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1. (a) A sample of a radioactive isotope contains N nuclei at
time t. At time (t + t), it contains (N N) nuclei of the
isotope.
For the period t, state, in terms of N, N and t,
(i) the mean activity of the sample,
activity =
(ii) the probability of decay of a nucleus.
probability =
(b) A cobalt-60 source having a half-life of 5.27 years is
calibrated and found to have an activity of 3.50 105 Bq. The
uncertainty in the calibration is 2%.
Calculate the length of time, in days, after the calibration has
been made, for the stated activity of 3.50 105 Bq to have a maximum
possible error of 10%.
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norashikinText Boxsource must decay by 8% C1A = A0 exp(ln2 t /
T) or A/ A0 = 1 / (2t/T) C10.92 = exp(ln2 t / 5.27) or 0.92 = 1 /
(2t/5.27) C1 t = 0.634 years = 230 days A1(allow 2 marks for A/ A0
= 0.08, answer 7010 daysallow 1 mark for A/ A0 = 0.12, answer 5880
days)
norashikinText BoxN / t (ignore any sign) B1 [1]
norashikinText BoxN / N (ignore any sign) B1 [1]
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2. A 0 meson is a sub-atomic particle. A stationary 0 meson,
which has mass 2.4 1028 kg, decays to form two -ray photons. The
nuclear equation for this decay is
0 + .
(a) Explain why the two -ray photons have the same energy.
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(b) Determine, for each -ray photon,
(i) the energy, in joule,
(ii) the wavelength,
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(iii) the momentum.
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3. Americium-241 is an artificially produced radioactive element
that emits -particles. A sample of americium-241 of mass 5.1 g is
found to have an activity of 5.9 105 Bq.
(a) Determine, for this sample of americium-241,
(i) the number of nuclei,
(ii) the decay constant,
(iii) the half-life, in years.
(b) Another radioactive element has a half-life of approximately
4 hours. Suggest why measurement of the mass and activity of a
sample of this element is not
appropriate for the determination of its half-life.
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4. The controlled reaction between deuterium(2 1 H) and
tritium(31 H) has involved ongoing research for many years. The
reaction may be summarised as
21
H + 31
H 42He + 10
n + Q
where Q = 17.7 MeV.
Binding energies per nucleon are shown in Fig. 8.1.
binding energy per nucleon/ MeV
21 H
10 n
42He
1.12
7.07
Fig. 8.1
(a) Suggest why binding energy per nucleon for the neutron is
not quoted.
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(b) Calculate the mass defect, in kg, of a helium 4 2He
nucleus.
(c) (i) State the name of the type of reaction illustrated by
this nuclear equation.
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[1]
(ii) Determine the binding energy per nucleon, in MeV, of
tritium (31
H).
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5. (a) State what is meant by the decay constant of a
radioactive isotope.
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(b) Show that the decay constant is related to the half-life t
12 by the expression
t 12 = 0.693.
[
(c) Cobalt-60 is a radioactive isotope with a half-life of 5.26
years (1.66 108 s).
A cobalt-60 source for use in a school laboratory has an
activity of 1.8 105 Bq.
Calculate the mass of cobalt-60 in the source.
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UCLES 20056.
6 The isotope Manganese-56 decays and undergoes -particle
emission to form the stableisotope Iron-56. The half-life for this
decay is 2.6 hours.Initially, at time t = 0, a sample of
Manganese-56 has a mass of 1.4g and there is no Iron-56.
(a) Complete Fig. 7.1 to show the variation with time t of the
mass of Iron-56 in the samplefor time t = 0 to time t = 11
hours.
[Fig. 7.1
(b) For the sample of Manganese-56, determine
(i) the initial number of Manganese-56 atoms in the sample,
(ii) the initial activity.
0 2 4 6 8 10 12
mass ofIron-56
t / hours
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(c) Determine the time at which the ratio
is equal to 9.0.
t
mass of Iron-56mass of Manganese-56
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7. (a) Define the decay constant of a radioactive isotope.
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(b) Strontium-90 is a radioactive isotope having a half-life of
28.0 years. Strontium-90 has a density of 2.54 g cm3.
