Download Topic_7_atomic_and_nuclear_energy_IB_problems

IB Physics
Topic 7
Atomics Physics & radioactive decay
1.
Which one of the following correctly gives the number of electrons, protons and neutrons in a
neutral atom of the nuclide 65
29 Cu ?
Number of electrons
Number of protons
Number of neutrons
A.
65
29
36
B.
36
36
29
C.
29
29
65
D.
29
29
36
(1)
2.
In the Geiger-Marsden experiment, α particles are scattered by gold nuclei. The experimental
results indicate that most α particles are
A.
scattered only at small angles.
B.
scattered only at large angles.
C.
absorbed in the target.
D.
scattered back along the original direction.
(1)
3.
A sample of radioactive carbon-14 decays into a stable isotope of nitrogen. As the carbon-14
decays, the rate at which the amount of nitrogen is produced
A.
decreases linearly with time.
B.
increases linearly with time.
C.
decreases exponentially with time.
D.
increases exponentially with time.
(1)
4.
Which one of the following provides direct evidence for the existence of discrete energy levels
in an atom?
A.
The continuous spectrum of the light emitted by a white-hot metal.
B.
The line emission spectrum of a gas at low pressure.
C.
The emission of gamma radiation from radioactive atoms.
D.
The ionization of gas atoms when bombarded by alpha particles.
(1)
1
5.
A sample of material initially contains atoms of only one radioactive isotope. Which one of the
following quantities is reduced to one half of its initial value during a time equal to the half-life
of the radioactive isotope?
A.
Total mass of the sample
B.
Total number of atoms in the sample
C.
Total number of nuclei in the sample
D.
Activity of the radioactive isotope in the sample
(1)
6.
The variation with thickness x of the number n of α-particles penetrating a material is shown
below.
n
0
0
x
What can be deduced from the graph about the α-particles?
A.
The α-particles have approximately the same initial energy.
B.
The range is independent of the initial energy.
C.
The α-particles produce high levels of ionization.
D.
The α-particles have a large mass.
(1)
7.
Isotopes provide evidence for the existence of
A.
protons.
B.
electrons.
C.
nuclei.
D.
neutrons.
(1)
2
8.
An isotope of radium has a half-life of 4 days. A freshly prepared sample of this isotope
7N
contains N atoms. The time taken for
of the atoms of this isotope to decay is
8
A.
32 days.
B.
16 days.
C.
12 days.
D.
8 days.
(1)
9.
Ag-102, Ag-103 and Ag-104 are three isotopes of the element silver.
Which one of the following is a true statement about the nuclei of these isotopes?
A.
All have the same mass.
B.
All have the same number of nucleons.
C.
All have the same number of neutrons.
D.
All have the same number of protons.
(1)
10.
Radioactive decay is a random process. This means that
A.
a radioactive sample will decay continuously.
B.
some nuclei will decay faster than others.
C.
it cannot be predicted how much energy will be released.
D.
it cannot be predicted when a particular nucleus will decay.
(1)
3
11.
This question is about nuclear reactions.
(a)
Complete the table below, by placing a tick ( ) in the relevant columns, to show how an
increase in each of the following properties affects the rate of decay of a sample of
radioactive material.
Effect on rate of decay
Property
increase
decrease
stays the same
temperature of sample
pressure on sample
amount of sample
(2)
Radium-226 ( 226
88 Ra) undergoes natural radioactive decay to disintegrate spontaneously
with the emission of an alpha particle (α-particle) to form radon (Rn). The masses of the
particles involved in the reaction are
radium:
226.0254 u
radon:
222.0176 u
α-particle:
(b)
(i)
4.0026 u
Complete the nuclear reaction equation below for this reaction.
226
88 Ra

