3.12 Turning points in physics Flashcards
1
Q
What happens when a potential difference is applied across a discharge tube with a low pressure gas inside of it?
A
- A cathode ray will be produced
- The tube will begin to glow with it glowing brightest at the cathode
2
Q
What was concluded about electrons from Thomson’s cathode ray experiment?
A
- They have a mass
- They have a negative charge
- They have the same properties no matter what gas is used in the discharge tube
- They have a very large charge to mass ratio
3
Q
What were cathode ray particles renamed?
A
Electrons
4
Q
Describe how the discharge tube begins to glow in Thomson’s cathode ray experiment.
A
- The high pd across the discharge tube pulls electrons off the gas atoms, forming ion and electron pairs
- The positive gas ions are accelerated towards the cathode, colliding with it to release more electrons
- The electrons are accelerated along the tube and collide with and excite gas atoms
- The atoms de-excite and release photons of light
5
Q
Why are the electrons in a discharge tube accelerated to high speeds?
A
The gas is at low pressure, so less kinetic energy is lost
6
Q
Why does it glow the brightest at the cathode in a discharge tube?
A
At the cathode the gas ions and electrons can recombine and emit photons of light.
7
Q
What is thermionic emission?
A
Where a metal is heated until the free electrons on its surface gain enough energy and are emitted.
8
Q
How do electron guns work?
A
- They use a pd in order to accelerate electrons, released from the cathode through thermionic emission, towards the anode
- The electrons pass through a small gap in the anode to form a narrow electron beam travelling at a constant velocity beyond it
9
Q
What is the work done on an electron accelerated through a potential difference V?
A
ΔW = eV
10
Q
Describe the energy of an accelerated electron as it moves from the cathode towards the anode.
A
Its electrical potential energy is converted into kinetic energy, so it speeds up.
11
Q
Describe the energy of an accelerated electron after it reaches the anode.
A
- Its kinetic energy will be equal to the work done on the electron by the electric field
- ½mv² = eV
12
Q
By what methods can the specific charge of an electron be determined?
A
- Fine beam tube - low pressure gas and uniform magnetic field
- Thomson’s crossed fields - magnetic and electric field perpendicular to each other
13
Q
What is a fine beam tube?
A
A piece of apparatus containing a low pressure gas with a uniform magnetic field passing through it.
14
Q
How can the specific charge of an electron be determined using a fine beam tube?
A
- An electron gun accelerates electrons which enter the fine beam tube perpendicular to the direction of the magnetic field
- Electrons move in a circular path as the magnetic field acts perpendicular to their motion, acting as a centripetal force
- Electrons collide with and excite gas atoms, which de-excite to release photons of light, making the path of the electrons visible, so the radius of their circular path can be measured
- mv²/r=Bev, ½mv²=eV, v=(2eV/m)^½, m((2eV/m)^½)/r=Be, 2mV/r²= B²e, e/m=2V/B²r²
15
Q
How can the specific charge of an electron be determined using a Thomson’s crossed fields?
A
- An electron gun accelerates electrons which enter perpendicular to the direction of both fields
- Electrons are deflected upwards by the electric field, and deflected downwards by the magnetic field
- The strengths of these fields are adjusted until the electron beam passes through the crossed fields undeflected
- Bev=eV/d, v=V/Bd, ½mv²=eVₐ, v ²=2eVₐ/m, 2eVₐ/m=V²/B²d², e/m=V²/2B²d²Vₐ (where Vₐ is the accelerating voltage)
16
Q
What was significant about the specific charge of an electron being constant whatever gas was used to produce the electrons?
A
It demonstrates that all atoms contain electrons
17
Q
What is the relationship between the specific charge of an electron and a proton?
A
The specific charge of an electron is around 1800 times larger than that of a proton.
18
Q
What was the purpose of Millikan’s oil drop experiment?
A
To calculate the charge of an electron
19
Q
Describe the set up of Millikan’s oil drop experiment.
A
- An atomiser sprays tiny droplets of oil, which are negatively charged due to friction
- They fall until they reach two parallel plates forming a uniform electric field, where the droplets experience an electric force
- The field strength can be adjusted by changing the pd between the plates, until the observed oil droplet becomes stationary, where QV/d = mg
20
Q
How was the charge of an electron determined in Millikan’s oil drop experiment?
