Wave – particle properties





1.
Chapter
7
explain the production of atomic absorption and emission spectra,
including those from metal vapour lamps;
interpret spectra and calculate the energy of photons absorbed or emitted, E = hf;
analyse the absorption of photons by atoms in terms of
- the particle-like nature of matter
- the change in energy levels of the atom due to electrons changing state
- the frequency and wavelength of emitted photons, E = hf = hc/λ
(not including the bombardment of atoms by electrons)
describe the quantised states of the atom in terms of electrons forming standing
waves, recognising this as evidence of the dual nature of matter;
Identify and apply safe and responsible practices when working with light sources,
lasers and related equipment.
[2 marks]
(2001 Q6)
The figure below is part of the emission spectrum for hydrogen taken from sunlight. Each
emission line is displayed with the wavelength in units of nanometres (nm).
Calculate the energy of the photon, in eV, that is indicated by the spectral line marked  in the
figure.
(h = 4.14 × 10-15 eV s, c = 3.0 × 108 m s-1)
2.
[2 marks]
(2001 Q7)
On the energy level diagram for hydrogen below, indicate with an arrow () the energy level
transition for the spectral line marked  above.
3.
[2 marks]
(2003 Q1)
Part of the emission spectrum of sodium vapour produces a photon of energy 1.65 eV.
Which one of the following transitions (A – D) on the energy level diagram below demonstrates
the change in atomic energy levels for the emission of a photon of energy 1.65 eV?
4.
[3 marks]
(2003 Q2)
The sodium atom is in the first excited state.
Calculate the wavelength of the photon of energy emitted as the excited atom returns to the
ground state.
(h = 4.14 × 10-15 eV s, c = 3.0 × 108 m s-1)
5.
[3 marks]
(2003 Q4)
Katie and Jane are discussing wave-particle duality. Jane wonders whether wave-particle
duality might explain why she missed hitting the softball in a recent match – maybe the wave
nature of the softball allowed it to diffract around the bat! Katie said that this was not a
reasonable explanation and that we cannot see the wave nature of a softball.
A softball has a mass of 0.20 kg and the pitcher throws it at about 30 m s-1.
Explain to Jane, using an appropriate calculation, why she would be unable to see the wave
nature of a moving softball.
(h = 6.63 × 10-34 J s)
6.
[3 marks]
(2004 Q6)
The figure below shows the energy levels of an atom.
For atoms in the 2nd excited state (6.7 eV), calculate all the possible energies of the photons
emitted from transitions back to the ground state.
7.
[2 marks]
(2004 Sample Q10)
The basic hydrogen energy level structure is in agreement with the Bohr model. Common
pictures are those of a shell structure.
Each shell is associated with a value of the principal quantum number n, as shown below.
What are the consequences of this model for the energy states in the hydrogen atom?
8.
[2 marks]
(2004 Sample Q11)
The pattern below is meant to represent the ‘standing wavestate’ of an electron in a hydrogen
atom. Which value of ‘n’ would best describe this pattern?
9.
[2 marks]
(2004 Pilot Q5)
The figure below shows the energy levels of a mercury atom. The atom is initially in the 2nd
excited state.
Which one or more of the following photon energies can be emitted by a mercury atom which
is initially in its 2nd excited state?
A.
8.8 eV
10.
[1 mark]
B.
4.9 eV
C.
2.1 eV
D.
1.8 eV
(2004 Pilot Q6)
A mercury atom is initially in the 2nd excited state.
Which one of the following photon energies could be absorbed by this atom and hence excite it
into the 3rd excited state?
A.
8.8 eV
B.
4.9 eV
C.
2.1 eV
D.
1.8 eV
11.
[2 marks]
(2004 Pilot Q11)
Which one of the following best represents the ‘standing wave’ state of an electron in a
hydrogen atom where the circumference is equal to four wavelengths?
12.
[2 marks]
(2005 Q8)
Light sometimes behaves as a particle and sometimes as a wave. Which one or more of the
following properties does light sometimes show?
