4 Electrons Waves And Photons Flashcards
Electric current definition
The rate of flow of charge
- the amount of charge passing a given point in a circuit per unit time
Current= change in charge/change in time
What is electric charge
Physical property
A measurement of ‘chargedness’
Positive and negative charges only
Delocalised electron model for metals
Fixed ions, delocalised electrons in metal
When connected to battery, electrons flow from neg to pos. travels through component, polarises the component. Electrons move towards the pos
When not connected to battery, no elec field, so electrons can randomly within the component
Metals conduct elec as they have delocalised electrons that can flow and carry current
Thermistor- as temp increases, current…
increases
LDR- as light increases, current…
Increases
Thermistor- increases temp, resistance…
Decreases
LDR- light levels increase, resistance…
Decreases
Charge of an electron
-1.6 x 10-19C
Charge of a proton
1.6 x 10-19C
Charge of Cu2+
2 x (1.6 x 10-19) Because it has 2 more protons than electrons
Net Flow of electrons in an electric Field produces an …
Electrical current
Drift velocity
Average velocity an electron has due to an electric field
An applied electric field will give the electron a net velocity in one direction
Mean drift velocity equation
v = I / n A e
e- charge (1.6 x 10-19C)
n- number density
As drift velocity increases, area …
Decreases
Indirectly proportional
Conductor properties
high number density of free electrons, allow current to flow relatively easily
Insulator properties
very low number density, have a very high resistance
Semiconductors properties
have number density and resistance values in between those of conductors and insulators.
In order to carry same current as conductors, electrons must move faster
This increases temp
Kirchhoffs first law
For any point in an electrical circuit, the sum of currents into that point is equal to the sum of currents out of that point
Series- equal everywhere
Parallel- current into junction= current out. Current splits
What is the gradient of a graph of charge transferred against time
Current
Emf
Electromotive force (volts) Used to describe when work is done on the charge carriers Essentially the charges are gaining energy as they pass through a component like a cell, battery or power pack
Electrical resistance
Collision between vibrating fixed ions and flowing electrons reduce the speed of the flow
Longer conductors have higher electrical resistance
Electrical resistance transfers electrical energy into…
Heat
Resistivity
Used to describe the electrical property of a material
E.g. different components of made form copper may have different resistances: copper wires may have different resistances as their lengths or cross sectional areas differ, but copper has a unique resistivity
As a wire gets hotter, its resistance…
Increases
Why does resistance increase when a wire gets hotter
The pos ions inside the wire have more internal energy and vibrate with greater amplitude about their positions
The frequency of collisions between the charge carriers (free electrons) and the pos ions increase and so the charge carriers do more work, meaning they transfer more energy as they travel through the wire
Filament lamp resistance IV graph
S shape
Diode resistance IV graph
Flat then increases rapidly
What effects resistance of wire
Material of wire
Temp of wire
Length of wire L
Cross sectional area of wire A
Resistance and length proportionality
Directly proportional
Resistance and cross sectional area proportionality
Inversely proportional
Rearrange R= pL/A for resistivity
p=RA/L
1C is equivalent to
1A/s
Most objects’ charge results from…
Either a gain or loss of electrons by the object
Net charge
Q=+-ne
n is number of electrons either added or removed
The charge on an object is described as quantised. Because charge can only have certain values. These values must be an integer of e
Current in metals
Movement of electrons
Current in electrolyte
Movement of ions
Conventional current
Before discovery of electron
Defined as a current from a positive terminal towards a negative one
Electron flow
Flow from negative terminal towards positive
In opposite direction to conventional current
Number density
a measure of the number of free electrons per cubic metre of material
The number of electrons in a given volume V is…
nV
Number density x volume
Total charge of the electrons in a volume is
neV
Another way of writing charge Q
neV
I=Q/t written in a different way
I= neV/t
Effect of changing cross sectional area of wire
Drift velocity changes
Narrower the wire- greater the drift velocity must be in order for the current to be the same
Resistor circuit symbol
Rectangle, no line through
Variable resistor circuit symbol
Rectangle
Arrow through from bottom left to top right
Fuse circuit symbol
Rectangle with line through
Thermistor circuit symbol
Rectangle
Hockey stick through
LDR circuit symbol
Little rectangle
Two arrows pointing at it on left
LED circuit symbol
Diode
Two arrows coming out of it on right
Capacitor
—| |—
Potential difference definition
A measure of the transfer of energy by charge carriers
One volt is the pd across a component when one joule of energy is transferred per unit charge passing through the component
1V=1J C-1
Electromotive force definition
The energy transferred from chemical energy (or another form) to electrical energy per unit charge
Emf equation
(E3)=W/Q
W is the energy transferred by charge Q
Emf unit
Volts V
Difference between pd and emf
Pd used to describe when work is done by the charge carriers (charges are losing energy as they pass through components)
Emf used to describe when work is done on the charge carriers (charges gain energy)
Energy transfer equations
W=VQ
W=(E3)Q
Ohms law
Current in wire is directly proportional to the pd across its ends
Kirchhoffs 2nd law
In any circuit, the sum of the electromotive forces is equal to the sum of the pds around a closed loop
Series- emf shared between resistors Vt=V1+V2+V3
Parallel- emf equal in every branch Vt=V1=V2=V3
Resistors in series
R= R1+R2
Resistors in parallel
1/R=1/R1+1/R2
Internal resistance
means the electrical resistance inside batteries and power supplies that can limit the potential difference that can be supplied to an external load.
