuclei of hydrogen.
RF used to disturb the spin motion of the nuclei of hydrogen then the RF stopped.
•
The hydrogen nuclei relaxing to their original state, producing RF waves which can be received by a detector, and by using of the computer that can produce tomography picture for the body, which can indicates the tumors.
Relation between photon wavelength and its linear momentum: C = λυ
λ= •
Summary
C ν
Multiply the fraction by h (Planck’s constant)
2007/2008
Unit Five
-51-
Chapter Twelve
λ=
hC hν
λ=
h hν C •
λ=
Linear momentum (PL) = mc =
hν C
h PL N.B.:
•
When photons fall on a surface, a comparison is made between the wavelength and the inter-atomic distance of the surface:
•
If λ is greater than the inter-atomic distance, these photons sense the surface as a continuous surface, and refract from it •
If λ is smaller than the inter-atomic distance, photons penetrate through the surface, such as what happens in case of X-Rays.
Wave properties of a particle: •
When electron moves with velocity (v), it accompanied with wave, and wavelength can be determined by using of De Broglie equation: λ=
h PL
The electron wave: •
Electron wave is similar to photon wave where both refract, reflect, interfere and diffract. •
Electron wave differ than photon wave, where it is not an electromagnetic wave, while it has probabilistic nature.
Summary
2007/2008
Unit Five
-52-
•
Chapter Twelve
According to Heisenberg the probability of electron waves denoted by ψ,
where the location of electron can’t determined precisely, but the probability ψ 2
•
indicates its distance from the nucleus.
The probability of being at distance zero is zero, or the electron will fall in the nucleus. •
The probability of being at distance infinity from the nuclei is zero, or the electron will escape and the atom ionized. • •
Atom has lower energy than its ion by the ionization energy
Electron circulates the nuclei in a path which has integer number of wavelength.
Summary
2007/2008
Unit Five
-53-
Chapter Twelve
Electron Microscope: •
Electron microscope has higher resolving power that optical microscope.
•
Electron microscope use electron waves, and magnetic lenses. •
Due to the short wavelength of electron waves, so it can detect very small objects.
Quantum Mechanics: Schrodinger stat the assumptions of quantum mechanics which used instead of the classical mechanics if the object is tightly bounded in a limited size: •
Electron energy has a certain value called energy levels, and the atoms does not emit any energy unless it falls from a high level to a lower level. •
Relaxation: The emission of atom is in form of photon whose energy (hυ) equals to the difference between the two energy levels.
•
Excitation: Absorption of photon does not occur unless the photon has energy exactly equal to the difference between two energy levels. •
Ionization: If the photon has energy greater than ionization energy, then the electron totally freed from the atom, and the atom becomes ionized. •
•
Relaxation and excitation are simultaneous processes.
There is a function which is always positive that describes the electron in the atom.
Summary
2007/2008
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