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Topic 13- Quantum Physics
IB Problems on Particle-Wave Duality
1.
When electrons of suitable energy travel through a thin layer of graphite, a pattern of concentric
circles is produced on a screen.
fine beam of electrons
graphite
fluorescent screen
The production of this pattern is evidence for
A.
the wave nature of the electron.
B.
the nuclear model of the atom.
C.
the particle nature of the electron.
D.
the existence of X-rays.
(1)
2.
The de Broglie wavelength of a particle that has kinetic energy Ek is λ. The wavelength λ is
proportional to
A.
Ek.
B.
1
.
Ek
C.
1
Ek
D.
Ek2.
(1)
1
3.
A particle has kinetic energy E and its associated de Broglie wavelength is λ. The energy E is
proportional to
A.
λ2 .
B.
λ.
C.
λ–1.
D.
λ–2.
(1)
4.
An α-particle having a de Broglie wavelength λi collides with a stationary carbon nucleus. The
α-particle moves off in a different direction as shown below.
final direction of –particle,
de Broglie wavelength f
initial direction of –particle,
de Broglie wavelength i
final direction of carbon nucleus,
de Broglie wavelength c
After the collision, the de Broglie wavelengths of the α-particle and the carbon nucleus are λf
and λc respectively.
Which of the following is a true statement related to the de Broglie wavelengths?
A.
λi  λf
B.
λi  λf
C.
λf = λc
D.
λi = λc
(1)
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5.
Which one of the following best shows the variation with kinetic energy E of the de Broglie
wavelength λ associated with a particle?
A.
B.
E
C.
E
D.
E
E
(1)
6.
An electron of mass me and a proton of mass mp are moving with the same speed. The de
Broglie wavelengths associated with the electron and with the proton are e and p respectively.
The ratio
A.
B.
C.
D.
mp
me
λp
λe
is equal to
.
me
.
mp
mp
me
.
me
.
mp
(1)
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7.
Light of wavelength 6.0 × 10–7 m is incident normally on a plane surface as shown below.
Incident light, wavelength 6.0 × 10–7 m
Surface
The light photons are absorbed by the surface.
(a)
Show that, for one photon of the light,
(i)
its energy is 3.3 × 10–19 J;
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(2)
(ii) its momentum is 1.1 × 10–27 kg m s–1.
(2)
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(b)
The light has intensity 5.0 W m–2. Determine, for an area of 1.0 m2 of the plane surface,
(i)
the number of photons incident per second.
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(1)
(ii)
the change in momentum per second of the photons.
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(1)
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(c)
(i)
Using your answers in (b), state the pressure exerted by the light on the surface.
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(1)
(ii) State and explain what would happen to this pressure if the light is reflected rather
than absorbed by the surface.
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(3)
(Total 10 marks)
8.
This question is about the wave nature of electrons.
(a)
Describe the de Broglie hypothesis.
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(2)
An experiment is carried out in which a beam of electrons is scattered from a single nickel
crystal. A schematic diagram of the apparatus is shown below.
Vacuum
Nickel
crystal
Incident
electron beam
Electron “gun”
Scattered electron beam
The electrons are accelerated in the electron “gun” by a potential difference of 75 V.
(b)
Determine the wavelength associated with the electrons as predicted by the de Broglie
hypothesis.
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(4)
5
The number n of electrons scattered per second through an angle θ is measured. The graph
below shows the variation with angle θ of n.
n
0
(c)
0
Suggest how the shape of this graph supports the de Broglie hypothesis.
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(3)
(Total 9 marks)
9.
This question is about the wave nature of matter.
(a)
Explain what is meant by the de Broglie wavelength of a particle.
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(2)
(b)
Calculate the de Broglie wavelength of an electron that has been accelerated from rest
through a potential difference of 5.0 kV.
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(4)
(Total 6 marks)
6
10.
This question is about the wave nature of matter.
(a)
Describe the concept of matter waves and state the de Broglie hypothesis
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(3)
(b)
An electron is accelerated from rest through a potential difference of 850 V. For this
electron
(i)
calculate the gain in kinetic energy.
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(1)
(ii)
deduce that the final momentum is 1.6 × 10–23 Ns.
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(2)
(iii)
determine the associated de Broglie wavelength. (Electron charge e = 1.6 × 10–19
C, Planck constant h = 6.6 × 10–34 J s)
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(2)
(Total 8 marks)
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