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most of the time we think of light as a wave , but there are some situations where it acts as a particle too . the most famous of these cases is the
photoelectric effect
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what is the photoelectric effect
- if you shine radiation of a high enough frequency onto the surface of a metal , it will instantly emit electrons . for most metals , this frequency falls in the u.v. range .
- Because of the way atoms are bonded together in metals , metals contain a sea of free de-localised electrons that are able to move about the metal . The free electrons on or near the surface of the metal absorb energy from the radiation , making them vibrate .
- if an electron absorbs enough energy , the bonds holding it to the metal break and the electron is released . This is called the photoelectric effect and the electrons emitted are called photoelectrons
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draw a diagram to show the photoelectric effect
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what are the main conclusion from the photoelectric effect
- 1) for a given metal no photoelectrons are emitted if the radiation has a frequency below a certain value called threshold frequency
- 2) the photoelectrons are emitted with a variety of kinetic energies ranging from zero to some maximum value . this maximum kinetic energy increases with the frequency of the radiation
- 3) the intensity of radiation is the amount of energy per second hitting an area of the metal
- 4) the number of photoelectrons emitted per second is proportional to the intensity of the radiation
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the key thing about the photoelectric effect is that it shows that
light can't just act as a wave . Certain observations of the photoelectric effect can't be explained by classic wave theory
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wave theory says that for a particular frequency of EM wave the energy carried should be proportional to
the intensity of the beam . The energy carried by the Em wave would also be spread evenly over the wave front
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if we assumed that light was only a wave and used wave theory , if we shone an EM wave on a metal
each free electron on the surface of the metal would gain a bit of energy from each incoming wave . Gradually each electron would gain enough energy to leave the metal . If the EM wave had a lower frequency i.e. (was carrying less energy) it would take longer for the electrons to gain enough energy but it would happen eventually . However electrons are never emitted unless the wave is above a threshold frequency - so wave theory can't explain the threshold frequency
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kinetic energy of photoelectrons
- the higher the intensity of the wave , the more energy it should transfer to each electron - the kinetic energy should increase with intensity
- wave theory can't explain the fact that kinetic energy depends only on the frequency in the photoelectric effect
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what did Max Planck suggest
he was the first to suggest that EM waves can only be released in discrete packets or quanta
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the energy , E , carried by one of these wave-packets is
- E = energy of one packet in J
- h = Planck constant = 6.63 x 10^-34 J
- f = frequency of light in Hz
- c = speed of light in a vacuum = 3.00 x 10^8 m/s
- other symbol = wavelength in m
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Einstein's photons
- Einstein went further by suggesting that EM waves (and the energy they carry) can only exist in discrete packets . He called these wave packets photons .
- he saw these photons of light as having a one-on-one particle like interaction with an electron in a metal surface . Each photon would transfer all its energy to one specific electron . the photon model could be used to explain the photoelectric effect
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the photon model of light can explain the observations and conclusions for the
photoelectric effect that the wave model of light can't
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when EM radiation hits a metal , the metal is bombarded by
photons
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if one of these photons collides with a free electron , the electron will gain energy equal to
hf (as E = hf)
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before an electron can leave the surface of the metal , it needs enough energy to break the bonds holding it there . this energy is called the
work function energy (symbol ø) and its value depends on the metal .