A
- 6πηrv = mg
- m = 4/3πr³ρ
- 6πηrv = 4/3πr³ρg
- r² = (9ηv)/(2ρg)
- QV/d = mg
- QV/d = 4/3πr³ρg
- Q = 4πr³ρgd/3V
21
Q
What was the significance of Millikan’s results?
A
- The charge of all the oil droplets observed was an integer multiple of 1.6x10^-19 C
- This shows charge is quantised, as it exists in discrete packets of 1.6x10^-19 C
- Which is the smallest possible magnitude of charge, the magnitude of charge carried by an electron
22
Q
What was Newton’s corpuscular theory of light?
A
Light was formed from small elastic particles called corpuscles which were continuously given out by luminous objects in all directions
23
Q
What was Newton’s explanation for reflection?
A
- Corpuscles collide with the surface and a repulsive force pushes them back, causing their component of velocity perpendicular to the surface to change direction, while their component of velocity parallel to the surface stays the same
- Angle of incidence = angle of reflection
24
Q
What was Newton’s explanation for refraction?
A
As corpuscles enter a denser medium, short-range forces of attraction cause their component of velocity perpendicular to the surface to increase, while the parallel component of velocity stays the same, resulting in the light bending towards the normal, and travelling faster in the denser medium
25
What are the flaws in Newton’s corpuscular theory of light?
- It couldn’t explain diffraction
- It states that light travels faster in denser mediums
26
What was Huygens’ explanation for light?
- Light was a longitudinal wave
- All points on the wavefront are point sources of secondary wavelets that spread out in the forward direction at the speed of the wave
27
What was Huygens’ explanation for reflection?
As the whole wavefront will not reach the surface at the same time (unless travelling along the normal), wavelets spread away from the surface once they reach it, and rejoin with others to reform the reflected wavefront
28
What was Huygens’ explanation for refraction?
It was assumed that light travels slower in a denser medium, therefore, as it entered a more optically dense medium, it would slow down and bend towards the normal
29
Why was the acceptance of Huygens’ wave theory of light delayed?
- Newton was more reputable at the time
- Took time for Newton’s theory to be disproved
30
What does Newton’s theory of light predict would happen in Young’s double slit experiment?
- An interference wouldn’t be formed
- Instead there would only be two bright fringes corresponding to the two slits
31
When was Newton’s theory of light disregarded?
When the speed of light was measured in water
32
Why was Newton’s theory of light disregarded?
It was found that light travels slower in water, contradicting Newton’s theory where corpuscles speed up when entering a denser medium.
33
What is the nature of electromagnetic waves?
- Formed of alternating sinusoidal magnetic and electric fields travelling perpendicularly in phase
- The direction of wave travel is perpendicular to the oscillations of the electric and magnetic field
34
Who predicted the existence of EM waves?
Maxwell
35
What does 𝜇₀ represent in Maxwell's formula and what does it relate to?
- The permeability of free space
- Relates to the magnetic flux density produced by a current-carrying wire in free space
36
What does 𝜀₀ represent in Maxwell's formula and what does it relate to?
- The permittivity of free space
- Relates to the electric field strength of the field formed by a charged object in free space
37
How did Hertz discover radio waves?
- Gap in a circuit opposite a copper wire detector loop with the same gap
- EM waves travelled through the air to induce a pd in the copper wire detector causing a spark to jump across the detector gap
38
Why did a spark cross the gap in the loop of wire in Hertz's experiment?
- It detected the EM wave's alternating magnetic field as the field entered the loop
- This caused a change in magnetic flux, inducing a pd
39
How did Hertz’s experiment support that electromagnetic waves are transverse?
- The radio waves could be polarised by rotating the detector
- The intensity of the sparks detected decreased to a minimum at 90°, and increased back to a maximum at 180°
40
How was Hertz able to determine the speed of radio waves from his experiment?
- Stationary wave made by placing a reflective surface behind the detector, making nodes, which he could measure the distance between to find the wavelength
- Frequency calculated from known laws of electricity
41
What was the significance of the value of the speed of radio waves calculated by Hertz?
