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G482
Electrons, Photons and Waves
MODULE 5:
Quantum Physics
Answer Booklet
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Lesson 35 and 36 questions – The Photoelectric effect
and photon energy and photoelectrons.
1)
Fig1.1 shows an electrical circuit including a photocell.
Fig 1.1
The photocell contains a metal plate X that is exposed to electromagnetic radiation.
Photoelectrons emitted from the surface of the metal are accelerated towards the positive
electrode Y. A sensitive ammeter measures the current in the circuit due to the
photoelectrons emitted by the metal plate X.
In this question, one mark is available for the quality of written communication.
Name and describe the process by which the photoelectrons are released from the plate X
by electromagnetic radiation.
………The process is called the photoelectric effect.……………………………………
………When a photon with enough energy (E=hf) hits a surface electron on the plate, it
can knock the electron off.…………………………………………………
………But only if the frequency of light = the threshold frequency.……………………
………The interaction in one photon to one electron so if the light is more intense, more
electrons will be emitted.…………………………………………………………
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Total [6]
2)a) State what property of electromagnetic radiation is demonstrated by the
photoelectric effect.
………………Particulate nature……………………………………………………… (1)
b)
Define each of the following terms
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i)
photon
…………A packet of em radiation with a specific amount of energy depending on its
frequency.……………………………………………………………………………… (1)
ii)
threshold frequency
………The minimum frequency of em radiation at which electrons will be emitted when
hit by that em radiation.……………………………………………………………… (1)
Total [3]
3)a) A radioactive material emits photons, each having an energy of 1.6 x 10-13 J.
Calculate the frequency of the electromagnetic radiation emitted by the radioactive
material.
…………E=hf………………………………………………………………………………
…………f=E/h……………………………………………………………………………
…………= 1.6 x 10-13 / 6.63 x 10-34 ……………………………………………………
…………= 2.4 x 1020 Hz…………………………………………………………………
………………………………………………………………………………………… (4)
b)
Calculate the wavelength of the electromagnetic radiation.
…………c=fλ………………………………………………………………………………
…………λ=c/f……………………………………………………………………………
……………=300000000/2.4 x 1020
……………=1.2 x 10-12 m…………………………………………………………… (2)
c)
State the principal type o electromagnetic radiation emitted by the material.
………………Gamma………………………………………………………………… (1)
Total [7]
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Lesson 37 – Einstein’s equation
1)
Einstein’s photoelectric equation may be written as hf = Φ + ½ mvmax2.
a)
Identify the terms:
hf
……Photon energy…………………………………………………………
Φ
……Work function energy…………………………………………………
½ mvmax2
……Maximum Kinetic energy of emitted photoelectron……………… (3)
b)
The surface of sodium metal is exposed to electromagnetic radiation of
wavelength 6.5 x 10-7m. This wavelength is the maximum for which photoelectrons are
released.
i)
Calculate the threshold frequency
……………c=fλ……………………………………………………………………………
…………… f=c/λ…………………………………………………………………………
………………=300000000/(6.5x10-7)……………………………………………………
………………=4.6x1014Hz………………………………………………………………
………………………………………………………………………………………… (3)
ii)
Show that the work function energy of the metal is 1.9 eV.
……………E=hf…and at threshold freq, E= Φ (K.E. = 0)………………………………
……………= 6.63x10-34 x 4.6x1014………………………………………………………
……………=3.0x10-19J……………………………………………………………………
…………1eV = 1.6x10-19J…………………………………………………………………
……………So E = 3.0x10-19J/1.6x10-19J
…………………=1.9eV………………………………………… (3)
c)
For a particular wavelength of incident light, sodium releases photoelectrons.
State how the rate of release of photoelectrons changes when the intensity of light is
doubled. Explain your answer.
……For each photon, one photoelectron is emitted therefore doubling the intensity
(which doubles the amount of photons) would double the amount of
photoelectrons.……………………………………………………………………………
………………………………………………………………………………………… (2)
Total [11]
2)a) Electrons are emitted from the surface of zinc when it is exposed to ultraviolet
radiation.
i)
Name this phenomenon
…………The photoelectric effect……………………………………………………… (1)
ii)
State the typical value for the wavelength of ultraviolet radiation in metres.
…………~10-8m……………………………………………………………………… (1)
b)
Electromagnetic radiation incident on a metal plate releases energetic electrons
from its surface. The metal plate is placed in an evacuated chamber. The energy of each
photon is 2.8eV. The metal has a work function energy of 1.1eV.
i)
Explain what is meant by the work function energy of the metal.
…………The energy to release an electron from the surface of a metal………………
………………………………………………………………………………………… (1)
ii)
State the speed of photons.
………………2.99x108m/s…………………………………………………………… (1)
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iii)
For an electron emitted from the surface of the metal, calculate
1.
its maximum kinetic energy in joules
………………K.Emax = E - Φ……………………………………………………………
………………………= 2.8eV – 1.1 eV…………………………………………………
………………………=1.7eV………………………………………………………………
……………… K.Emax (in Joules) = 1.7 x 1.6 x 10-19
…………………………………= 2.7 x 10-19 J…………………………………….. (3)
2.
its maximum speed.
