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Answers on Answer Sheet
Topic 7, 12 - Selected Problems
SL SKIP ONLY 10-12
HL DO ALL
1. Determine missing element X :
235
U +
92
1
n
0

137
Te +
52
X
+
1
2 n
0
2.
3. 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
4.
5.
6.
7.
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.
In a fission chain reaction,
A.
energy from one fission reaction causes further fission reactions.
B.
nuclei produced in one fission reaction cause further fission reactions.
C.
neutrons from one fission reaction cause further fission reactions.
D.
gamma radiation produced in one fission reaction causes further fission
reactions.
Which one of the following correctly identifies the atomic (proton) number and mass
(nucleon) number of a nucleus that has neutrons n and protons p?
Atomic number
Mass number
A.
p
n
B.
p
n+p
C.
n
p
D.
n+p
p
7
The binding energy per nucleon of the nucleus 3 Li is approximately 5 MeV. The
total energy required to completely separate the nucleons of this nucleus is
approximately
A.
15 MeV.
B.
20 MeV.
C.
35 MeV.
D.
50 MeV.
(1)
2
(1)
8.
The source of the Sun’s energy is
A.
fission.
B.
radioactivity.
C.
fusion.
D.
ionization.
9. This question is about nuclear binding energy.
(a)
(i)
Define nucleon.
(ii)
Define nuclear binding energy of a nucleus.
The axes below show values of nucleon number A (horizontal axis) and average
binding energy per nucleon E (vertical axis). (Binding energy is taken to be a
positive quantity).
3
(b)
Mark on the E axis above, the approximate position of
(i)
the isotope
56
Fe
26
(ii)
the isotope
2
H
1
(iii)
the isotope
238
U
92
(label this F).
(label this H).
(label this U).
( 11 cont.)
(c)
Explain the difference between U and H in terms of binding energy and
nuclear reactions.
(d)
Use the following data to deduce that the binding energy per nucleon of the
isotope 23 He is 2.2 MeV.
nuclear mass of 23 He
mass of proton
mass of neutron
In the nuclear reaction
(e)
2
2
3
1 H  1 H  2 He
= 3.01603 u
= 1.00728 u
= 1.00867 u
 01 n energy is released.
State the name of this type of reaction.
4
10 – 12 HL ONLY
10. Two different models have been developed to explain the existence of atomic energy
levels. The Bohr model and the Schrödinger model are both able to predict the
principal wavelengths present in the spectrum of atomic hydrogen.
Outline – use drawings . Note: in explanation must state refer to fig…. or
you will no receive credit by IB examiners.
(i)
the Bohr model, and
(ii)
the Schrödinger model.
11. This question is about radioactive decay.
(a) The decay constant for a particular isotope is λ = 0.048 s–1. A sample of the isotope initially
contains 2.0 x 1012 nuclei of this isotope.
(i) Define decay constant.
(ii) Estimate the number of nuclei that will decay in the first second.
5
12. This question is about the wave nature of electrons.
(a)
Describe the de Broglie hypothesis.
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.
6
13-14 SL and HL
13. This question is about atomic spectra.
An electron undergoes a transition from an atomic energy level of 3.20  10
–15
energy level of 0.32  10
14.
–15
J to an
J. Determine the wavelength of the emitted photon.
This question is about nuclear reactions.
(a)
(b)
State the meaning of the terms
(i)
nuclide
(ii)
isotope
The isotope sodium-24 undergoes radioactive decay to the stable isotope
magnesium-24.
(i)
Complete the nuclear reaction equation for this decay.
24
24
11 Na  12 Mg
(2)
(ii)
One of the particles emitted in the decay has zero rest-mass. Use the
data below to estimate the rest mass, in atomic mass units, of the other
24
particle emitted in the decay of 11 Na
rest mass of
24
11 NA
24
12 Mg
= 23.99096u
rest mass of
= 23.98504u
energy released in decay = 5.002160 MeV
NOTE: rest mass = mass
(c)
The isotope sodium-24 is radioactive but the isotope sodium-23 is stable.
Suggest which of these isotopes has the greater nuclear binding energy.
7
8