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5 Nuclear decay test solutions

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5 Nuclear decay test solutions

  1. 1. ~MERICAN ACADEMY LARNACA VII PHYSICS: SEMESTER 2: TEST 2 [Date: ] NAME I !GRADE I BLANK PAGE TURN OVER FOR QUESTION I .. ./2
  2. 2. -2- . Questions 1- 10: Choose the right answer from choices A, B, C or D (or E). o If two systems are in thermal equilibrium with each other they must be at the same temperature. B have the same thermal capacity. C have the same internal energy. D be at the same pressure. What is the internal energy of a system? A the maximum amount of work that can be extracted from the system ® the sum of kinetic energies and potential energies of the molecules C the total amount of work which has been done on the system o the thermal energy needed to raise the temperature of the system by one kelvin E the thermal energy which remains in the system when it is cooled to absolute zero Which of the following statements about heat and work is not-true? :~;;. In an adiabatic change, no heat transfer takes place. ® In an isothermal change, no work is done. e Internal energy of an ideal gas depends only on temperature. D Internal energy can be changed by heat transfer and by work input. E When the volume of gas changes gradually, work is done. ~ Air contains a mixture of gases with different molar masses M. In a sample of air at constant temperature, the Lm.S. speed of the molecules of each of the different constituents is proportional to A l/M ® 1/.jM e .jM D M E M2 1.. f-. < c,"- 7 - - ~~, N ----- " :: ~ (4W>~ m I I I I < c..~7 01.... -L I ~ I I o I j<"'~~7 0/.... 1- Vrn V The graph shows how the number of molecules N 41'- with speeds between v and v + Llv in a fixed mass ~f gas ~t kelvin temperature T varies with v. N m is the maximum value of N., which occurs when v = vrn• If the temperature is doubled A the peak in the graph is sharper B the area under the graph increases' C the value of N m increases ® the value of Vrn increases to flvrn E the value of Vrn increases to 2vm .. ./3
  3. 3. -3- If the amount of fissile material in the reactor exceeds the critical mass, the fission reactions ® B can be can be controlled by a suitable absorber of neutrons. controlled by a suitable moderating material. C can be controlled if the coolant flows at a fast rate. D cannot be controlled. ~ Which-line, A to D, in the table gives a combination of materials that is commonly used for moderating, controlling and shielding respectively in a nuclear reactor? moderating controlling shielding A graphite carbon lead B cadmium carbon concrete C cadmium boron lead ~ @ graphite boron concrete I I "Which one of the following statements correctly describes the changes that occur when a uranium nucleus undergoes fission? I ~ g) /A, B © The The binding binding energy energy per per nucleon nucleon decreases decreases and one or more neutrons are released. and one or more protons are released. I The binding energy per nucleon increases and one or more neutrons are released. I ~ D The binding energy per nucleon increases and one or more protons are released. I A nucleus of 2~~U absorbs a neutron and undergoes fission. Which one of the following gives possible products of this process? II 2:.- A n~ 7..% I A 9'" 22He -S8Ra 7.."6 qL C(c...~ ~ Cl V -~ Lt !("{. i I ® 141 56Ba 92 " + 36 Kr + .J on 1 Z.>fo Cf"L I C @ o 2_le ?36 94PU 1..>(. '{"L I I D -g,jPo ~ 4 2 He '1' 8 on I 21b ~"L I .. ./4
