as h 12 quantumphenomena
TRANSCRIPT
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The photoelectric effect The photoelectric effect is the
emission of electrons from thesurface of a material due to theexposure of the material toelectromagnetic radiation.
For example zinc emits electrons
when exposed to ultraviolet radiation. If the zinc was initially negatively
charged and placed on a gold leafelectroscope, the electroscopes goldleaf would be initially deflected.
However, when exposed to the uvradiation the zinc loses electrons andtherefore negative charge.
This causes the gold-leaf to fall.
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Experimental observations
Threshold frequencyThe photoelectric effect only occurs if the frequency of theelectromagnetic radiation is above a certain threshold value, f0
Variation of threshold frequency
The threshold frequency varied with different materials.
Affect of radiation intensityThe greater the intensity the greater the number of electrons emitted,but only if the radiation was above the threshold frequency.
Time of emission
Electrons were emitted as soon as the material was exposed.
Maximum kinetic energy of photoelectrons
This depends only on the frequency of the electromagnetic radiationand the material exposed, not on its intensity.
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Problems with the wave theory
Up to the time the photoelectric effect was firstinvestigated it was believed that electromagneticradiation behaved like normal waves.
The wave theory could not be used to explain theobservations of the photoelectric effectin particularwave theory predicted: that there would not be any threshold frequencyall frequencies
of radiation should eventually cause electron emission
that increasing intensity would increase the rate of emission atall frequenciesnot just those above a certain minimum
frequency that emission would not take place immediately upon exposure
the weaker radiations would take longer to produce electrons.
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Einsteinsexplanation
Electromagnetic radiation consisted ofpackets or quanta of energy called photons
The energy of these photons:
depended on the frequency of the radiation only
was proportional to this frequency
Photons interact one-to-one with electrons in the material
If the photon energy was above a certain minimum amount(depending on the material)
the electron was emitted
any excess energy was available for electron kinetic energyEinstein won his only Nobel Prize in 1921 for this explanation. This explanation also beganthe field of Physics called Quantum Theory, an attempt to explain the behaviour of verysmall (sub-atomic) particles.
http://en.wikipedia.org/wiki/Einsteinhttp://en.wikipedia.org/wiki/Einstein -
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Photon energy (revision)
photon energy (E) = h x f
where h= the Planckconstant = 6.63 x 10-34Js
also as f = c / ;
E = hc /
Calculate the energy of a photon of ultraviolet light(f = 9.0 x 1014Hz) (h= 6.63 x 10-34Js)
E = h f= (6.63 x 10-34Js) x (9.0 x 1014Hz)
= 5.37 x 10-19J
http://en.wikipedia.org/wiki/Planckhttp://en.wikipedia.org/wiki/Planck -
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The photoelectric equation
hf = + EKmax
where:
hf= energy of the photons of electromagnetic radiation
= work function of the exposed material
EKmax= maximum kinetic energy of the photoelectrons
Work function,This is the minimum energy required for anelectron to escape from the surface of a material
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Threshold frequency f0
As: hf = + EKmax
If the incoming photons are of the thresholdfrequency f0, the electrons will have the minimumenergy required for emission
and EKmaxwill be zero
therefore: hf0=
and so: f0= / h
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Question 1
Calculate the threshold frequency of a metalif the metals work function is 1.2 x 10 -19J.
(h= 6.63 x 10-34Js)
f0= / h
= (1.2 x 10-19J) / (6.63 x 10-34Js)
threshold frequency = 1.81 x 1014Hz
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Question 2
Calculate the maximum kinetic energy of thephotoelectrons emitted from a metal of workfunction 1.5 x 10 -19J when exposed with photonsof frequency 3.0 x 1014Hz.
(h= 6.63 x 10-34Js)
hf = + EKmax(6.63 x 10-34Js) x (3.0 x 1014Hz) = (1.5 x 10-19J) + EKmaxEKmax = 1.989 x 10
-19- 1.5 x 10-19
= 0.489 x 10-19
J
maximum kinetic energy = 4.89 x 10 -20J
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The vacuum photocell
Light is incident on a metalplate called thephotocathode.
