3 - TURNING POINTS

Absolute motion

Idea that everything moves relative to the ether, which was believed to be the substance that permeated the entire universe

beam splitter

partially reflective surface

Compensating plate

glass block

interfometer

measures the absolute speed of the Earth through the ‘ether‘

Michelson-Morley experiment

experiment to find the absolute speed of the Earth through the ‘ether‘

inertial frames of reference

those which move at constant velocity relative to each other, (a frame that is accelerating or rotating cannot be inertial frame of reference

Time dilation

consequence of special relativity, (meaning it only occurs in inertial frames) which causes time to run at different speeds depending on the motion of the observer

Stationary observer

Stationary relative to the frame of reference where an event is occurring, while to an external observer the frame of reference is in motion

Proper time t₀

the amount of time passed experienced by the stationary observer

Length contraction

Consequence of special relativity, (meaning it only occurs in inertial frames) which causes the length of objects moving at high speeds to appear shorter to an external observer

Proper length l₀

an object’s length as measured by an observer who is at rest relative to the object. Where v is the velocity at which the object is travelling

Relativistic mass m

the larger value of mass

Relativistic speeds

over 1/10^th of the speed of light (c)

Bertozzi’s experiment

Provides evidence for the increase in mass of an object with speed

Michelson-Morley experiment process

The beam splitter would reflect some light will allowing some to pass through, creating 2 means of light moving perpendicular to each other. These travel towards the 2 mirrors which are set up at the same distance from the beam splitter. The glass block is used to make sure that the 2 beams of light pass through the same amount of glass. After being reflected on the mirrors, the 2 beams return to a detector and the interference pattern they form can be recorded

Michelson-Morley experiment conclusion

It was believed that the speed of light travelling parallel to the motion of the Earth would be affected, while the speed of light travelling perpendicular would be left unaffected, therefore rotating the apparatus by 90^o would cause a shift in the interference pattern. However, there was no shift. It was concluded that the ether doesn’t exist or the Earth drags the ether along with it as it moves, and the speed of light is invariant in free space, meaning that the speed of light is independent of the motion of the source or the observer

Einstein’s theory of special relativity assumptions

The speed of light in free space is invariant (speed of light is independent of the motion of the source or the observer), the laws of physics have the same form in all inertial frames (laws will act in the same way in all frames)

Evidence of time dilation

Muon decay - as muon enters the atmosphere at very high speeds, they experience it significantly which affects how quickly they decay

Measuring muon decay for special relativity process

Place one detector at a high altitude and one much further down to measure the change in muon count rate. Measure the distance between the 2 detectors (d) and the speed they are travelling at (v).

First calculate the expected count rate at the 2nd detector by calculating the time taken for the muon to move between the detectors (t=s/v) and then calculating the number of half-lives expected to occur in this time.

Then calculate the expected count rate at the 2nd detector acknowledging the effect of special relativity by calculating the time the same way but then using that to calculate the proper time and using that to calculate the number of half-lives expected to occur.

The second value calculated must be closer to the actual value, proving its existence

Evidence of length contraction

Muon decay - as muon enters the atmosphere at very high speeds, they appear shorter than the distance as viewed by an external observer

Measuring muon decay for length contraction process

Place one detector at a high altitude and one much further down to measure the change in muon count rate. Measure the distance between the 2 detectors (d) and the speed they are travelling at (v).

First calculate the expected count rate at the 2nd detector by calculating the time taken or the muon to move between the detectors (t=s/v) and then calculating the number of half-lives expected to occur in this time.

Then calculate the expected count rate at the 2nd detectors, considering length contraction by calculating the proper length, using that to calculate the time to travel that distance and then calculating the number of half-lives expected to occur

The second value calculated must be closer to the actual value, proving it occurs

What special relativity proves

Mass and energy are interchangeable - transferring energy to an object will cause its mass to increase, while transferring energy away will cause its mass to decrease. Because of this, the faster an object travels, the more massive it becomes

Bertozzi’s experiment process

The electrons are released in pulses by the accelerator, and the time taken for them to travel between detectors A & B is calculated using the oscilloscope by measuring the distance between peaks on the display (and multiplying the time base). The distance between A & B is measured and the speed of the electrons are calculated. The electrons are directed at the aluminium target and when they collide with it, their kinetic energy is transferred to the target in the form of heat. The change in temperature of the traget is measured using the temperature sensors, meaning the kinetic energy can be directly measured, with mcΔθ/n.