Terminal pd
the potential difference measured across the terminals of an e.m.f. source
Terminal pd= Electromotive force - lost volts
Factors effecting current
Cross-sectional area, number density, mean drift velocity
Electron gun
An electrical device used to produce a narrow beam of electrons
Potential dividers circuits
Circuits used to get the required p.d. using a ratio of resistances
Potential dividers equation
V1/V2=R1/R2
Vout= (R1/R1+R2)xVin
Producing a varying Vout
Have circuit with fixed resistor and variable resistor
Resistors I – V graph
Potential difference across the resistor is directly proportional to the current in the resistor
Resistor obeys ohms law and so can be described as an ohmic conductor
The resistance of the resistor is constant
Filament lamps I – V graph
The PD across the filament lamp is not directly proportional to the current through the resistor
A filament lamp does not obey ohms law and so can be described as a non-ohmic component
The resistance of the filament lamp is not constant
The diode
Only allows the current in one particular direction
Light emitting diode
A diode made of the material that emits light when they conduct
I – V characteristics for a diode
The PD across the diode is not directly proportional to the current through it
A diode does not obey ohms law and so can be described as a non-ohmic component
Resistance of the diode is not constant
The diodes behaviour depends on polarity
What is three factors of a wire affects the resistance (besides temperature)
Material of the wire
Length of wire
Cross-sectional area of wire
The resistance of a wire is… Proportional to its length
Directly
The resistance of a wire is… Proportional to its cross-sectional area
Inversely
The thermistor
An electrical component made from a semiconductor with a negative temperature coefficient
As the temperature of the thermistor increases, its resistance drops
I – V characteristics of thermistors
Thermistors are non-ohmic
As the current increases the temperature increases
This temperature increase leads to a drop in resistance because the number density of charged particles increases
An increase in temperature leads to an increased number density of free electrons. This means that the resistance of the thermistor decreases the temperature increases
The light dependent resistor
Made from a semiconductor in which the number density of charge carriers changes depending on the intensity of the incident light
In dark conditions that LDR has a very high resistance. The number density of the free electrons inside the semiconductor is very low, so the resistance is very high
When light shines on the LDR, the number density of the charge carriers increases dramatically, leading to a rapid decrease in the resistance of this component
Emf equation - internal resistance
E=I(R+r)
Lost volts=
Ixr
Potential divider equation
Vout= (R2/R1+R2)xVin
Ratio of resistances
V1/V2=R1/R2
Producing a varying Vout
Use fixed pair of resistors in Series and a potential divider
Replace one of fixed resistors with a variable resistor
Increasing resistance of variable resistor will increase Vout and vice versa
Progressive waves
An oscillation that travels through matter. All progressive waves transfer energy from one place to another, but not matter.