It was found to be the same as Maxwell's predicted value of the speed of EM waves, helping to confirm that radio waves were EM waves.
42
What was the setup of Fizeau’s experiment?
- A pulsed beam of light is passed through a gap in a rotating toothed wheel
- The beam of light reflects on a mirror a large distance behind the wheel causing it to return back through the same gap between teeth in the wheel
43
How did Fizeau determine the speed of light from his experiment?
- When the speed of rotation of the wheel was low, light reflected back to the observer through the same gap it passed through
- The speed of rotation of the wheel was increased until light couldn’t be seen by observer, as it is blocked by a tooth next to the gap it could previously pass through
- The speed of light was determined by measuring the distance from the wheel and mirror, the frequency from the wheel’s rpm, and number of teeth in wheel
44
Why was the value of the speed of light calculated by Fizeau significant?
It was very close to the value predicted by Maxwell, providing evidence that light was an EM wave.
45
What is a black body?
An object that absorbs and emits all possible wavelengths of EM radiation
46
What is black body radiation?
EM radiation that peaks according to temperature
47
What did wave theory predict about the relationship between the wavelength and intensity of EM radiation?
As the wavelength of radiation decreases, the intensity of the radiation increases, leading to a prediction of emission of an infinite amount of UV radiation.
48
What is the UV catastrophe?
The widely accepted wave theory predicted an impossible amount of UV radiation and it could not be used to explain experimental measurements.
49
How could the UV catastrophe be resolved?
By Planck’s interpretation of EM waves
50
What was Planck’s interpretation of EM waves?
EM waves travel in discrete packets called quanta that have an energy directly proportional to their frequency
51
Why can wave theory not explain the existence of a threshold frequency?
It suggests that any frequency of light should be able to cause photoelectric emission as the energy absorbed by each electron will gradually increase with each incoming wave.
52
What was Einstein's explanation of the relationship between frequency and photoelectric emission, and the existence of a threshold frequency?
- When a photon interacts with an electron, all its energy is transferred to it
- An electron can only interact with a single photon
- A photoelectron is only emitted if this energy is above the work function
- As E=hf, the threshold frequency is when photon energy is equal to the work function of the metal
53
Why can wave theory not explain the immediacy of the photoelectric effect?
It suggests time is needed for the energy supplied to the electrons to reach the work function.
54
What was Einstein's explanation of the immediacy of the photoelectric effect?
The photon energy is transferred to the electron immediately when they interact, so photoelectrons are emitted immediately.
55
Why can wave theory not explain the intensity of the light in the photoelectric effect?
It suggests that increasing the intensity of the light increases the speed of photoelectric emission.
56
What was Einstein's explanation of the intensity of light in the photoelectric effect?
- Intensity is equal to the number of photons released per second
- A higher intensity increases the number of photoelectrons emitted because more photons interact with electrons per second
57
What about the energy of emitted photoelectrons couldn’t be explained by wave theory?
Photoelectrons are released with a range of kinetic energies
58
What was Einstein’s explanation of why photoelectrons are released with a range of kinetic energies?
- All electrons receive the same amount of energy from a photon
- But electrons deeper in the metal lose energy through collisions when leaving the metal, so have a lower kinetic energy
59
What happens to the kinetic energy of photoelectrons if the metal surface is positively charged and why?
- The kinetic energy of the photoelectrons decreases as they must do work against the electrostatic force of attraction towards the surface
- As the potential on the surface is increased, the number of photoelectrons released decreases, as there are less photoelectrons with a high enough kinetic energy to be emitted
60
Describe the electron diffraction experiment.
- Electron gun accelerates electrons though a vacuum tube towards a crystal lattice
- Electrons interact with the small gaps between the atoms to form a diffraction pattern on a fluorescent screen behind the crystal
61
What is the relationship between the accelerating voltage and the de Broglie wavelength of electrons?
As the accelerating voltage increases, the speed of electrons increases, decreasing their de Broglie wavelength, decreasing the fringe spacing
62
What is resolving power?
A microscope’s ability to distinguish structures which are close to each other
63
Why do electron microscopes have a much higher resolving power than light microscopes?
The wavelength of an electron beam is much smaller than that of light
64
How is the wavelength of electrons related to the resolving power of the microscope?