.........
.........
……
+
.........
.........
Rn
(2)
(ii)
Calculate the energy released in the reaction.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(3)
(c)
The radium nucleus was stationary before the reaction.
(i)
Explain, in terms of the momentum of the particles, why the radon nucleus and the
α-particle move off in opposite directions after the reaction.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(3)
4
(ii)
The speed of the radon nucleus after the reaction is vR and that of the α-particle is
v
vα. Show that the ratio  is equal to 55.5.
vR
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(3)
(iii) Using the ratio given in (ii) above, deduce that the kinetic energy of the radon
nucleus is much less than the kinetic energy of the α-particle.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(3)
(d)
Not all of the energy of the reaction is released as kinetic energy of the α-particle and of
the radon nucleus. Suggest one other form in which the energy is released.
.....................................................................................................................................
(1)
Another type of nuclear reaction is a fusion reaction. This reaction is the main source of the
Sun’s radiant energy.
(e)
(i)
State what is meant by a fusion reaction.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(3)
(ii)
Explain why the temperature and pressure of the gases in the Sun’s core must both
be very high for it to produce its radiant energy.
High temperature: ............................................................................................
............................................................................................
............................................................................................
5
............................................................................................
High pressure:
............................................................................................
............................................................................................
............................................................................................
............................................................................................
(5)
(Total 25 marks)
12.
This question is about atomic and nuclear structure.
In a nuclear model of the atom, most of the atom is regarded as empty space. A tiny nucleus is
surrounded by a number of electrons.
(a)
Outline one piece of experimental evidence that supports this nuclear model of the atom.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(3)
(b)
Explain why the protons in a nucleus do not fly apart from each other.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(2)
(c)
In total, there are approximately 1029 electrons in the atoms making up a person.
(i)
Estimate the electrostatic force of repulsion between two people standing 100 m
apart as a result of these electrons.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
6
...........................................................................................................................
...........................................................................................................................
(4)
(ii)
Explain why two people standing 100 m apart would not feel the force that you
have calculated in part (i).
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
(Total 11 marks)
13.
This question is about atomic models.
The Bohr model was developed in order to explain the atomic spectrum of hydrogen.
(a)
Explain how the Bohr model was used to explain the spectrum of atomic hydrogen.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(4)
(b)
State one limitation of the Bohr model.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(1)
14.
This question is about the nuclear structure of the atom and atomic energy levels.
When the electron was first discovered it led to the idea that an atom consists of a lump of
positive charge in which the electrons are embedded.
In 1912 Geiger and Marsden carried out an experiment to test the validity of this idea. The
results of their experiment in fact suggested that the atom is mostly empty space with an
electrically charged nucleus of relatively large mass occupying only a small amount of space.
(This is the so-called nuclear model of the atom). Their experiment involved “firing” alpha
particles at a thin sheet of gold foil.
7
(a)
State the nature of an alpha particle.
.....................................................................................................................................
(1)
The diagram below shows a small part of the gold foil with two alpha particles A and B
approaching the foil.
A
B
gold foil
(b)
(i)
Some alpha particle trajectories lead to the idea that most of the atom is empty
space. On the diagram, draw such a trajectory for the alpha particle A.
(1)
(ii)
Some other alpha particle trajectories lead to the idea that the atom has an
electrically charged, relatively massive nucleus. On the diagram, draw such a
trajectory for the alpha particle B.
(1)
(iii)
Describe briefly how these trajectories lead to the idea of the nuclear model of the
atom.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(4)
8
n=
8
In 1914 Niels Bohr suggested that the electrons in an hydrogen atom occupy discrete energy
levels. The diagram below shows some of the principal energy levels.
n=3
n=2
energy
n=1
(c)
(i)
Label with the letter X, the energy level in which an electron will have zero
potential energy.
(1)
(ii)
Explain how the line spectra of atomic hydrogen supports the idea of discrete
energy levels. You may use the diagram above to support your answer.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(4)
(Total 12 marks)
15.
This question is about radioactivity and nuclear energy.
(a)
Define the following terms,
(i)
Isotope
...........................................................................................................................
...........................................................................................................................
(1)
(ii)
Radioactive half-life
(1)
...........................................................................................................................
...........................................................................................................................
9
Thorium-227 (Th-227) results from the decay of the isotope actinium-227.
(b)
(i)
Complete the following reaction equation.
227
227
89 Ac  90Th

(1)
Th-227 has a half-life of 18 days and undergoes -decay to the isotope Ra-223 (Ra-223). A
sample of Th-227 has an initial activity of 32 arbitrary units.
(ii)
Using the axes below, draw a graph to show the variation with time t (for t = 0 to
t = 72 days) of the activity A of Th-227.
32
24
16
activity /
arbitrary units
8
0
0
18
36
54
72
time / days
(2)
(iii)
Determine from your graph, the activity of thorium after 50 days.
...........................................................................................................................
(1)
(iv)
Outline the experimental procedure to measure the activity of Th-227.
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
...........................................................................................................................
(2)
10
In the decay of a Th-227 nucleus, a γ-ray photon is also emitted.
(c)
Use the following data to deduce that the energy of the γ-ray photon is 0.667 MeV.
mass of Th-227 nucleus
mass of Ra-223 nucleus
mass of helium nucleus
energy of α-particle emitted
unified atomic mass unit (u)
= 227.0278 u
= 223.0186 u
= 4.0026 u
=5.481 MeV
= 931.5 MeV c–2
You may assume that the Th-227 nucleus is stationary before decay and that the Ra-223
nucleus has negligible kinetic energy.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
(3)
(Total 11 marks)
11