Bertozzi’s experiment conclusions

By plotting kinetic energy against speed, it was found the calculated values were very close to thos predicted by Einstein’s theory of special relativity

Why an object cannot reach the speed of light

As the speed approaches the speed of light, its mass approaches infinity and so its energy also approaches infinity which is impossible

time (measured by external observer) time dilation equation

t₀ / √(1 - v²/c²)

length (measured by observer) for length contraction equation

l₀ √(1 - v²/c²)

relativistic mass equation

m₀ / √(1 - v²/c²)

Total energy in special relativity equation

m₀c² / √(1 - v²/c²)

kinetic energy in special relativity equation

(m₀c² / √(1 - v²/c²)) - m₀c²

kinetic energy of 1 electron Betozzi’s experiment equation

mc∆θ / n

Newton’s corpuscular theory

Light consists of particles called corpuscles

Huygen’s wave theory

light was a wave and at every point on a wavefront is a point source to secondary wavelets which spread to form the next wave

electromagnetic waves

Formed of an alternating mag and electric fields traveling in phase at right angles to each other. Direction of wave travel is perpendicular to the oscillation of the electric and mag fields

Maxwell prediction

EM waves existed and theorised a formula for their speed in a vacuum

Hertz’s radio wave experiment

Metal sheet in front of apparatus reflects to produce stationary waves – wavelength can be measured from node spacing.

dipole receiver

detects electric field, made by placing a second set of charged plates parallel to those forming high voltage sparks

a loop of wire with a gap detector

detects the alternating mag field

Fizeau’s speed of light measurement

Experiment which measures the speed of light using a toothed wheel where there are equal numbers of gaps and teeth

black body

Absorbs and emits all possible wavelengths of radiation

Wave theory

As wavelength of radiation decreases, the intensity of radiation would increase, leading to a predicting infinite amount of UV radiation being emitted - this lead to the UV catastrophe

Stopping potential

The work needed to be done by photoelectrons against the electrostatic force of attraction

Planck’s interpretation of EM waves

EM waves travel in discrete packets called quanta, which have an energy directly proportional to their frequency

Resolving power of a microscope

It’s ability to distinguish structures which are close to each other

Transmission electron microscope (TEM)

A type of electron microscope that uses and electron gun to produce electrons by thermionic emission and uses their reflection to scan a surface

Scanning tunnelling microscope (STM)

A type of electron microscope that uses a fine-tipped metal probe to scan the surface at a height around 1 nm

De Broglie hypothesis

States all particles have a wave-like nature and a particle nature

Explanation of reflection in Newton’s corpuscular theory

The corpuscles collide with the surface and a repulsive force pushed them back, causing a component of velocity perpendicular to surface to change direction, while the parallel component of velocity stays the same.

Explanation of refraction in Newton’s corpuscular theory

As corpuscles approach 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, bending light towards the normal. According to this theory, light travels faster in a denser medium

Newton’s corpuscular theory can’t explain

diffraction

Explanation of reflection in Huygens’s wave theory

As a whole wavefront won’t reach the surface at once, the wavelets spread away from the surface once they reach it and rejoin with the others to reform the reflected wavefront

Explanation of refraction in Huygens’s wave theory

It was assumed light travels slower in more dense mediums, therefore as it entered a denser medium, it would slow down and bend towards the normal

Significance of Young’s double slit experiment

If Newton was correct, an interreference pattern wouldn’t have formed - instead there would be 2 bright fringes matching the 2 slits. It shows diffraction and interference of light, which are both properties of Huygen’s wave theory, proving his theory. However, it was only when the speed of light was measured in water that Newton’s theory was disregarded

Discovery of radio waves

Using an apparatus which allowed high voltage sparks to jump a gap of air

Hertz’s radio wave experiment detection methods

dipole receiver, a loop of wire and a gap

Hertz’s radio wave experiment detection conclusions

Measured wave speed matches Maxwell’s prediction, confirming radio waves are EM waves/ When the receiver rotates about line between transmitter and detectors , signal varies from max to min value after 90 degrees - showed that produced radio waves were polarised.