If the lights frequency is
above the metals thresholdfrequency electrons areemitted.
These electrons passingacross the vacuum to the
anode constitute andelectric current which canbe measured by themicroammeter.
The photocell is an applicationof the photoelectric effect
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Obtaining Plancks constant
By attaching a variable voltagepower supply it is possible tomeasure the maximum kineticenergy of the photoelectronsproduced in the photocell.
The graph opposite shows howthis energy varies with photon
frequency.hf = + EKmax
becomes:
EKmax= hf
which has the form y = mx +c
with gradient, m = hHence Plancks constant can befound.
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Ionisation
An ion is a charged atom Ions are created by adding or
removing electrons from atoms
The diagram shows thecreation of a positive ion fromthe collision of an incoming
electron. Ionisation can also be caused
by:
nuclear radiationalpha, beta,gamma
heating passing an electric current
through a gas (as in afluorescent tube)
incoming electron
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Ionisation energy
Ionisation energy is the energy
required to remove one electron from
an atom.
Ionisation energy is often expressed in eV.
The above defines the FIRST ionisation
energythere are also 2nd, 3rdetc
ionisation energies.
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Excitation
Excitation is the promotionof electrons from lower tohigher energy levels withinan atom.
In the diagram someof the
incoming electrons kineticenergy has been used to movethe electron to a higher energylevel.
The electron is now said to be
in an excited state. Atoms have multiple excitation
states and energies.
incoming
electron
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Question
An electron with 6 x 10-19J of kinetic energy can cause
(a) ionisation or (b) excitation in an atom.
If after each event the electron is left with
(a) 4 x 10-19
J and (b) 5 x 10-19
J kinetic energycalculate in eVthe ionisation and excitation energy of the
atom.
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Electron energy levels in atoms
Electrons are bound to thenucleus of an atom byelectromagnetic attraction.
A particular electron will occupythe nearest possible position to
the nucleus. This energy level or shell is called
the ground state.
It is also the lowest possibleenergy level for that electron.
Only two electrons can exist inthe lowest possible energy levelat the same time. Furtherelectrons have to occupy higherenergy levels.
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Electron energy levels in atoms
Energy levels are measured withrespect to the ionisation energylevel, which is assigned 0 eV.
All other energy levels aretherefore negative. The ground
state in the diagram opposite is- 10.4 eV.
Energy levels above the groundstate but below the ionisation levelare called excited states.
Different types of atom havedifferent energy levels.
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De-excitation
Excited states are usually
very unstable.
Within about 10 - 6 s the
electron will fall back to a
lower energy level.
With each fall in energy
level (level E1down to
level E2) a photon of
electromagnetic radiationis emitted.
em it ted pho ton energy
= hf = E1E2
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Energy level question
Calculate the frequencies of
the photons emitted when anelectron falls to the ground
state (at 10.4 eV) from
excited states (a) 5.4 eV and(b) 1.8 eV.
(h= 6.63 x 10-34Js)
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Complete:
transition photon
E1/ eV E2/ eV f/ PHz / nm
5.4 10.4 1.20 250
1.8 10.4 2.08 144
1.8 5.4 0.871 344
1.8 4.5 0.653 459
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Excitation using photons
An incoming photon may nothave enough energy to causephotoelectric emission but itmay have enough to causeexcitation.
However, excitation will onlyoccur if the photons energy isexactly equalto the differencein energy of the initial and finalenergy level.
If this is the case the photon willcease to exist once its energy isabsorbed.
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FluorescenceThe diagram shows an incoming
photon of ultraviolet light of energy5.7eV causing excitation.
This excited electron then de-excites intwo steps producing two photons.
The first has energy 0.8eV and will beof visible light. The second of energy4.9eV is of invisible ultraviolet of slightlylower energy and frequency than theoriginal excitating photon.
This overall process explains why
certain substances fluoresce withvisible light when they absorb ultravioletradiation. Applications include thefluorescent chemicals are added aswhiteners to toothpaste and washingpowder.
Electrons can fall back totheir ground states in steps.