When a progressive wave travels through a medium like air or water, the particles in the medium move from their original equilibrium position to a new position. The particles in the medium exert forces on each other. A displaced particle experiences a restoring force from its neighbours and it is pulled back to its original position
Types of progressive waves
P-waves – longitudinal waves
S waves – transverse waves
Transverse waves
The oscillations or vibrations are perpendicular to the direction of energy transfer
Transverse waves have peaks and troughs where the oscillating particles are at a maximum displacement from the equilibrium position
Examples: waves on the surface of water, any electromagnetic wave, waves on stretched strings and S-waves produced in earthquakes
Longitudinal waves
Oscillations are parallel to the direction of energy transfer
Examples: soundwaves and P-waves produced in earthquakes
Longitudinal waves are often called compression waves. When they travel through a medium they create a series of compressions and rarefactions
When soundwaves travel through air, air particles are displaced and bounce off their neighbours. These collisions provide the restoring force. As the wave moves, regions of higher pressure and regions of lower pressure travel through the air, but no single air particle travels along the way. Instead they oscillate about their equilibrium positions
Displacement
Symbol- s
Unit – m
Distance from the equilibrium position in a particle direction; a vector, so it can have either a positive or negative value
Amplitude
Symbol- A
Unit- m
Maximum displacement from the equilibrium position. Can be positive or negative
Wavelength
Symbol– upsidedown Y
Units – m
Minimum distance between two points in phase on adjacent waves, for example, the distance from one peak to the next or from one compression to the next
Period of oscillation
Symbol – T
Units –s
The time taken for one oscillation or time taken for wave to move one whole wavelength past a given point
Frequency
Symbol – f
Unit – Hz
The number of wavelengths passing a given point per unit time
Wavespeed
Symbol – v
Unit – ms-1
The distance travelled by the wave per unit time
The wave equation
Wave speed= frequency X wavelength
Frequency= 1/time period
Wave profile: displacement – distance graphs
A graph showing the displacement of the particles in the wave against the distance along the wave
The wave profile can be used to determine the wavelength and amplitude of both types of waves. As the displacement of the particles in the wave is continuously changing, the wave profile changes shape over time
Phase difference
Describes the difference between the displacement of particles along a wave, or the difference between the displacement of particles on different waves.
It’s most often measured in degrees or radians, with each complete cycle or wave representing 360° or two pi radians
If particles are oscillating perfectly in step with each other then they described as in phase. They have a phase difference of zero
If two particles are separated by a distance of one whole wavelength, we say the phase difference is 360°, or 2 pi radians. If they are two complete cycles out of steps the phase difference is 720° or 4 pi radians and so on.
If particles are oscillating completely out of step with each other then they are described as being in anti-phase. There is a phase difference of 180° or pi radians.
Two particles can have any phase difference as phase difference depends on the separation of particles in terms of the wavelength
In phase
When particles are oscillating perfectly in step with each other (they both reach their maximum positive displacement at the same time)
They have a phase difference of zero
Anti-phase
When particles are oscillating completely out of step with each other (one reaches its maximum positive displacement at the same time as the other reaches its maximum negative displacement).
They have a phase difference of 180° or pi radians
Displacement – time graphs
Can be used to show how the displacement of a given particle of the medium varies with time as the wave passes through the medium
A graph of displacement against time can easily be used to determine the period T and amplitude of both types of wave
Reflection
Occurs when a wave changes direction at a boundary between two different media, remaining in the original medium
When waves are reflected the wavelength and frequency do not change. This can be seen by reflecting water waves using a ripple tank
Law of reflection
The angle of incidence is equal to the angle of reflection
Refraction
Occurs when a wave changes direction as it changes speed when it passes from one medium to another. Whenever a wave refracts there is always some reflection off the surface (partial reflection)
If the wave slows down it will refract towards the normal, if it speeds up it refracts away from the normal. Soundwaves normally speed up when they enter a denser material, where as electromagnetic waves, like light, normally slowdown. This results in waves refracting in different directions.
Refraction does have an affect on the wavelength of the wave, but not its frequency. If the wave slows down its wavelength decreases and the frequency remains unchanged and vice versa
Refraction of water waves
The speed of water waves is affected by changes in the depth of the water, which gives us an easy way to investigate refraction of water waves. When a water wave enters shallower water, it slows down and the wavelength gets shorter
Diffraction
When waves pass through a gap or travel around an obstacle, they spread out
All waves can be diffracted. The speed, wavelength, an frequency of a wave don’t change when diffraction occurs
How much a wave diffracts depends on the relative sizes of the wavelength and the gap or obstacle
Polarisation
The particles in waves oscillate along one direction only (e.g. up and down in the vertical direction), which means the wave is confined to a single plane
The plane of oscillation contains the oscillation of the particles and the direction of travel of the wave. The wave is said to be plane polarised
Light from an unpolarised source, like a filament lamp, is made up of oscillations in many possible planes. As light is a transverse wave, these oscillations are always at 90 degree to the direction of energy transfer.