Fizeau’s speed of light measurement process

A pulsed beam of light is passed through a gap in the toothed wheel rotating at slow speed. The beam of light reflects on a mirror far away behind the wheel, reflecting through the same gap between the teeth. The speed of rotation of wheel is increased until the light beam can no longer be seen because it is blocked by tooth in wheel next to the gap it would previously pass through.

Reasons why the wave theory couldn’t explain the photoelectric effect

It suggests any frequency of light should be able to cause it as the energy absorbed by each electron will gradually increase and so can’t explain the existence of the threshold frequency

It is immediate, which contradicts the theory which suggests time is needed for energy supplied to the electron to reach the work function

Increasing intensity of incident of light doesn’t increase speed it occurs as would be suggested by wave theory, but instead increases the num of e released per second

Photoelectrons are released with a range of kinetic energies

Measuring stopping potential

Allows to find the max kinetic energy of the released photoelectron

Breakdown of stopping potential

If a potential is applied across a metal surface that makes it positive, the kinetic energy of the photoelectrons will decrease as they must do work against the electrostatic force of attraction towards the surface. As this potential increases, the number of photoelectrons released will decrease as there are only few that have enough kinetic energy to be emitted

Einstein’s expansion of Photon theory

Suggested EM waves are released in discrete packets which he called photons, which have particle-like interactions.

What Photon theory explained that wave theory couldn’t

When a photon interacts with an electron, all its energy is transferred to it, and an electron can only interact with a single photon, explaining threshold frequency

Photon energy is transferred to the electron immediately when they interact, causing immediate emission

Intensity is equal to the number of photons released per sec, because more photons interact with electrons per second

All electrons will receive the same amount of energy from a photon, but the electron which are deeper in the metal will lose energy through collisions when leaving the metal, and so kinetic energy will decrease. Electrons will also need to do work if the surface of the metal is positively charged

Evidence of Einstein’s theory of light

measuring stopping potential and drawing it on the graph (stopping potential as y-axis, frequency as x-axis). The x-intercept is the threshold frequency, and the gradient is h/e

Why electrons have higher resolving power

wavelength of an electron beam < wavelength of light. As wavelength of the electrons decreases, the resolving power of the microscopes increases

Transmission electron microscope breakdown

An electron gun produces electrons by thermionic emission from a heated filament and accelerates them through a hole in a metal anode. The magnetic condenser lens produces a B-field that forces the electrons into a parallel beam directed at a very thin sample. The objective lens deflects the scattered electrons to form an enlarged inverted first image of the sample. Magnifier lens focuses the electrons from the central area of the image to form a magnified final image

Scanning tunnelling microscope breakdown

A fine-tipped metal probe scans the surface at a height of around 1nm. The probe is negatively charged relative to the surface, because the gap between the tip and the surface is tiny, there is a small but finite probability the electrons can ‘tunnel‘ across the gap, and the closer to the surface the more likely that the electrons will tunnel.

STM onstant height configuration

Change of current is used to generate an image of the surface provided the probe’s vertical position is unchanged

STM constant current configuration

gap width is kept constant by feeding back changes in tunnelling current to the piezoelectric transducer that controls the tip height. The signal to the transducer is recorded and used to map the height of the surface on a computer screen

Electron diffraction process

Accelerated electrons shoot through a vacuum tube towards a crystal lattice, where they interact with small gaps between atoms and form a diffraction pattern. Accelerating voltage and electron charge equal to the kinetic energy. As accelerating voltage is increased, the speed of the electron increases so the de Broglie wavelength decreases - electrons are diffracted more and fringe spacing will decrease and vice versa.

Electron diffraction conclusions

It follows wave theory, which states fringe spacing in the diffraction pattern will increase as wavelength increases, providing evidence for de Broglie hypothesis

Fizeau’s experiment calculating speed of light

(for n teeth and n gaps)

after 1/2n of a revolution a tooth will replace a gap

Time = 1/f → tooth will replace every 1/2nf seconds

distance = d, speed = 2d/ 1/2nf → 4dnf

Maxwell’s prediction of speed in a vacuum

C = 1/√(μ₀ x ε₀ )

Measuring stopping potential

E_k(max) = eV_s - V(derived from energy = Q x V)