  4. 4. -4- binding energy per Q R nucleon P o~------------------------------A o The graph shows how the binding energy per nucleon of a nucleus varies with nucleon number, A. Which one of the following statements is not true? Energy is released in nuclear fission reactions from nuclei in region P. Nuclei in region Q are more stable than nuclei in region R. Nuclear fusion reactions bring nuclei closer to region Q. The binding energy per nucleon increases most significantly at lower nucleon numbers. (Total for Questions 1 - 10 = 10 marks) .. ./5
  5. 5. -5- A heating coil is used to warm water that flows past it at a steady rate of 0.24 kg S-i. The I Leave heating coil remains at a constant working temperature of 350 DC. blank Wanner water at 19.0 DC Insulation Heating coil / Cold water at 17.0 DC The specific heat capacity of water is 4200 J kg' K-1• Calculate the rate of absorption of energy by the cold water assuming no energy is lost to the surroundings . . ..~.~ ~ ~ ..~ ~~ ~ 0..:. 7:-~.~.~~~ ~ 41:tr.o..2.~.§~~ .. ·0:,: .. .~ X ~ .......... ~~ ~ ~~ . Rate of absorption = h~.Q~~ .. . ~ (3) The heating coil is operating at its normal working temperature of 350 DC. The equation ~u = ~Q + ~w may be applied to the coil. State and explain the value of each quantity for each second of operation. boU= 0 . Reason ~~ ~ . "0 = L.l_ - 2.OJV"> ........................•..................................................................................•...............................................••.... Reason k~.k ~~ ~~~ .. . boW - - ''LOG)""> :1:: . Reason ~er.<h. cXo~ .~ 4:, +; ~ ..~;, ~ f Q.~.e.y. . ........................... ~~.~ . (6) (Total 9 marks)
  6. 6. -6- Leave blank OJ (a) Explain what is meant by (i) the specific heat capacity of water, ··········~········~tw.·~········~ ··VlA.Y.··· ..···~ ~.:tM..~ ........... .~b ~ ~ J.k . (ii) the specific latent heat of fusion of ice . ............. ~-t ~~.~d ~ ~.: ·I·.···~..········. · ............. ~:) t . (4) (b) A sample of solid material, which has a mass of 0.15 kg, is supplied with energy at a constant rate. The specific heat capacity of the material is 1200 J kg'" K-1 when in the solid state. During heating, its temperature is recorded at various times and the following graph is plotted. 94 ---------------------------- temperature/'C 58 --------~----------~ 18 o 5 12 16 time/minutes Assume there is no heat exchange with the surroundings. (i) Show that energy is supplied to the material at a rate of 24 W. ·······~·····~·~·.;.::······~·~··~········· ..···~·~ ·. · .. .. k . ~~ ~ O-~ .....................................................~>..~> ~~.~.~£~.s.~ Q.k ~..... ': O .. .... ~ ... 1 ~.. I ..................................................................................................................................... ~.~ . - .. /1'
  7. 7. ::z. -r- t Leave blank (ii) Calculate the specific latent heat of fusion of the material . ...... "? b »..~ ~ - 6-:t.~..:':: .. A:1-.Q ..~ ? . ""'- j 6 . , S ..::. ••.......•••.••.....••.•..•..•....•.•.•••••••••• " L;:t k> k~ --, 90 •.••••••••••.•••••• ••.•••••.••••••••.•...•••.•..........•..••••••..........•.•...••.. (iii) Calculate the specific heat capacity of the material when in the liquid state . ....... ( ::: ~ ..!>..:Q ~~ - -a , ::= ~.~ ..~~ . ................................................. C."?: l~ ::: ~1~ .. ~::ty.~ .. ~ .. . :-~ C)"~s.~ '>C )C:.~ ..................................................................................... ::: l.J.~.2.~;;~~~..... (6) .. ~ (c) (i) On the axes below, the original graph is shown by a dotted line. Sketch a graph on the same axes indicating how you would expect the results of the experiment in part (b) to differ if there were a significant heat loss from the material to surroundings which were at 15°C. temperaturef'C 94 / / / / / / / / .: 58 18 I o 5 12 16 time/minutes (ii) Explain the shape of the first section of the graph you have drawn in part (c)(i) . ............... §>~.It:.:: ~ :;"? ~~ ~ ~ ~ t: . - ~ ............... ~ Ii' t . (3) (13)