In longitudinal waves, the oscillations are always parallel to the direction of energy transfer, so longitudinal waves cannot be plane polarised.
Partial polarisation
When transverse waves reflect off a surface they become partially polarised. This means there are more waves oscillating in one particular plane, but the wave is not completely plane polarised. For example, light reflected off the surface is partially polarised. Most of the light reflected off the surface becomes horizontally polarised. Some sunglasses contain polarising filters. These only allow light oscillating in one plane to pass through them, reducing the glare reflected off flat surfaces like lakes
Intensity of a wave
The radiant power passing through a surface per unit area. Intensity has units watts per square metre
Intensity= radiant power / cross sectional area
I=P/A
Intensity and distance relationship
Inverse square relationship
When the wave travels out from a source the radiant power spreads out, reducing the intensity. For a point source of wave, the energy and power spread uniformly in all directions, that is, over the surface of a sphere
The total radiant power P at a distance r from the source is spread out over an area equal to the SA of the sphere (A=4pir^2)
I=P/A =P/4pir^2
Intensity and amplitude relationship
Intensity (directly proportional sign) amplitude^2
Decreased amplitude mean a reduced average speed of the oscillating particles. Halving the amplitude results in particles oscillating with half the speed, and a quarter of the kinetic energy (Ek=0.5xmxv^2)
So for any wave the intensity is directly proportional to the square of the amplitude. Double the amplitude of a wave and the intensity will quadruple
Electromagnetic waves
Don’t need a medium
Transverse wave
Electric and magnetic fields oscillating at right angles to each other
The electromagnetic spectrum
Classified by wavelength- longest to shortest
Radio waves, microwaves, infrared, visible, ultraviolet, xrays and gamma rays
Properties of EM waves
Transverse
Can be reflected, refracted and diffracted
Can be plane polarised
All travel at the same speed through a vacuum, 3 x 10^8 ms-1
Speed through vacuum= frequency x wavelength
Using polarising filters
Unpolarised electromagnetic waves can be polarised using filters called polarisers
The nature of the polariser depends on the part of the electromagnetic spectrum to be polarised, but each filter only allows waves with a particular orientation through
Name one use for the polarisation of EM waves
Aligning aerials
In order to reduce interference between different transmitters, some transmit vertically plane polarised waves and others nearby transmit horizontally plane polarised waves
An aerial aligned to detect vertically polarised radio waves will suffer less interference from horizontally polarised waves and vice versa
Refractive index
Different materials refract light by different amounts. The angle at which the light is bend depends on the relative speeds of light through the two materials. Each material therefore has a refractive index, calculated using the equation
Refractive index of the material= speed of light through a vacuum / speed of light through the material
n=c/v
Refraction law
Refractive index of the material x sin(angle between the normal and the incident ray) = constant n sin(-) = k
We can apply this equation to describe what happens when light travels from one medium to another n1 sin(-)1 = n2 sin(-)2
Total internal reflection
TIR of light occurs at the boundary between two different media
When the light strikes the boundary at a large angle to the normal, it is totally internally reflected. All the light is reflected back into the original medium
There is no light energy refracted out of the original medium
Conditions for total internal reflection
The light must be travelling through a medium with a higher refractive index as it strikes the boundary with a medium with a lower refractive index.
The angle at which the light strikes the boundary must be above the critical angle. This angle depends on the refractive index of the medium
Determining refractive index from the critical angle experiment
- On a sheet of white paper, draw around a semi-circular glass block.
- Remove the glass block. Locate the centre of the flat side, and, using a protractor, draw a normal.
- Replace the glass block carefully on its outline.
- Direct ray of light from ray box along a radius of the block towards the normal. Angle of incidence should be about 15o
- Observe the refracted ray – away from the normal into air. Note that there is also a weak reflected ray inside the glass block.
- Slowly inc the angle of incidence, until the angle of refraction is 90o. The angle of incidence in the glass block is the critical angle (Note that there is still a reflected ray inside the glass block but it is stronger now.)
- Mark the position of the incident ray with two pencil Xs.
- Remove the glass block. Use a ruler and a pencil to join the Xs to the normal.
- Use a protractor to measure the critical angle
Noise cancelling headphones
Relies of the principle of superposition of waves to remove unwanted sounds from the listener’s surroundings, allowing them to focus on the music. A microphone on the outside of the headphones detects the background noise. The speakers inside the headphones then produce waves that aim to perfectly cancel out all external sounds.