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if the energy gained from a photon is greater than the work function energy
the electron is emitted . If it isn't , the electron will just shake about a bit , the release the energy as another photon . The metal will heat up but no electrons will be emitted . Since , for electrons to be emitted hf must be equal or greater than or equal to the work function energy . the threshold frequency must be equal to the work functyion energy/h
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the energy transferred from EM radiation to an electron is
the energy it absorbs from one photon , hf .the kinetic energy is the EM radiation will be carrying when it leaves the metal is hf - any other energy losses . these energy looses are the reason the electrons emitted from a metal have a range of kinetic energies
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the minimum amount of energy an electron can loose is the
work function energy , so the maximum kinetic energy , Ek , is given by the equation Ek = hf - the work function energy . rearranging this equation gives you the photoelectric effect equation
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this means the maximum kinetic energy a photoelctron can have is
E k = 1/2mv 2
m = mass of an electron = 9.11 x 10 -31 v = maximum velocity of an electron emitted
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you can use this to write out the photoelectric equation as
hf = work function energy + 1/2 mv2
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the kinetic energy of the electrons is
independent of the intensity because they can only absorb one photon at a time
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the energies of electrons in an atom are usually so tiny that it makes sense to use a more appropriate unit than the joule . The electron volt is defined as
the kinetic energy carried by an electron after it has been accelerated through a potential difference of 1 volt
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the energy gained by an electron is equal to
to the accelerating voltage
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you can convert between eV and J with this formula
1eV = 1.6 x 10-19 J
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electrons in an atom can only exist
in certain well-defined energy levels .
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each energy level is given a number , with n=1 representing the
lowest energy level an electron can be in - the ground state
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we say an electron is excited when
one or more of its electrons is in an energy level higher than the ground state
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electrons can move down an energy level by
emitting a photon . Since these transitions are between a definite energy levels , the energy of each photon emitted can only take a certain allowed value .
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the energy carried by a photon emitted after a transition is equal to
the difference in energies between the two levels of the transition
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electrons can also move up energy levels if
- they absorb a photon with the exact energy difference between the two levels
- ΔE must equal hf
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the movement of an electron to a higher energy level is called
excitation
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ionization
when an electron has been removed from an atom the atom has been ionized .
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The energy of each energy level within an atom shows the
amount of energy needed to remove an electron from that level
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the ionization energy of an atom is
the amount of energy needed to remove an electron from the ground state atom
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what do Fluorescent tubes use to emit light
the excitation of electrons and photon emission . They contain mercury vapor , across which a high voltage is applied . When fast moving electrons (emitted by electrodes in the tube and accelerated by high voltage) collide with the electrons in the mercury atoms . the atomic mercury electrons are excited to a higher energy level . when these excited electrons return to their ground states , they lose energy by emitting high energy photons in the UV range . the photons emitted have a range of energies and wavelengths that correspond to the different transitions of the electrons . a phosphorous coating on the inside of the tube absorbs these photons exciting its electrons to much higher energy levels . These electrons then cascade down the energy levels and lose energy by emitting many lower energy photons of visible light
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if you split the light from a fluorescent tube with a prism or a diffraction grating you get a
- line spectrum . a line emission spectrum is seen as a series of bright lines against a black background . each line corresponds to a particular wavelength of light emitted by the source
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line spectra provide evidence that
the electrons in atoms exist in discrete energy levels . atoms can only emit photons with energy energies equal to the difference between the two energy levels . since only certain photon energies are allowed , you only see the corresponding wavelengths in the line spectrum
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the spectrum of white light is
- continuous . if you split the light up with a prism , the colours all merge into each other - there aren't any gaps in the spectrum . Hot things emit a continuous spectrum in the visible and infra-red
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draw a diagram to show the continuous spectrum of white light , the emission lines of white light and the absorption lines of white light
- <--------------------- decreasing wavelength
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what are line absorption spectra
you get a line absorption spectrum when a continuous spectrum of energy (white light) passes through a cool gas . at low temperatures , most of the electrons in the gas atoms will be in their ground state . Photons of the correct wavelength are absorbed by electrons to excite them to higher energy levels . these wavelengths are then missing from the continuous spectrum when it comes out of the other side of the gas . you see a continuous spectrum with black lines in it corresponding to the absorbed lines
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if you compare the absorption and emission spectra of a particular gas ,
the black lines in the absorption spectrum match up to the bright lines in the emission spectrum
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the gas in the absorption spectra is ....
the gas in the emission spectra is .....