A.
mass
B.
momentum
C.
charge
D.
energy
13.
[2 marks]
(2005 Q9)
The spectrum of photons emitted by excited atoms is being investigated. Shown below is the
atomic energy level diagram of the particular atom being studied. Although most of the atoms
are in the ground state, some atoms are known to be in n = 2 and n = 3 excited states.
What is the lowest energy photon that could be emitted from the excited atoms?
14.
[2 marks]
(2005 Q10)
Calculate the wavelength of the photon emitted when the atom changes from the n = 2 state to
the ground state (n = 1).
Data: h = 4.14 × 10-15 eV s , c = 3.0 × 108 m s-1.
15.
[3 marks]
(2005 Q11)
Describe how the wave-particle duality of electrons can be used to explain the quantised energy
levels of the atom.
16.
[2 marks]
(2006 Q5)
The figure shows the energy levels of a sodium atom.
A sodium atom is initially in an n = 4 excited state.
Calculate the highest frequency of light that this sodium atom could emit.
17.
[2 marks]
(2006 Q6)
The figure shows that electrons in a sodium atom can only occupy specific energy levels.
Describe how the wave nature of electrons can explain this.
Use the following information to answer Questions 18 and 19.
18.
[2 marks]
(2007 Q4)
Neutrons are subatomic particles and, like electrons, can exhibit both particle-like and wavelike behaviour.
A nuclear reactor can be used to produce a beam of neutrons, which can then be used in
experiments.
The neutron has a mass of 1.67 × 10-27 kg.
The neutrons have a de Broglie wavelength of 2.0 × 10-10 m.
Calculate the speed of the neutrons.
19.
[2 marks]
(2007 Q5)
The neutron beam is projected onto a metal crystal with interatomic spacing of 3.0 × 10-10 m.
Would you expect to observe a diffraction pattern? Explain your answer.
Use the following information to answer Questions 20 and 21.
20.
[3 marks]
(2007 Q7)
Part of the visible region of the spectrum of light emitted from excited hydrogen gas has three
lines as shown below.
The energy level diagram for the hydrogen atom is shown below. The binding energy is 13.6
eV.
What is the energy of the photons with a wavelength 434.1 nm?
21.
[2 marks]
(2007 Q8)
A different photon has an energy of 3.0 eV.
On the figure above, indicate with an arrow the electron transition that leads to emission of a
photon of light with this energy.
22.
[3 marks]
(2007 Q9)
The figure below shows part of the emission spectrum of hydrogen in more detail.
With a spectroscope, Val examines the spectrum of light from the sun. The spectrum is
continuous, with colours ranging from red to violet. However there were black lines in the
spectrum, as shown below.
Explain why these dark lines are present in the spectrum from the sun.
23.
[2 marks]
A class looks at spectra from two sources.
i. an incandescent light globe
ii. a mercury vapour lamp
They observe that the spectra are of different types.
(2007 Q10)
In the spaces below, state the type of spectrum seen from each source.
i. Incandescent light globe
ii. Mercury vapour lamp
24.
[2 marks]
(2007 Q11)
State the electron mechanism, in each of the sources below, that produces each spectrum.
i. Incandescent light globe
ii. Mercury vapour lamp
25.
[2 marks]
(VCE 2008 Q10)
The figure shows the spectrum of light emitted from a hydrogen vapour lamp.
The spectral line, indicated with the arrow, is in the visible region of the spectrum.
What is the energy, in eV, of a photon of this wavelength?
Show working.
Use the following information to answer the next two questions.
The figure below shows the quantised energy levels in the hydrogen atom, relative to the
ground state.
26.
[2 marks]
(VCE 2008 Q11)
A photon has an energy of 2.6 eV.
Indicate, by an arrow, on the energy level diagram (above), the transition corresponding to the
emission of this photon.
27.
[2 marks]
(VCE 2008 Q112)
What is the shortest wavelength photon that can be emitted when an atom decays from the
n = 4 level?