The principle of superposition
When two waves meet at a point the resultant displacement at that point is equal to the sum of the displacement of the individual waves
As displacement is a vector quantity, when the displacements of two waves are added together the resultant can be greater of smaller than the individual displacements of each wave
Superposition
When two waves of the same type meet, they pass through each other. Where the waves overlap, or superpose, they produce a single wave, whose instantaneous displacement can be found using the principle of superposition of waves
interference
When two progressive waves continuously pass through each other they superpose and produce a resultant wave with a displacement equal to the sum of the individual displacements from the two waves. This effect is called interference
Constructive interference
If two waves are in phase then the max positive displacements (the peaks in a transverse wave) from each wave line up, creating a resultant displacement with increased amplitude
As intensity is proportional to amplitude^2, the increase in amplitude resulting from constructive interference increases the intensity: sounds waves are louder, and light is brighter
Destructive interference
If two progressive waves are in antiphase, then the max positive displacement (the peak in a transverse wave) from one wave lines up with the max negative displacement (the trough) from the other, and the resultant displacement is smaller than for each individual wave
If the waves have the same amplitude the resultant wave will have zero amplitude- it’s cancelled out completely
The reduction in the displacement results in a drop in intensity at that point. Sounds are quieter, and light is dimmer. If the resultant wave has zero amplitude, the intensity falls to zero
Coherence
Refers to waves emitted from two sources having a constant phase difference. In order to be coherent the two waves must have the same frequency
What is an interference pattern?
A pattern of regions of constructive and destructive interference produced by coherent sources of waves
What path difference is required for waves to be in phase
A whole number of wavelengths
What path difference is required for waves to be in anti phase
An odd number or half wavelengths
Relationship between path difference and phase difference for coherent sources?
(Path difference/wavelength) x 2pi
What term describes a phase difference of zero between waves
In phase
What term describes a phase difference of pi radians between two waves?
in Antiphase
Double slit equation
Wavelength= ax/D
a=distance between the double slits
x= fringe separation
D= distance between the double slots and the screen
Young double-slit experiment
Two coherent waves are needed to form an interference pattern. Young devised the method to achieve this. He used a monochromatic source of light (which can be achieved using a colour filter that allows only a specific frequency of light to pass) and a narrow single slit to diffract the light
Light diffracting from the single slit arrives at the double slit in phase. It then diffracts again from the double slit. Each slit acts as a source of coherent waves, which spread from each slit, overlapping and forming an interference pattern that can be seen on a screen as alternating bright and dark regions called fringes.
The experiment successfully demonstrated the wave nature of light. Young used his experiment to determine the wavelength of various different colours of visible light
Formation and properties of stationary waves
It forms when two waves with the same frequency travelling in opposite directions are superposed
As they have the same frequency, at certain points they’re in antiphase. At these points their displacements cancel out. This forms a node, a point where the displacement is always zero, and therefore the amplitude and the intensity are zero
At other points when the two waves are always in phase, an antinode is formed- the point of greatest amplitude and therefore intensity
The separation between two adjacent nodes (or antinodes) is equal to half the wavelength of the original progressive wave, and the frequency is the same as that of the original waves. The wave profile for the stationary wave changes over time, creating the characteristic nodes and antinodes.
As the two progressive waves are travelling in opposite directions, there is no net energy transfer by a stationary wave, unlike a single progressive wave
Phase difference along a stationary wave
In between adjacent nodes all the particles in a stationary wave are oscillating in phase with each other. They all reach their maximum positive displacement at the same time. However, their amplitudes differ, with the maximum amplitude at the antinode.
On different sides of a node the particles are in antiphase (have phase diff of pi radians). The particles on one side of a node reach their maximum positive displacement at the same time as those on the other reach their maximum negative displacement
Progressive and stationary wave energy transfer comparison
Progressive- energy transferred in direction of wave
Stationary- no net energy transfer
Progressive and stationary wave wavelength comparison
P- minimum distance between two adjacent points oscillating in phase, e.g. the distance between two peaks or two compressions.