As the wavelength of the electrons decreases the resolving power of the microscope increases
65
What does TEM stand for?
Transmission electron microscope
66
How are images formed in a TEM?
- An electron beam produced by thermionic emission is accelerated using an anode
- The electrons are focused by magnetic lenses, so that any at the edge are deflected towards the centre
- They are then focused on a sample by a condenser lens and pass though the sample
- The projector lens creates the final image on a fluorescent screen
67
Why is the sample used in a TEM very thin?
So that the electrons passing through do not slow down and their wavelength remains unchanged
68
What does the condenser lens do in a TEM?
Deflects the electrons so that they form a wide parallel beam
69
What does the objective lens do in a TEM?
Forms an image of the sample
70
What does the projector lens do in a TEM?
Magnifies the image made by the objective lens and projects it onto the fluorescent screen
71
How does increasing the accelerating voltage of the electron gun increase the resolving power of the microscope?
The speed of the electrons increases, decreasing their wavelength
72
How is the resolving power of a TEM limited?
- Sample thickness
- Electrons travelling at different speeds
73
How does sample thickness limit the resolving power of a TEM?
As electrons pass through a thick sample they slow down, increasing their wavelength and decreasing the resolving power.
74
How does electrons travelling at different speeds limit the resolving power of a TEM?
- Some electrons may lose kinetic energy after being emitted through thermionic emission from the electron gun due to collisions
- They travel at different speeds, so have different wavelengths and are diffracted by different amounts, causing aberration
75
What is aberration?
- Electrons travelling at different speeds causing blurring of the image
- They have different wavelengths and are therefore diffracted by different amounts
76
What will the diameter of the de Broglie wavelength of the electron beam have to be in order to resolve details around the size of an atom?
Around 0.1nm (the diameter of an atom)
77
What does STM stand for?
Scanning tunnelling microscope
78
How does an STM form an image?
- Quantum tunnelling of electrons
- A tipped probe at a constant potential moves across the surface of a material to create a tunnelling current between the probe and the surface so electrons cross the gap from positive to negative
79
What is quantum tunnelling?
- Electrons in the surface have to overcome the potential barrier
- Electrons have insufficient energy so due to wave properties of electrons, there is a probability of electrons crossing from the sample to the tip
80
Why is the probe of an STM kept at a constant potential?
So that electrons can only travel in one direction
81
What is the tunnelling current?
The movement of electrons across the gap between the tip of the probe and the surface of the object
82
What is the relationship between the size of the gap between the probe and the surface, and the tunnelling current?
As the gap becomes larger, tunnelling current decreases
As the gap becomes smaller, tunnelling current increases
83
In what ways an STM can operate?
- Constant-height mode
- Constant-current mode
84
How does an STM form an image in constant-height mode?
- The gap width varies as the tip scans across the surface at a constant height
- The current changes due to varying electron transfer as the gap width varies
- The current decreases as the gap width increases (or vice versa)
- The variation of current with time is used to map the surface
85
How does an STM form an image in constant-current mode?
- The tip of the probe is maintained a certain distance (about 1nm) above the surface
- The current decreases as the gap width increases (or vice versa)
- Feedback is used to move the tip to change the current to its original value
- The variation of height of the probe tip with time is used to map the surface
86
Describe the Michelson-Morley interferometer setup.
Monochromatic light sent through a semi-silvered mirror at 45°, splitting the light into 2 beams, both sent to their own mirror to be reflected back to the semi-silvered mirror, to both be sent to a detector to show an interference pattern of fringes.
87
What is the role of the compensator in the Michelson-Morley experiment?
It makes up for the extra distance travelled by the beam of light reflected by 90° at the semi-silvered mirror
88
What is the ‘ether’?
A medium in space proposed to carry light waves.
89
What was the purpose of the Michelson-Morley experiment?
To test the existence of an ‘ether’, by testing the speed of light waves travelling in different directions with the same distance to see if there was a motion changing the speed of one of the light waves.
90
What was the result of the Michelson-Morley experiment?
After rotating the setup 90°, the interference pattern did not change, showing the time taken for light to travel was unaffected by rotation of the apparatus.
91
What conclusions were drawn from the result of the Michelson-Morley experiment?