  8. 8. -&- Leave blank I~ (a) A student investigates how the pressure of a gas depends on its temperature. (i) To carry out this experiment, two variables must be kept constant. What are they? 1 ~S~ . 2 ~~!.r.. c- ~.Q.~ {. ~~~~ . (2) (ii) Draw a labelled diagram of the apparatus the student could use. (4) (iii) State one precaution the student should take to improve the quality of the results. ·······y.~~····~·······V·~~······ .. ·······~·~· ~ ..·····5·~ . ~~ (1)
  9. 9. I Leave i blank I (b) In the space below sketch a graph to show how the pressure of an ideal gas depends i I on its temperature. Add any key values to your temperature axis, - - I ! I I I I I ~C-.-_----- 0,0 (3) (Total 10 marks) The kinetic theory of gases is based on a number of assumptions. One assumption is that the I~ average distance between the molecules is much larger than the molecular diameter. A second assumption is that the molecules are in continuous random motion. State and explain one observation in support of each assumption. First assumption ............ §.~ ~ ~.~.~ ...~~ i . ............. ~~~.~ s..~ ~~ ~ k ~~ :. Second assumption ~.~.~.~.~ .............. ~.Q.b~ ~., . .............. ~.w.~ ~ ~ ~~'d.":'••~ .. ••••••.•• ~.~·~·4 ······ .. · ............... ~ ~~.o ~h .~~ ~ ~~.~O..~ f.. t?~J(.~.( . -d::t.: . ...............~.~.9 ..~ ..~ . (Total 4 marks) ... ~IIO
  10. 10. -/0- /~ A cubic box with sides of length 0.50 m contains a gas. There are 1.5 x 1024 Leave molecules inside the box. blank 400ms-1 Cubic box of side 0.50m MOl~~ ~------~------~--~ A molecule is moving at 400 m s-I in a direction perpendicular to the shaded face. The average rate of change of momentum for this molecule at the shaded face is 1.6 x 10-20 kg m S-2. State the two assumptions that the kinetic theory makes about the collisions of this molecule with the shaded face . ............. .~fA.?:-: .~~ . .............. ~ ~~ . (2) One third of all the molecules strike the shaded face. Calculate the average force exerted by these molecules if their average speed is 400 m S-I . .............. . :::' F .. J.~)( J.t?~4 .x....J .. ~.y ....... 0 -~.~.~.i".~ ~ .•. . ................................~ ~ ..:;: f. ~ ..R.~ . -.---/ ~ ~U~~- .......................... ~~ .•...~~~.~ . ~,,~ S~C7<..AA f' Average force = .5t.Q.~~.y. . ~~ m .. ·111
  11. 11. -If - Hence calculate the gas pressure on the shaded face. Leave blank ···..·····f·?·····f ::: ~.~ . 1 lo·c;o,",,)~ Gas pressure = 3.3..~Y.'.t..... . -=====-==- 1(2) I The formula from kinetic theory for the pressure exerted by a gas is given by State what the term (Cl) represents. .: ....................... ~~ ~.~ ~f.~~ . , (1) (Total 8 maJkS)