S- twice the distance between adjacent nodes (or antinodes) is equal to the wavelength of the progressive waves that created the stationary wave
Progressive and stationary wave phase differences comparison
P- the phase changes across one complete cycle of the wave
S- all parts of the wave between a pair of nodes are in phase, and on different sides of a node they are in antiphase
Progressive and stationary wave amplitude comparison
P- all parts of the wave have the same amplitude (assuming no energy is lost to the surroundings)
S- Maximum amplitude occurs at the antinode then drips to zero at the node
Stationary waves on strings
If a string is stretched between two fixed points, these points act as nodes. When the string is plucked a progressive travels along the string and reflects off its ends. This creates two progressive waves travelling in opposite directions that then form a stationary wave
When the string is plucked it vibrates in its fundamental mode of vibration. The wavelength of the progressive wave is double the length of the string
Harmonics and wavelength - stationary waves on strings
the fundamental frequency f0 is the minimum frequency of a stationary wave for a string. Along with this fundamental mode of vibration, the string can form other stationary waves called harmonics at higher frequencies
For a given string at a fixed tension, the speed of progressive waves along with the string is constant. V=f(wl), as the frequency increases the wavelength decreases in proportion. At a frequency of 2f0, the wavelength is half the wavelength at f0
First 5 harmonic examples
1 f=20 f0 wavelength= 2L 2 f=40 2f0 wavelength= L 3 f=60 3f0 wavelength= 2/3L 4 80 4f0 1/2L 5 100 5f0 2/5L
Stationary waves with sound
Sound waves reflected off a surface can form a stationary wave. The original wave and the reflected wave travel in opposite directions and superpose
Stationary sound waves can also be made in tubes by making the air column inside the tube vibrate at frequencies related to the length of the tube. The stationary wave formed depends on whether the ends of the tube are opened or closed
Stationary waves in a tube closed at one end
For stationary wave to form there must be an antinode at the open end and a node at the closed end. The air at the closed end cannot move, and so must form a node. At the open end, the oscillations of the air are at their greatest amplitude, so must be an antinode
The fundamental mode of vibration simply has a node at the base and an antinode at the open end. Harmonics are also possible
Unlike stationary waves on stretched strings, in a closed tube at one end it is not possible to form a harmonic at 2f0 - there’s no second (fourth or sixth etc) harmonic. The frequencies of the harmonics are always an odd multiple of the fundamental frequency
Stationary waves in open tubes
A tube open at both ends must have an antinode at each end in order to form a stationary wave. Harmonics at all integer multiples of the fundamental frequency (f0 2f0 3f0…) are possible in an open tube
Evidence for wave nature of electromagnetic radiation
Young double split
Photons
A quantum of electromagnetic energy- photon energy E is given by E=hf
h is Planck constant
f is frequency of the electromagnetic radiation
Photon History
In 1900 Max Planck discovered that electromagnetic energy could only exist in certain values - it appeared to come in little packets (quanta). His new model proposed that electromagnetic radiation has a particulate nature - it was tiny packets of energy, rather than a continuous wave. Einstein coined a new term for these packets, photons
Different models to describe electromagnetic radiation
Photon Model- used to explain how EM radiation interacts with matter
Wave model- used to explain its propagation through space
Photon Energy
The energy of each Photon is directly proportional to its frequency
E=hf
We combine this equation with the wave equation c=fWL to express the energy of a photon in terms of its wavelength and c (speed of light through a vacuum)
E=hc/WL
Electronvolt
A derived unit of energy used for subatomic particles and photons, defined as the energy transferred to or from an electron when it passes through a pd of 1 volt
1eV is equivalent to 1.6 x 10-19J
Wavelengths of different colours in visible light
Largest- red
Green
Lowest- blue
LEDs and the Planck constant experiment
LEDs converts electrical energy into light energy. They emit visible photons when the pd across them is above a critical value (the threshold pd)
When the pd reached the threshold pd the LED lights up an starts emitting photons of a specific wavelength. At this pd the work done is given by W=VQ. This energy is about the same as the energy of the emitted photon. We can use the voltmeter to measure the minimum pd that is required to turn on the LED. A black tube placed over the LED helps to show exactly when the LED lights up. If we also know the wavelength of the photons emitted by the LED we can determine the Planck constant
At the threshold pd, the energy transferred by an electron in the LED is approximately equal to the energy of the single photon it emits
Threshold pd x charge on electron = energy of emitted photon
V e = h f
Expressing this in terms of the WL of the emitted photon:
eV = hc/WL
We can use this equation for a single LED and calculate h, but in order to obtain a more accurate value we should gather data using a variety of different wavelength LEDs (threshold pd dictates the colour of the LED)
We can then plot a graph of V against 1/WL.
