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PHYSICS SL Thursday 19 June 2015
Content : 8 IB’s Problems Part I
of Papers two
Name:_____________
————————————————————————————————————————–—
Problem 1 [ 10 marks ]
Turn over
(a) State the nature of an D-particle.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
[1]
(b) In the Rutherford-Geiger-Marsden experiment to investigate the structure of the atom,
D-particles were directed towards a gold foil. Explain why D-particles, rather than
electrons, were used in this experiment.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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[2]
(c) Uranium-238 92
238 U� undergoes D-decay to form thorium (Th). The half-life of
uranium 92
238 U is 4.5s109 years.
� � �L�� 'H¿QH�half-life.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
[2]
(ii) Write down the nuclear equation for the D-decay of uranium to thorium.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
[2]
(d) Thorium is radioactive and further decays occur, eventually giving lead which is
stable. These further decays all occur within a time that is short compared to the
half-life of 92
238 U. In a sample of rocks the ratio of the number of uranium atoms to
the number of lead atoms is 1
7.
(i) Estimate the age of the rocks assuming that no lead was initially present in
the rocks.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
[2]
(ii) State one further assumption that is made in this estimate.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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[1]
1
Problem 2 [ 12 marks ]
(a) The nucleon number (mass number) of a stable isotope of argon is 36 and of a radioactive
isotope of argon is 39.
(i) State what is meant by a nucleon.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
[1]
(ii) Explain, in terms of the number of nucleons and the forces between them, why
argon-36 is stable and argon-39 is radioactive.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
[4]
(b) A particular nucleus of argon-39 undergoes the decay shown by the nuclear reaction
equation below.
(i) State the proton (atomic) number and the nucleon (mass) number of the
potassium (K) nucleus.
Proton number: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Nucleon number: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
[2]
(ii) Use the following data to determine the maximum energy, in J, of the B particle in
the decay of a sample of argon-39.
Mass of argon-39 nucleus 38.96431 u
Mass of K nucleus 38.96370 u
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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[3]
(This question continues on the following page)
18
39 Ar Km � B
2
(c) The graph below shows the variation with time t of the activity A of a sample of
argon-39.
activity / Bq
1750
1600
1450
1300
1150
1000
850
700
550
400
250
100 0 1 2 3 4 5 6 7 8 9 10 11 12
time / � 102 years
Use the graph to determine the half-life of argon-39. Explain your reasoning.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
[2]
3
Problem 3 [ 10 marks ]
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� 1XFOHRQ�QXPEHU��� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �
[2]
� � �LL�� 7KH�KDOI�OLIH�RI�UDGLXP����LV������\HDUV���'HWHUPLQH�WKH�OHQJWK�RI�WLPH�WDNHQ�IRU�
�� 5� � �RI�WKH�UDGLXP�WR�GLVLQWHJUDWH�
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� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �
� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �
[2]
� �E�� ,PPHGLDWHO\�DIWHU� WKH�GHFD\�RI�D�VWDWLRQDU\� UDGLXP�QXFOHXV�� WKH�DOSKD�SDUWLFOH�DQG� WKH�
UDGRQ�QXFOHXV�PRYH�RII�LQ�RSSRVLWH�GLUHFWLRQV�DQG�DW�GLIIHUHQW�VSHHGV�
radon.
� � 2XWOLQH�WKH�UHDVRQV�IRU�WKHVH�REVHUYDWLRQV�
� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �
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� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �
� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �
� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �
[3]
� �F�� 2XWOLQH�ZK\�D�EHWD�SDUWLFOH�KDV�D�ORQJHU�UDQJH�LQ�DLU�WKDQ�DQ�DOSKD�SDUWLFOH�RI�WKH�VDPH�
HQHUJ\�
� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �
� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �
� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �
� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �
� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �
� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �
[3]
4
Problem 4 [ 5 marks ]
(b) The sketch graph below shows the variation with mass number (nucleon number) A of
the binding energy per nucleon E of nuclei.
E
A
One possible nuclear reaction that occurs when uranium-235 is bombarded by a neutron
to form xenon-142 and strontium-90 is represented as
92
235
0
1
54
142
38
90
0
14U n Xe Sr n� m � � .
(i) Identify the type of nuclear reaction represented above.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
[1]
(ii) On the sketch graph above, identify with their symbols the approximate positions
of the uranium (U), the xenon (Xe) and the strontium (Sr) nuclei. [2]
(This question continues on the following page)
(iii) Which of all nucleus is know to have the greatest stability ?