A sample of Strontium-90 has an activity of 6.4 109 Bq.
Calculate
(i) the decay constant , in s1, of Strontium-90,
(ii) the mass of Strontium-90 in the sample,
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(iii) the volume of the sample.
(c) By reference to your answer in (b)(iii), suggest why dust
that has been contaminated with Strontium-90 presents a serious
health hazard.
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8 A positron ( 0+1e ) is a particle that has the same mass as an
electron and has a charge of +1.6 1019 C.
A positron will interact with an electron to form two -ray
photons.
0+1e +
01e 2
Assuming that the kinetic energy of the positron and the
electron is negligible when they interact,
(a) suggest why the two photons will move off in opposite
directions with equal energies,
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(b) calculate the energy, in MeV, of one of the -ray
photons.
energy = ........................................... MeV [3]
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8. Fig. 7.1 illustrates the variation with nucleon number A of
the binding energy per nucleon Eof nuclei.
Fig. 7.1
(a) (i) Explain what is meant by the binding energy of a
nucleus.
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(ii) On Fig. 7.1, mark with the letter S the region of the graph
representing nucleihaving the greatest stability.
(b) Uranium-235 may undergo fission when bombarded by a neutron
to produce
n Xenon-142 and Strontium-90 as shown below.
U + n Xe + Sr + neutrons
(i) Determine the number of neutrons produced in this fission
reaction
n
9038
14254
10
23592
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E
00 A
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(ii) Data for binding energies per nucleon are given in Fig.
7.2.
Fig. 7.2
Calculate
1. the energy, in MeV, released in this fission reaction,
2. the mass equivalent of this energy.
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isotope binding energy per nucleon/ MeV
Uranium-235Xenon-142Strontium-90
7.598.378.72
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9 Uranium-234 is radioactive and emits -particles at what
appears to be a constant rate.
A sample of Uranium-234 of mass 2.65g is found to have an
activity of 604 Bq.
(a) Calculate, for this sample of Uranium-234,
(i) the number of nuclei,
(ii) the decay constant, (iii) the half-life in years.
(iii) the half-life in years.
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(b) Suggest why the activity of the Uranium-234 appears to be
constant.
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(c) Suggest why a measurement of the mass and the activity of a
radioactive isotope is notan accurate means of determining its
half-life if the half-life is approximately one hour.
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10 (a) Explain what is meant by the binding energy of a
nucleus.
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(b) Fig. 7.1 shows the variation with nucleon number (mass
number) A of the binding energy per nucleon EB of nuclei.
0
BE
0 A
Fig. 7.1
One particular fission reaction may be represented by the
nuclear equation23592U +
10n
14156Ba +
9236Kr + 3
10n.
(i) On Fig. 7.1, label the approximate positions of
1. the uranium (23592U) nucleus with the symbol U, 2. the barium
(14156Ba) nucleus with the symbol Ba, 3. the krypton ( 9236Kr)
nucleus with the symbol Kr. [2]
(ii) The neutron that is absorbed by the uranium nucleus has
very little kinetic energy. Explain why this fission reaction is
energetically possible.
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(c) Barium-141 has a half-life of 18 minutes. The half-life of
Krypton-92 is 3.0 s. In the fission reaction of a mass of
Uranium-235, equal numbers of barium and krypton
nuclei are produced. Estimate the time taken after the fission
of the sample of uranium for the ratio
number of Barium-141 nucleinumber of Krypton-92 nuclei
to be approximately equal to 8.
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tutorial 14 a2 a.pdf9702_s09_qp_4 16.pdf9702_s10_qp_41
14.pdf9702_s10_qp_41 15.pdf9702_s10_qp_42 15.pdf9702_w09_qp_41
16.pdf9702_w09_qp_42 18.pdf
9702_s05_qp_4 14.pdf9702_s05_qp_4 15.pdf9702_s07_qp_4
14.pdf9702_s07_qp_4 15.pdf9702_s08_qp_4 18.pdf9702_w05_qp_4
14.pdf9702_w05_qp_4 15.pdf9702_w06_qp_4 14.pdf9702_w06_qp_4
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