Planck constant can be determined by the gradient, hc/e
The photoelectric effect
The emission of photoelectrons from a metal surface when electromagnetic radiation above a threshold frequency is incident on the metal
Photoelectrons
Electrons emitted from the surface of a metal by the photoelectric effect
The photoelectric effect history
In 1887 Heinrich Hertz reported that when he shone UV radiation onto zinc, electrons were emitted from the surface of the metal
This is the photoelectric effect. The emitted electrons are sometimes called photoelectrons
The gold-leaf electroscope
Demonstrates the photoelectric effect
Briefly touching the top plate with the negative electrode from a high-voltage power supply will charge the electroscope. Excess electrons are deposited onto the plate and the stem of the electroscope. Any charge developed on the plate at the top of the electroscope spreads to the stem and the gold leaf. As both the stem and gold leaf have the same charge, they repel each other, and the leaf lifts away from the stem. If a clean piece of zinc is placed on top of a negatively charged electroscope and UV radiation shines onto the zinc surface, then the gold leaf slowly falls back towards the stem. This shows that the electroscope has gradually lost its negative charge, because the incident radiation (in this case the UV) has caused the free electrons to be emitted from the zinc, photoelectrons
Three key observations from the photoelectric effect
- photoelectrons were emitted only if the incident radiation was above a certain frequency (threshold frequency f0) for each metal.
- if the incident radiation was above the threshold frequency, emission of photoelectrons was instantaneous
- if the incident radiation was above the threshold frequency, increasing the intensity of the radiation did not increase the maximum kinetic energy of the photoelectrons. Instead more electrons were emitted. The only way to increase the max KE was to increase the frequency of the incident radiation
Why does in incident radiation have to be above a threshold frequency for photoelectrons to be emitted?
If a photon doesn’t carry enough energy on its own to free an electron, the number of photons makes no difference
However when the frequency is above the f0 for the metal, then each individual photon has enough energy to free a single surface electron and so photoelectrons are emitted
Work function
The minimum energy needed to remove a single electron from the surface of a particular metal
Measured in J
PE effect- increasing intensity of radiation
Means more photons per second hit the metal surface. As each photon interacts one-to-one with a single surface electron, as long as the radiation has frequency above the threshold frequency for the metal, more photons per second means a greater rate of photoelectrons emitted from the metal
PE effect- why is there no time delay?
As long as the incident radiation has frequency greater than f0, as soon as photons hit the surface, photoelectrons are emitted. Electrons cannot accumulate energy from multiple photons. Only one-to-one interactions are possible between photons and electrons
Conservation of energy and the PE effect
Einstein realised that the energy of each individual photon must be conserved. This energy does two things:
- it frees a single electron from the surface of the metal in a one-to-one interaction
- any remainder is transferred into the kinetic energy of the photoelectron
Einstein’s photoelectric effect equation
Energy of a single photon= minimum energy required to free a single electron from the metal surface + maximum kinetic energy of the emitted electron
hf= o(work function) + KEmax
Graph of KEmax against incident frequency
Gradient = Planck constant
Y axis intercept= -o (minus work function)
Graph flat then increases at f0
Wave-particle duality
A model used to describe how all matter has both wave and particle properties
De Broglie realised that all particles travel through space as waves. Anything with mass that is moving has wave-like properties.
Electron diffraction
If an electron gun fires electrons at a thin piece of polycrystalline graphite, which has carbon atoms arranged in many different layers, the electrons pass between the individual carbon atoms in the graphite. The gap between the atoms is so small that it is similar to the wavelength of the electrons and so the electrons diffract, as waves, and form a diffraction pattern seen on the end of the tube
Why don’t we normally notice the wave nature of electrons?
We need a tiny gap in order to observe electrons diffracting. For diffraction to happen the size of the gap through which the electrons pass must be similar to their wavelength
How does electron diffraction show both the wave and particle nature of electrons?
They are behaving as particles when they are accelerated by the high pd, they behave as waves when they diffract, and they behave as particles again as they hit the screen with discrete impacts
De Broglie equation
WL= h/p
p is the momentum of the particle in kg m s-1
What is the interference pattern of diffracted electrons
As the electrons pass between the carbon atoms in the graphite they diffract and overlap, forming on interference pattern
Forms rings