…………… K.Emax = ½ mvmax2 ………………………………………………………
…………………v = ((½ mp)/ K.Emax)……………………………………………………
……………………=((2.7 x 10-19)/(½ 1.67x10-27))………………………………………
……………………=18000m/s……………………………………………………….. (2)
iv)
State the change, if any, to your answer for the maximum speed of an electron
emitted from the surface of the metal when the intensity of the incident electromagnetic
radiation is doubled.
……………None…………………………………………………………………………
………………………………………………………………………………………… (1)
Total [10]
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Lesson 38 – The Photon Model
1)
In this question, 2 marks are awarded for the quality of written communication.
According to wave-particle duality, electromagnetic radiation can either behave as a
wave or as a photon (which exhibits particle-like behaviour).
Describe the behaviour which supports this dual nature of electromagnetic radiation.
Wave behaviour: Any four from
……Light shows diffraction…………………
……It is diffracted by holes (slits)…
……Diffraction is noticeable when the wavelength is similar to the slit
……There is experimental evidence for fringes and rings
……The equation v=fλ can be used to find its frequency and wavelength as in other
waves
……It shows polarisation…………………………………
……It shows interference…………………………………
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Particle-like behaviour Any 4 from
……This behaviour explains how light interacts with matter
……Evidence provided by the photoelectric effect
……e.g. the one to one interaction between photon and electron
…………energy is conserved in emission…
…………The frequency is crucial, below a certain threshold nothing happens, above it
the emission of electrons occurs immediately……………………………
…………Surface electrons are involved……
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Quality of written communication (2) 1 mark for spelling of keywords and
1 mark for spelling, punctuation and grammar
Total [10]
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Lesson 39 questions – Wave particle duality
1)a)
State the de Broglie equation. Define any symbols used.
λ=h/mv
………… λ is the de Broglie wavelength………………………………………………...
…………h is Planck’s constant………………………………………………………...
…………m is the mass of the particle……………………………………………………...
…………v is the velocity of the particle……………………………………………… (2)
b)
Outline the evidence for believing that electrons behave like waves.
………In electron diffraction as electrons pass through thin foil……………………...
………Electrons form a circular patterns of constructive and destructive interference…...
……………………………………………………………………………………………...
………………………………………………………………………………………… (2)
c)
High speed electrons may be used to probe inside atomic nuclei.
i)
Calculate the de Broglie wavelength for a single electron which has a
momentum (mv) of 2.3 x 10-19kgms-1.
…………… λ=h/mv……………………………………………………………………...
………………=6.63x10-34/2.3x10-19……………………………………………………...
………………=2.9m……………………………………………………………………...
………………………………………………………………………………………… (2)
ii)
Explain how your answer to (c)(i) would change for
1
a neutron of the same momentum
………………………Same ie 2.9m…………………………………………………...
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2
an electron of half the momentum
………………………Double the wavelength i.e. 5.8m…………………………………...
………………………………………………………………………………………… (3)
Total [9]
2)
In this question, 1mark is available for the quality of written communication.
Describe and interpret the experimental evidence for the wave-like behaviour of
electrons.
Any 5 from
………Electrons travel as a wave…………………………………………………………
………Electrons show diffraction/interference……………………………………………
………Diffraction is noticeable when the wavelength is similar to the gap size………
………The de Broglie equation describes the wavelength: λ=h/mv ……………………
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………With: λ is the de Broglie wavelength, h is Planck’s constant, m is the mass of the
particle, v is the velocity of the particle ………
Graphite or thin foil necessary to diffract electrons…………………………
………Experimental evidence from fringes or diffraction rings (can score from diagram)
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Written communication (1) For organisation of ideas
Total [6]
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Lesson 40 notes - Spectra
just got bright lines of certain colors. (Actually, "color" isn't the
right term, because only some of the lines were visible, but for
now we'll just talk about visible light.)
That would mean that the atoms were only emitting waves of certain
frequencies. Do all atoms create the same colors?
No. Each type of atom gives off a unique set of colors. The
colored lines (or Spectral Lines) are a kind of "signature" for
the atoms.
Kind of like wearing your team colors.
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Team Oxygen
Team Carbon
Exactly. If you put light from a common streetlamp through a prism, or
look at the light through a diffraction grating, you will see distinct lines.
Two common kinds of street lights use sodium vapor and mercury
vapor bulbs. Each of these lights has a different spectral "signature",
and you can tell what kind of lamp it is by its spectral lines.
Pick an element from the menu to see its spectral signature.
Is that why different street lights seem to be different colors?
You got it. This technique is so reliable that scientists can tell what
elements they are looking at just by reading the lines. Spectroscopy (this
page is currently under construction) is the science of using spectral
lines to figure out what something is made of. That's how we know the
composition of distant stars, for instance.
Wait a second. We learned earlier that radiation is caused by wiggling
charges, and the rate of the wiggling determines the wavelength. If only
some wavelengths are coming out of the atom, that would mean that the
electrons are wiggling at only some frequencies. How does that happen?