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Fluorescent tubes A fluorescent tube consists of a
glass tube filled with lowpressure mercury vapour and aninner coating of a fluorescentchemical.
Ionisation and excitation of the
mercury atoms occurs as thecollide with each other and withelectrons in the tube.
The mercury atoms emitultraviolet photons.
The ultraviolet photons areabsorbed by the atoms of thefluorescent coating, causingexcitation of the atoms.
The coating atoms de-excite andemit visible photons.
See pages 37 and 38 for further
details of the operation of a
fluorescent tube
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Line spectra
A line spectrum is produced from the excitation of a low
pressure gas.
The frequencies of the lines of the spectrum are
characteristic of the element in gaseous form.
Such spectra can be used to identify elements.
Each spectral line corresponds to a particular energy level
transition.
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Question
Calculate the energy level transitions (ineV) responsible for (a) a yellow line of
frequency 5.0 x 1014 Hz and (b) a blue line
of wavelength 480 nm.
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The hydrogen atom
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With only one electron, hydrogenhas the simplest set of energylevels and corresponding linespectrum.
Transitions down to the loweststate, n=1 in the diagram, give riseto a series of ultraviolet lines calledthe Lyman Series.
Transitions down to the n=2 stategive rise to a series of visible lightlines called the Balmer Series.
Transitions down to the n=3, n=4etc states give rise to sets of infra-red spectral lines.
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The discovery of helium
Helium was discovered in the Sun before it wasdiscovered on Earth. Its name comes from theGreek word for the Sun helios.
A pattern of lines was observed in the Suns
spectrum that did not correspond to any knownelement of the time.
In the Sun helium has been produced as theresult of the nuclear fusion of hydrogen.
Subsequently helium was discovered on Earthwhere it has been produced as the result ofalpha particle emission from radioactiveelements such as uranium.
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The wave like nature of light
Light undergoes diffraction(shown opposite) and displaysother wave properties such aspolarisation and interference.
By the late 19thcentury mostscientists considered light andother electromagnetic
radiations to be like waterwaves
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The particle like nature of light
Light also producesphotoelectric emissionwhich can only beexplained by treating
light as a stream ofparticles.
These particles withwave properties arecalled photons.
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The dual nature
of electromagnetic radiation Light and other forms of electromagnetic radiation
behave like waves and particles.
On most occasions one set of properties is the mostsignificant
The longer the wavelength of the electromagnetic wavethe more significant are the wave properties.
Radio waves, the longest wavelength, is the mostwavelike.
Gamma radiation is the most particle like Light, of intermediate wavelength, is best considered tobe equally significant in both
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Matter waves
In 1923 de Broglie proposed that particles such aselectrons, protons and atoms also displayed wave likeproperties.
The de Broglie wavelengthof such a particle depended
on its momentum, paccording to the de Broglie relation:= h / p
As momentum = mass x velocity= mv
= h / mv
This shows that the wavelength of a particle can be alteredby changing its velocity.
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Question 1
Calculate the de Broglie wavelength of an
electron moving at 10% of the speed of light.
[me= 9.1 x 10-31kg]
(h= 6.63 x 10-34Js; c= 3.0 x 108ms-1)
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Question 2
Calculate the de Broglie wavelength of a person
of mass 70 kg moving at 2 ms-1.
(h= 6.63 x 10-34Js)
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Question 3
Calculate the effective mass of a photon of
red light of wavelength 700 nm.
(h= 6.63 x 10-34Js)
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Evidence for de Broglies hypothesis
A narrow beam of electrons in a vacuum tube is directed at a thinmetal foil. On the far side of the foil a circular diffraction pattern isformed on a fluorescent screen. A pattern that is similar to that formedby X-rays with the same metal foil.
Electrons forming a diffraction pattern like that formed by X-raysshows that electrons have wave properties.
The radii of the circles can be decreased by increasing the speed ofthe electrons. This is achieved by increasing the potential differenceof the tube.
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Energy levels and electron waves
An electron in an atom hasa fixed amount of energythat depends on the shell itoccupies.
Its de Broglie wavelengthhas to fit the shape and sizeof the shell.