E = hf = ϕ + E_k(max) → hf = ϕ + eV_s

V_s = hf/e - ϕ/e (Rearrange to make Vs the subject)

De Broglie wavelength derivation

0.5 mv² = eV (accelerating V and e q equal to kinetic)

m²v² = 2meV → mv = √2meV → λ = h / (√2meV)

Thomson’s cathode ray experiment

When a potential different is applied across discharge tubes with low pressure gas, the tube begins to glow, the brightest being at the cathode

Thermionic emission

Emission of free electrons from a metal when heated

cathode rays

electrons present in all atoms

Milikan’s oil drop experiment

Used to determine charge of electron

Thomson’s cathode ray experiment process

A high potential difference ionises gas atoms in the tubes. The positive ions accelerate to the cathode, releasing electrons. These electrons accelerate through the tube and collide with gas atoms, causing them to excite. The de-excitation emits visible light photons - this is responsible for the glow (the glow is brightest at the cathode because here gas ions and electrons recombine and emit light photons)

Thomson’s cathode ray experiment conclusions

Cathode rays have the same mass, have negative charge, have the same properties regardless of the gas used, and have very large charge-to-mass ratio. Cathode rays are electrons present in all atoms

Thermionic emission experiment process

The cathode is heated, which causes thermionic emission (emits electrons). The potential difference accelerates the electrons which passes through the anode gap, and forms a narrow beam and travels at a constant velocity. The work done on a charged particle is the ΔW = QΔV, therefore for an electron ΔW = eV. As the electron moves from the cathode to the anode, its electrical potential energy is converted to kinetic, speeding up. Once the anode is reached, the kinetic energy = work done by the electrical field so 0.5 mv² = eV

Determining specific charge of an electron using Thomson’s crossed fields

Electrons are accelerated using an electron gun and enters perpendicularly to the direction of both the electric and magnetic fields. They deflect up by the electric and down by the magnetic field. By adjusting the strengths of both of the fields, the electron beam can be ‘unbent’ - this would mean that the electric and magnetic forces are equal. Through this specific charge can be found.

Determining specific charge of an electron using circular motion in the fine beam tube

The filament V supply causes thermionic motion which emits electrons from the metal. A magnetic field is applied to the beam which is perpendicular, causing the beam to move into a circular path - the radius of the beam can be determined using e/m_e. The magnetic field on the electron is equal to the centripetal force, and the work done is expressed on the voltage done by the anode, you can find the specific charge.

Milikan’s determination of the electronic charge

Oil droplets (which are negative due to friction) are sprayed above charged plates. Once they reach the plates, which form an electric field, they experience an electric force. The strength of this field can be adjusted by changing potential difference between the plates till the droplet is stationary - here the weight must equal the electric force. To find the mass, the voltage is removed and the droplet free falls, experiencing a drag force which can be calculated. Since the it reaches a terminal velocity, the drag force and the weight must be equal. Substitute the equations and rearranging to find Q

Milikan’s oil drop experiment conclusions

Will show that charge is always a multiple of 1.6 × 10-19, showing charge is quantised meaning it exists in discrete packets

Thomson’s crossed fields finding specific charge

eE = Bev → E=Bv (the mag and electric forces are equal)

E = V/d → Bv = V/d (sub in)

v = V/Bd (Rearrange for velocity)

0.5mv² = eV_A (kinetic energy equation equals electric potential energy)

e/m_e - V² / 2B²d²V_A (sub into E_k equation and rearrange for e/m_e)

Circular motion in the fine beam tube finding specific charge

F = Bev (mag force on e)

mv² / r = Bev → v = Bre / m (centripetal force = mag force)

W = QV_A → 0.5 mv² = eV_A (express in terms of anode V)

e/m = 2V_A / B²r² (subbing 2 expressions and rearrange)

Thermionic emission equation

∆W = Q∆V → ∆W = eV (work done on an electron)

0.5 mv² = eV (kinetic = work done)

Millikan’s oil drop experiment finding electronic charge

mg = EQ (weight equals electric force)

E = V/d → mg = QV/d (subbing in E=V/d)

F = 6πηrv (drag force)

mg = 6πηrv (drag force equals weight)

m = 4/3 πr³ρ → 4/3 πr³ρ g =6πηrv (subbing in m = vd)

r² = 9ηv / 2ρg (rearranging for r²)

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