That was the big puzzle. Fortunately, a Danish physicist named Niels
Bohr came up with an answer...
Bohr's Atom
To explain the spectral line puzzle, Bohr came up with a radical model
of the atom which had electrons orbiting around a nucleus.
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That doesn't sound so radical. We've already seen how electrons can
orbit around a positively charged nucleus.
Yes, but in order to explain the "signature colors," Bohr came
up with an extraordinary rule the electrons had to follow:
Electrons can only be in "special" orbits. All other orbits
just were not possible. They could "jump" between these
special orbits, however, and when they jumped they would
wiggle a little bit...
And that would cause radiation!
To see this happening, try clicking on different orbits in the model of an
atom below.
Hey, when I click on a smaller orbit, a little colored squiggle goes
shooting out, but when I click on a bigger orbit, a squiggle comes in
and kind of "bumps" the electron up.
Those squiggles are little bursts of light (electromagnetic energy). We
call them photons.
But when we played with the orbits earlier, we saw that just about any
orbit and any speed is possible. It doesn't make sense that only some
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orbits would be "allowed."
Now you can see why the Bohr model was considered so radical! It said
that energy could only change in little jumps. These are called quanta
and that's why this kind of physics is called Quantum Mechanics.
Is that where the term "quantum leap" comes from?
Yup. Ironically, everyday use of the term has come to mean a big jump,
but physicists use it to mean a jump between allowable orbits, which is
usually very, very tiny. The important part is that these jumps cannot be
broken down into smaller steps. For an electron on the move it's all or
nothing.
Energy Levels
So that's it? Atoms really look like little solar systems with electrons
making quantum jumps between special orbits?
Well, not quite. The idea of an electron actually flying around in little
circles turned out to have lots of problems, and physicists were
eventually forced to discard that model.
But we just finished talking about how well that worked! Why do we
have to throw the whole thing away?
We're not going to start from scratch. The concept of "special orbits" was
extremely useful, it's just the orbits themselves that we're not going to
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use anymore. Instead, we're going to think about electrons being in special
energy levels. We just use this rule:
Bigger Orbit = Higher Energy
Oh, that's easy enough. But why bother? Why not just call them orbits?
Well, first of all, some orbits have the same energy as other orbits, so
sometimes changing orbits wouldn't emit radiation. Also, it turns out that
electrons don't really move in little circular orbits. We can take a little
detour to see how the Schrödinger Atom more accurately depicts what is
happening inside atoms.
Actually, thinking about energy levels makes
more sense, anyway, because if the energy
goes down the extra energy has to go
somewhere, so it comes out as electromagnetic
radiation.
Yeah, and in order for the energy to go up it
has to come from somewhere, so it takes
some incoming radiation!
This next applet shows the Bohr model along with a diagram showing
the energy level. This "energy level" picture of an atom is so useful that
most physicists prefer it over the orbital picture.
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Hold on. Earlier we were saying that when an electron changes its speed
or direction, it gives off electromagnetic radiation. Now we're saying that
when an electron changes its orbit (or "energy level") it gives off
electromagnetic radiation. Which is it?
You're changing your story on us! Are you making this up as you go
along or what?
Change in velocity was a classical idea, but the quantum physicists
realized the important part is that the energy of the electron changes,
and electromagnetic radiation makes up the difference. If the energy
goes down, the extra energy appears as a photon. And for the electron
to get more energy, it needs to absorb a photon. Now let's look at how
this theory neatly explains spectral lines...
Atomic Spectra
We've seen how photons are created or destroyed when interacting with
atoms, but an important thing to realize is that transitions between the
same energy levels always produce the same color photon. (Actually,
photons don't have colors but often that is a convenient way of thinking
about their wavelength or frequency.)
I can show you how to compute the energy (and thus the frequency and
wavelength) of these photons...
In the following experiment, there is a device below the Bohr model that
works like a prism or a diffraction grating. It shows the atomic spectrum
for a hydrogen atom. Whenever a photon is emitted, it shows up on the
spectrum according to its wavelength.
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Click on an orbit to make the electron jump energy levels.
Huh. Each time the electron jumps down a level it produces a photon,
and the same jumps produce the same colors.
When you have a whole lot of atoms, I'll bet you get all these different
lines appearing at once.
Exactly, and that's what scientists mean by the atomic spectrum. By the
way, the converse is true, too. Those same color photons are the only
ones that will bump the electron up to higher levels. Photons of other
frequency will pass right through the atom.
That would mean atoms are kind of "transparent" to all light except their
own "team colors."
We keep talking about the "color" of these photons. Does that mean that
atoms only interact with visible light? What about other kinds of
electromagnetic radiation?
We've been talking about visible light because it's the easiest to
experiment with. But you're right, we should talk about the "frequency"
or "wavelength" of the photons, not their color. In fact, we're now going
to talk about how heavier atoms, which have lots of electrons, tend to
interact with higher energy waves, like x-rays. We can go ahead and
talk about these heavier atoms, or look at some specific examples, such as how
hospital x-ray machines create the x-rays, or how they absorb them to make
images.
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