1. The ether doesn’t exist
2. The speed of light is invariant in free space
92
What are inertial frames of reference?
- Those which move at constant velocity relative to each other
- A frame accelerating or rotating cannot be an inertial frame of reference.
93
What does Einstein’s theory of special relativity apply to?
Inertial frames of reference
94
What are the two postulates of Einstein’s theory of special relativity?
1. The speed of light in free space is invariant
2. The laws of physics have the same form in all inertial frames
95
Explain what is meant by the postulate ‘the speed of light in free space is invariant’.
The speed of light is independent of the motion of the source or the observer.
96
Explain what is meant by the postulate ‘the laws of physics have the same form in all inertial frames’.
The laws of physics will act in the same way in all inertial frames of reference.
97
What is time dilation?
A consequence of special relativity, meaning it only occurs in inertial frames, and causes time to run at different speeds depending on the motion of an observer.
98
What is meant by a stationary observer?
Someone stationary relative to the frame of reference where an event is occurring.
99
What is meant by an external observer?
The perspective where the frame of reference is in motion.
100
What is the proper time (t₀)?
The amount of time passed experienced by the stationary observer during an event.
101
What does v represent in the special relativity equations?
The velocity at which the stationary observer is travelling.
102
Which will always be smaller, the proper time or the time measured by an external observer?
The proper time will always be shorter than the time measured by an external observer.
103
What provides experimental evidence for time dilation?
Muon decay, as muons enter the atmosphere at very high speeds and so experience significant time dilation, affecting how quickly they decay.
104
What is length contraction?
A consequence of special relativity, meaning it only occurs in inertial frames, and causes the length of objects moving at high speeds to appear shorter to an external observer.
105
What is the proper length (l₀)?
An objects length as measured by an observer who is at rest relative to the object.
106
What property of an object remains constant during length contraction?
The width
107
What provides experimental evidence for length contraction?
Muon decay, as the muons are travelling at such a high speed the distance they travel will appear shorter than the distance as viewed by an external observer.
108
What is the relationship between energy and mass as proved by the theory of special relativity?
Mass and energy are interchangeable, E=mc²
109
Explain how the mass of an object is relative, in terms of energy transfer.
- Transferring energy to object will cause its mass to increase, while transferring energy away from an object will cause its mass to decrease
- Because of this, the faster an object travels, the more massive it becomes
110
What does m₀ represent?
The rest mass.
111
When does the classical calculation of kinetic energy by using the formula ½mv² not apply to objects?
When objects are moving at relativistic speeds, over 1/10th of the speed of light.
112
Why does the classical calculation of kinetic energy by using the formula ½mv² not apply to objects moving at relativistic speeds?
The mass of the object changes significantly.
113
What does the total energy of a relativistic object consist of?
Kinetic energy and rest energy, E = Ek + E₀
114
What is the formula for the kinetic energy of a relativistic object?
- Ek = E - E₀
- Ek = (m₀c²)/√(1-v²/c²) - m₀c²
115
What did Bertozzi’s experiment provide experimental evidence for?
The increase in mass of an object with speed.
116
Describe the setup of Bertozzi’s experiment.
- Particle accelerator which could emit electrons at varying kinetic energies
- Two detectors, A and B, connected to an oscilloscope
- Aluminium plate connected to a temperature sensor
117
Describe Bertozzi’s experiment.
1. Electrons released in pulses, the time taken for them to travel between detectors A and B calculated using oscilloscope by measuring distance between peaks on the display (and multiplying by the time base)
2. Distance between A and B measured and speed of the electrons calculated
3. Electrons directed at aluminium target, colliding with it to transfer their kinetic energy to the target in the form of heat
4. Change in temperature of the target measured using temperature sensor, so the kinetic energy of the electrons could be directly measured
118
What is the formula for the kinetic energy of one electron?
Ek = mc∆θ/n
119
What was the result of Bertozzi’s experiment?
When the results were plotted as a graph of kinetic energy against speed, the values were very close to those predicted by Einstein’s theory of special relativity, so the experiment provided evidence to support it.
120
Why can an object not reach the speed of light according to special relativity?
As an object’s speed approaches the speed of light, its mass approaches infinity, so its energy approaches infinity, which is impossible as you cannot have an infinite amount of energy.
