Download IB HL Physics More Problems on Quantum and Nuclear Physics_

IB HL Physics
More Problems on Quantum and Nuclear Physics_ AHL Topic 13
1. The diagram shows some of the energy levels of a hypothetical atom.
The atom is excited to the energy level n = 4. Which of the following transitions will produce
a photon of the longest and the shortest wavelength?
Longest wavelength
Shortest wavelength
A.
4→3
4→1
B.
4→1
4→3
C.
2→1
4→3
D.
4→3
2→1
2. A proton is confined within a nucleus. What is the order of magnitude of the uncertainty in
its momentum?
A.
10–30 Ns
B.
10–20 Ns
C.
10–10 Ns
D.
1 Ns
3. The radii of nuclei may be determined by
A.
scattering charged particles off the nuclei.
B.
injecting the nuclei in a mass spectrometer.
C.
measuring the de Broglie wavelength of the nuclei.
D.
observing the spectrum of the nuclei.
4. A proton and an alpha particle have the same de Broglie wavelength.
Which of the following is approximately the ratio
A.
1
4
B.
1
2
C.
2
D.
4
speed of alpha particle
?
speed of proton
5. A free electron is confined within a one dimensional region of fixed length. Which of the
diagrams below shows the four lowest energy levels of the electron?
6.
This question is about electrons.
(a)
In 1924, Davisson and Germer carried out an experiment in which electrons were
accelerated through a potential difference of 54 V. The electrons were scattered at the
surface of a nickel crystal.
(i)
Outline how the results of the experiment suggested that electrons exhibit wave
properties.
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(2)
(ii)
Calculate the de Broglie wavelength of the electrons.
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(3)
(b)
Explain how the de Broglie hypothesis is used with the “electron in a box” model to
understand the origin of atomic energy levels in the atom.
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(5)
(Total 10 marks)
7.
This question is about nuclear processes.
Radium-226 decays with the emission of α-particles to radon (Rn).
(a)
Complete the nuclear reaction equation.
226
88 Ra
→
Rn +
(2)
b)
The decay constant of radium-226 is 1.4 × 10–11 s–1 and each emitted α-particle has an
energy of 7.6 × 10–13 J.
(i)
Calculate the half-life of radium-226.
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(1)
(ii)
Determine the rate, in watts, of emission of energy from 1.0 g of radium-226.
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(4)
8.
This question is about calculating the distance of closest approach of an α-particle to a
nucleus.
An -particle approaches a nucleus of palladium. The initial kinetic energy of the -particle
is 3.8 MeV. The particle is brought to rest at point P, a distance d from the centre of the
palladium nucleus. It then moves back along the path from which it came as shown in the
diagram below.
palladium nucleus
-particle
P
d
(a)
Calculate the value, in joules, of the electric potential energy of the α-particle at point
P. Explain your working.
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(2)
(b)
The atomic (proton) number of palladium is 46. Calculate the distance d.
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(3)
(c)
Gold has an atomic (proton) number of 79.
Explain whether the distance of closest approach of this -particle to a gold nucleus
would be greater or smaller than your answer in (b).
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(1)
(d)
The radius R of a nucleus of mass (nucleon) number A is given by
R 1.2 10
(i)
15
1
A3
m.
State in terms of the unified atomic mass unit u, the approximate mass of a
nucleus of mass number A.
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(1)
(ii)
4R 3
. Deduce that the
3
density of all nuclei is approximately 2 1017 kg m–3.
The volume of a sphere of radius R is given by V 
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(1)
(Total 8 marks)