Give its approximate position on the sketch graph above. [ 2 ]
5
Problem 5 [ 15 marks ]
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7
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8
Problem 6 [ 15 marks ]
Each colour has a different wavelenght and therefor a different frequency, for example in vacuum:
For this question, we will assume that for a given optical material, the refractive index of
depends of the frequency. That implies the refracive angle ar fifferent for red, blue and yellow.
(a) Define the term refractive index as applied to an optical material [ 2 ]
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
!"(%5#,7.,8%-(6*:%$"*:$%)"(%9,)"%/*66*:(5%-;%,%.,;%*/%.(5%6#7")%)",)%#$%#+0#5(+)%*+%*+(%/,0(%*/%,
76,$$%9.#$8%,)%,+%,+76(%!%)*%)"(%+*.8,61
!"!"!"!"!"!"!"!"!"!"!"!"
!
<*.8,6
=+0#5(+)%-(,8
(b) (i) The red light is now replaced by blue light. [ 2 ]
On the diagram sketch the corresponding path followed by a ray
of blue light incident at the same angle θ.
(ii) State and explain whether the refractive index for red light in the glass [ 2 ]
is greater than, equal or smaller than the refractive index of the blue light.
..................................................................................................................................................
..................................................................................................................................................
..................................................................................................................................................
9
(c) Let us condider a ray of red light with wavelenght λ= 680 nm. ( in vaccuum ) [ 2 ]
What is its wavelenght in glass ( of refractive index n= 1.6 ) ?
..................................................................................................................................................
..................................................................................................................................................
..................................................................................................................................................
(d) Which side of the prism as shown above we could perhaps observe a total reflexion ?
( left side, right side or horizontal bottom ? Explain ! ) [ 2 ]
..................................................................................................................................................
..................................................................................................................................................
(e) That could be possiblbe by increasing of decreasing angle θ ? [ 1 ]
..................................................................................................................................................
(f)B%$).,#5")%*C)#0%/#-.(%",$%4(+5)"%D6E%?7%,+2%2#,7()(.%D6F%776%%G#5")%#$%.(/4(0)(2%,4*+5%)"(%/#-.(%,$
$"*8+%-(4*86
D6E%?7
%
B)%(,0"% .(/4(0)#*+=% )"(% ,+54(% */% #+0#2(+0(% #$% (&',4% #+% 1,4'(% )*% )"(% 0.#)#0,4% ,+54(6% %!"(% .(/.,0)#1(
#+2(3%*/%)"(%54,$$%*/%)"(%/#-.(%#$%D6H6
D6F%77
!$#:-; I(2'0(%)",)%)"(%4(+5)"%*/%)"(%4#5")%C,)"%,4*+5%)"(%*C)#0%/#-.(%#$%,-*')%D6J%?76
Deduce that the lenght of the light path along the optic fibre is about 1.8 km. [ 4 ]
10
Problem 7 [ 9 marks ]
(a) 'H¿QH�VSHFL¿F�ODWHQW�KHDW�RI�IXVLRQ.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
[1]
(b) Solar radiation is incident on a pond of area 12 m2. The pond is covered by a layer of ice
of thickness 3.0 cm. The temperature of the ice is 0.0 oC.
(i) The density of ice is 900 kg m–3. Deduce that the mass of ice on the pond is
approximately 320 kg.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
[2]
(ii) The average power per unit area incident on the ice over a period of 6.0 hours
is 340 W m–2. Deduce that the energy incident on the pond in this time is 8.8s107 J.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
[1]
(iii) The VSHFL¿F latent heat of fusion of ice is 330 kJ kg–1. Determine whether all the
ice on the pond will melt in the 6.0 hour time period.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
[2]
(iv) State one assumption you made in reaching your answer to (b)(iii).
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
[1]
(c) During the night, the air temperature drops to –5 oC. The ice that melted during the day
freezes again. Outline one mechanism by which thermal energy is lost by the ice.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
[2]
11
Problem 8 [ 10 marks ]
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14
Content : 20 IB’s Problems Part II
of Papers one
( The questions 1 to 14 come from the same IB Paper 1 May 2014 , the last one from BI 2007 & 2011 )
———————————————————————————————————————————–
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16.
19. Which of the following diagrams best shows the path of a ray of monochromatic light through a
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17.
29. Which of the following statements best describes the random nature of radioactive decay?
A. The decaying nucleus emits either an A-particle , or a B-particle or a photon.
B. The type of radiation emitted by the decaying nucleus cannot be predicted.
C. The time at which a particular nucleus will decay cannot be predicted.
D. The decay of a nucleus is unaffected by environmental conditions.
G-ray
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30. The graph below illustrates the variation with nucleon number (mass number) N of the binding energy
per nucleon E of nuclei.
Which of the labelled nuclei is the most stable?
E
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A
N
25