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when a beam of light passes through a narrow gap , it spreads out . this is called
diffraction
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diffraction can only be explained using
waves . If light was acting as a particle , the light particles in the beam would either not get through the gap (if they were too big) or just pass straight through and the beam would be unchanged
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the results of photoelectric effect experiments can only be explained by
thinking of light as a series of particle like photons . If a photon of light is a discrete bundle of energy , then it can interact with an electron in a one to one way . all the energy in the photon is given to one electron
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the photoelectric effect and diffraction show that light behaves as both a particle and a wave this is known as
wave particle duality
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Louis De Broglie made a bold suggestion in his PhD thesis . He said that if wave like light showed particle properties ,
particles like electrons should be expected to show wave like properties
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the De Broglie equation relates
a wave property (wavelength) to a moving particle property (momentum)
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the De Broglie equation is
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The De Broglie wave of a particle can be interpreted as
a probability wave . Many physicists at that time weren't very impressed his ideas were just speculation . But later experiments confirmed the wave nature of electrons and other particles
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diffraction patterns are observed when
accelerated electrons in a vacuum tube interact with the spaces in a graphite crystal
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what proves electrons have wave like properties
diffraction patterns are observed when accelerated electrons in a vacuum tube interact with the spaces in a graphite crystal . As electrons pass through the spaces they diffract just like waves passing through a narrow slit and produce a pattern of rings
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according to the wave theory , the spread of lines in the diffraction pattern increases
if the wavelength of the waves is greater .
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in electron diffraction experiments a smaller accelerating voltage , i.e. slower electrons gives
widely spaced rings .
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increase the electron speed and the diffraction pattern circles
squash together towards the middle . This fits in with the De Broglie equation - if the velocity is greater the wavelength is shorter and the spread of the lines is smaller
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in general wavelength for electrons accelerated in a vacuum tube is about the same size as
electromagnetic waves in the Xray part of the spectrum
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you only get diffraction if a particle
interacts with an object about the same size as its De Broglie wavelength . so you only get electrons acting as a wave if the electron interacts with an object the same size as the De Broglie wavelength of the electron
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a tennis ball , with a mass of 0.058kg and a speed of 100ms-1 has a De Broglie wavelength of 10-34m . that's 10-19 times smaller than the nucleus of an atom and there's
nothing that small for it to interact with , and so it acts as a particle
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an electron of mass 9.11 x 10-31 kg is fired from an electron gun at 7 x 106 ms-1 . what size object will the electron need to interact with in order to diffract
- an electron will diffract when the size of the object is roughly the same size as it's De Broglie wavelength , so we need to find the wavelength
- momentum of electron = mv
- 9.11x10-31 x 7x106 = 6.377 x 10-24 kgms-1
- substitute this into the De Broglie's equation
- wavelength = h/mv
- 6.63x10-34/6.377x10-24 = 1x10-10 m (2sf) so only crystals with an atom layer spacing around this size are likely to cause the diffraction of this electron
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electrons with a wavelength of 1.7x10-10m are diffracted as they pass between atoms in a crystal lattice . calculate the velocity of the electrons
- substitute wavelength = 1.7x10-10m and h=6.63x10-34 js and m=9.11x10-31 kg into the De Broglie equation
- wavlength = h/mv
- 1.7x10-10 = 6.63x10-34/9.11x10-31 x v
- rearrange and solve for v
- v = 6.63x10-34/9.11x10-31 x 1.7x10-10 = 4,280,000 ms-1 (to 3sf)
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a shorter wavelength gives
less diffraction effects
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a shorter wavelength gives less diffraction effects . this fact is used in the electron
microscope
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diffraction effects ..... .... on an image
blur detail
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if you want to resolve a tiny detail in an image , you need a
shorter wavelength
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Light blurs out detail more than
electron waves do , so an electron microscope can resolve finer detail than a light microscope . they can let you look at things as tiny as a single strand of DNA
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