# 1.11 Wave-particle duality

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UNIT 1 PREP: WAVE-PARTICLE DUALITY

Practical write-ups need completing.

Classwork: “1.11 AQA Wave-particle duality”. You should aim to do as much of this as possible.
Answers are on portal and you should discuss problems with your teacher.

Do (and check answers in the back):        AQA    Q3 (p43)
Q4 (p43)

Hand in:                                   AQA    Q6 (p45)                                  (7 marks)

Hand in also: past paper questions
Q1. The diagram shows some of the electron energy levels of an atom.
-18
level                   energy / 10         J

D                           - 0.21

C                           - 0.44

B                           - 0.90

(ground state) A                          - 1.94

-18                      6   -1
An incident electron of kinetic energy 4.1 × 10 J and speed 3.0 × 10 ms collides with the atom
represented in the diagram and excites an electron in the atom from level B to level D.

(a) For the incident electron, calculate
(i)    the kinetic energy in eV,
(ii)   the de Broglie wavelength.                                                    (4 marks)

(b) When the excited electron returns directly from level D to level B it emits a photon. Calculate the
wavelength of this photon.                                                                   (3 marks)

Q2. A proton and an electron have the same velocity.
-8
The de Broglie wavelength of the electron is 3.2 × 10 m.
(a) Calculate,
(i)    the velocity of the electron,
(ii)   the de Broglie wavelength of the proton.                                       (4 marks)

(b)   (i)      State what kind of experiment would confirm that electrons have a wave-like nature.
Experimental details are not required.
(ii)     State why it is easier to demonstrate the wave properties of electrons than to
demonstrate wave properties of protons.                                  (2 marks)
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Q3(a) (i)    State what is meant by the wave-particle duality of electromagnetic radiation.
(ii)   Which aspect of the dual nature of electromagnetic radiation is demonstrated by the
photoelectric effect?                                                          (2 marks)
15
(b) A metal plate is illuminated with ultra-violet radiation of frequency 1.67 × 10 Hz.
–19
The maximum kinetic energy of the liberated electrons is 3.0 × 10 J.
(i)    Calculate the work function of the metal.
(ii)   The radiation is maintained at the same frequency but the intensity is doubled. State
what changes, if any, occur to the number of electrons released per second and to the
maximum kinetic energy of these electrons.
(iii)  The metal plate is replaced by another metal plate of different material. When illuminated
by radiation of the same frequency no electrons are liberated.
Explain why this happens and what can be deduced about the work function of the new
metal.                                                                           (8 marks)

Q4. The apparatus shown below is used to investigate the wave nature of electrons.

The table shows how the kinetic energy of the electrons leaving the electron gun affects the
wavelength associated with the electrons.

–16                                 –11
kinetic energy Ek/10       J             wavelength λ/10       m

3.2                                    2.7

5.6                                    2.0

8.0                                    1.7

(a) The de Broglie equation suggests that wavelength is inversely proportional to the momentum of
the particle. Show that the data in the table above are consistent with this suggestion. (3 marks)

(b) In the experiment using the apparatus shown above the electrons sometimes behave like waves
and sometimes like particles.
In this experiment, state one way in which the electrons behave like
(i)   waves,
(ii)  particles.                                                              (2 marks)

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