  12. 12. -/~- Leave blank 16) Helium is a monatomic gas for which all the internal energy of the molecules may be considered to be translational kinetic energy. molar mass of helium = 4.0 x 10-3 kg the Boltzmann constant = 1.38 x 10-23 J K-1 the Avogadro constant = 6.02 x 1023 mol " (a) Calculate the kinetic energy of a tennis ball of mass 60g travelling at 50 m s" . ...........;:;~~ ..r.~ f..~.. ~ ~ .. ~ .Q.:.O..~.Q..~.~ x (.s..Q..~.~"':~)~ . ................................................. ~ 1.~.2. . - (1) (b) Calculate the internal energy of 1.0 g of helium gas at a temperature of 48 K. ............ E·,c··:7:·· .. i··· <.. ~.? :?. ~ h1 ~ k·::t ~ ..·..·~· ..f·~·~··· .......... ?E-~.~~~~ x J... 1. ; b.:y..~.~K)~~ ~ .2. X k~.~.l 4-?- + 2... +~K ..... . ~~......... . ~ . .............•.......•..........•..............••.•......•.•.•.•.•••• ~ ..••.• I. s.9.? : ~ . (3) =- (c) At what temperature would the internal energy of LOg of helium gas be equal to the kinetic energy of the ball in part (a) . ............ -;r..$.2. >.<: 4.¥ .. ~ ~ ~ Z,4-..k . Iso-s - (1) ... /13
  13. 13. -13- It is possible to use a graph of either neutron numbers or nucleon numbers, plotted against proton numbers, to predict whether a given nuclide will undergo one or other of the various kinds of nuclear decay. (a) Sketch, on the axes provided, a graph of either neutron number or nucleon number against proton number for the stable isotopes. Add a scale to the axis used for proton number to illustrate the ranges of values involved. [2J - {Vi u..A..~ /' ./ /0 ':e / - ~~ /' -: -: v-: I ( Proton number t: [trO (b) Explain, with reference to your sketch graph, how predictions about the two types of beta decay may be made. [*1 i , ~c>k~ -h, Z tdt" ck '>~ cL, ~~ ,, '- ,- ~ hrc.2 W'.g, ,....,.. '" f~ -0 '" ~ ~ ,J~. ,.L~ ~ ,n.+- Se. ""-~ f --' '" LE', t "= !~l for Question 17 = 6 marks!.. .. ./14
  14. 14. Examiner only /~ (a) Explain what is meant by radioactive decay. [1] ........................ ck..~ ~ ~.~ J~: A.~~~.~.~ ~ . .........................~.~ ~.~.~ ~.l. w.:- ~.~.k.~ . (b) The rate of decay of a radioactive sample was measured with a Geiger counter over a period of a day. The graph below shows the results of this experiment. -? ~):._:_::~ •• ··.:Il:I.,T.'H- ..-i-·+++·-jtJ:EnTft·±:t:l~±![tt~I:I]:J~[i:.i~lIHtl~j:rl:J.1JI!Jtt-jItj : ; i , 1 ! ; ; ; ; ; , ! , . I! ; l----L 1 ! i . 400 ,~. . : ; i : I i : ! ; h· .. · j! , ! I I I , ' •• :; I ;'. .... .: j,tJ--£Fti'_1--;'-ri-H-+"1',~~. -'i~$tf-1EJ1~tt1-'j~jth-Hf-) i ..: , ~', ~~t: •. ,,·+P+1ff :"'",+.'-I..!.,:.,'...: ".I·.+,+J.,i"=+11.:;trltl ..!..,:.+..,.. O~0~~IWt~~4W=~~~+8~=+I!=t412~tq~~I'~621~WJ'==;~Ojdi+==~2+4~ t u~I)]:~:Jhm il -l~ -----i.~ Time (hours) 'L Use the graph to estimate (i) the background activity in becquerel, [1 ] .............................. ~Q ::::... ,. ~t- . ~()~ ................................................................................................................................................................. (ii) the half-life of the sample . [3] ~ x .. ... ?: 4h .................................... 2.. 2k.~.,:~ ~ . 10 i21
  15. 15. -15- BLANI(PAGE TURN OVER FOR QUESTION 19 .. ./16
  16. 16. _/6- Leave blank I~ A smoke detector contains a small radioactive source. A typical source contains 1.2 x 10-8 g of americium-241 , which has a half-life of 432 years. Show that the decay constant of americium-241 is approximately 5 x 10-11 S-I . ......... A ., ~ ~ l.,L- ~ ··· ······· > " L . , tt ~ "'t.. '>c' ~~ S.. "2..~ '>C 'Z..4- >c S {,]V ( s J(; ).."'- ............................................................................................................................................... =.. <;.. o <6")0( o- e - ...............................: ? ······························(2) Calculate the number of nuclei in 1.2 x 10-8 g of americium- 241, given that 241 g contains 6.0 x1023 nuclei . ..............:.1.,..~ 0.-:-.~. s x 6:. Q ~ .. ~.o. ~~ . ,;2..AtJ, .............................................................................................................................................. ') Number of nuclei = 3.:.~ ~ ~.Q . (1) Hence calculate the activity of 1.2 x 10-8 g of americium-241. ........... s» - ? A.~ ; ~.:.Q..~ ~Q~~.~~~ ~.~.()?': ~ ~U.~~ . ~~ .............................................................................................................................................. Activity = J.: ?:~~.~.t: .. . - (2)
  17. 17. I Leave1 biank . The diagram below shows the principle of the smoke detector. I I Current / detector I Radioactive source ~.--+-: l~=--_~ r----J // ~ Metal plates Radiation from the source ionises the air between the plates, and a small current is detected. If smoke enters the detector, the ions 'stick' to the smoke particles, reducing the current and triggering an alarm. Arnericium-241 is an alpha emitter. Explain why an alpha emitter is a suitable source for this apparatus . ................. .h~.).: n:M.~"?.~ ~ ,,~ <.M..~ . ................... s~~~ ~ ~ ~~ -:-:-> ~.~ .. k.. . (2) Discuss other features of this americium sample which make it a suitable source for the smoke detector. .................... h~ .. ~ ~ . ••••••••.•••••........ $:.<>. ....•.. O"'c.;.~.~.~ (. ~.~ ~.~ .. ~ O..~ ................................ ..~ S:~""'-A; -..%~c ~ k.~ . ••• a ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• , (3) (Total 10 marks)
  18. 18. -/g- I ~0 (a) The principal thermonuclear fusion process by which the Sun produces energy is a sequence of three separate fusion reactions. This process effectively combines four protons into one helium nucleus, releasing an amount of energy that is equivalent to the I mass difference between four :H atoms and one ;He atom. II Show that the energy released by the process is about 27 Me V. 1 mass of IH atom = 1.00783 u 4 mass of 2He atom = 4.00260u ..······~·:·~·~··~~·9.·~· .. ..··~· ·l·~· ······q:p·~·~·>.··~~ .. ~ ~ . ........ ~ · qJ)..J:'.i3. ..~.~ It... :~ ~: ~.~.~.Q .. .. Y 7. 9.:..Q.::?~.I.'C..~ ..........0.:..Q.~~.:!.A ~ ...:. .. ... ~~~~.~ ... ... .. .. .. o..~~.~.'.)"to ... . . ~ ~ ~.... .. ~ 2 l1:~ ~ ~ ~ .by 0 -~) ~ V-' .............................................................................................................................................. ........................ ?-:-.~:~ ..K..~.v ~ .. . (2 marks) (b) It has been calculated that, in the absence of any atmospheric absorption, energy from the Sun would reach the Earth at a rate of 1350Wm-2• Show that the mean rate of energy production by the Sun is approximately 4 x 1026 W. Assume that there is no absorption between the Sun and the Earth. mean radius of Earth's orbit = 1.50 x to'' m ••••••••••••••• .r ~ ~~ ••••••••••••••••••••••••••••••••••••••••••••••••••••••• -::/:e;- 40 Q"t T" JIIIrjo'f ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• ................ ~~~~ :'t~~ t.:~g~.. .J..' .. ~ ..~)~ ? ~ 3.s..9..W. "' ::: S·~ ~" lv ........................................................................ ~ 0 . (2 marks) . - -/lfJ
  19. 19. -/9- (c) From parts (a) and (b), and any data needed from the Data Sheet, calculate (c) (i) the rate at which the mass of the Sun is decreasing, ... 1.~ ::=: a.~ :: 1:.r ~ ~Q~.~.ty :~ 1.:..-:..~ '! Q~ ~~. c.,"'- T~ (vo « 0 ¥ "",s~')" tc.~ <;.--, (c) (ii) the number of ~He nuclei that are produced per day by the fusion process described in part (a) . ....... ..~ 0.~~.~ ~ (}.'i.. .. .~.~.~~ ~:.¥. ~~ . ............. ~..~.Q~..~ ~..~..~ !-?~~~~ ~.~ . ~"'L ........ ~ ?:.:..=f x..o i . =- (5 marks)

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