Binding Energy and Mass defect

Transcription

1 Binding Energy and Mass defect Particle Relative Electric Charge Relative Mass Mass (kg) Charge (C) (u) Electron x x x Proton x x Neutron x u = x kg 1eV = 1.60 x Joules 1u is converted into MeV Solutions. 1) 1. a) Mass of component parts m = 2p+2n = 2( x ) + 2( x ) m= x kg Mass defect = x kg x kg = 5.03 x kg b) Binding energy using E =mc 2 = [5.03 x kg] x [3 x 10 8 ] 2 E = 4.53 x Joules c) Binding energy = 4.53 x x 1.60 x ) a) U Th + 4 2α = 2.83 x 10 7 ev [= 28.3 MeV ] b) First calculate mass change u - ( u u) mass change = 5.6 x 10-3 u Convert to kg = 5.6 x 10-3 u x x kg Mass defect = x Energy released E=mc 2 = x x (3x10 8 ) 2 = x J

2 3) Calculate the mass defect and binding energy the nuclide 10 5B where the mass of 10 5B atom = u 10 5B has 5 protons and 5 neutrons Total mass of nucleons = mass of protons + mass of neutrons = 5 [ u] + 5 [ u] = u = u Mass defect = Mass of nucleons - mass of 10 5B nucleus = u u = Mass defect in Kg = x Kg Binding Energy E = mc 2 = x x (3 x 10 8 ) 2 = x J Binding Energy in ev = x J / 1.6 x = x 10 7 ev = 624 MeV 17 4) O-17 8 O has 8 protons in the nucleus and 9 neutrons Total mass of nucleons = mass of protons + mass of neutrons = 8 [ u] + 9 [ u] = u u = u Mass defect = Mass of nucleons - mass of O17 nucleus = u u = u Mass defect in Kg = x x = x Kg Binding Energy E = mc 2 = x x (3 x 10 8 ) 2 = x J Binding Energy in ev = x J / 1.6 x = x 10 8 ev = 123 MeV

3 5) Write out the reaction first (words will do here) Thorium Radium + alpha particle Calculate mass of products and reactants in terms of u Reactants Products u u Calculate the difference = = 0.004u Energy released E = mc 2 = x 1.66 x x (3 x 10 8 ) 2 = x J ) (a) (b) H + 1H 2He + 0 n Calculate mass of products and reactants in Kg Reactants Products x x Kg x Kg + mass of neutron x x x Mass difference = x x = x Energy released E = mc 2 = x x (3x10 8 ) 2 = 2.80 x J

4 MARK SCHEME! 1. (a) Deduct for each error or omission, stop at zero 2 max Property temperature of sample pressure on sample amount of sample Effect on rate of decay increase decrease stays the same 4 (b) (i) He/ 4 2 2α ; Rn ; 2 mass defect = u; energy = mc 2 = / 1 u = 930 MeV; = J / 4.86 MeV; 3 max (c) (i) (linear) momentum must be conserved; momentum before reaction is zero; so equal and opposite after (to maintain zero total); 3 0 = mv + mrnvrn; v v Rn m Rn m α 222 = = 55.5; 3 4 Ignore absence of minus sign. (iii) kinetic energy of α-particle = ½mv 2 ; 2 V α ; 222 kinetic energy of radon nucleus = 1 2 m this is 1 / 55.5 of kinetic energy of the α-particle; Accept alternative approaches up to [3 max]. 3 max (d) eg (-ray) photon energy or radiation; 1 (e) (i) two (light) nuclei; combine to form a more massive nucleus; with the release of energy / with greater total binding energy; 3 high temperature means high kinetic energy for nuclei; so can overcome (electrostatic) repulsion (between nuclei); to come close together / collide; high pressure so that there are many nuclei (per unit volume); so that chance of two nuclei coming close together is greater; 5 10

5 2. (a) (i) fission: nucleus splits; into two parts of similar mass; radioactive decay: nucleus emits; a particle of small mass and / or a photon; 4 (iii) 235 U n ; Sr Xe 1 4 n ; Allow ecf for RHS if LHS is incorrect. mass number unchanged; atomic number increases by +1; 2 (b) (i) kinetic energy of neutrons; and energy of gamma ray photons; 2 Accept other valid possibilities but do not accept heat. p 2 use of Ek = / equivalent; m correct conversion of MeV to joule ( J); correct conversion of mass to kilogram ( kg) momentum = N s; 4 (iii) total momentum after fission must be zero; must consider momentum of neutrons (and photons); 2 (iv) xenon not opposite to strontium but deviation < 30 ); arrow shorter / longer; 2 (c) (i) probability of decay / constant in expression dn dt = N; dn per unit time / and N explained; 2 dt = ln 2 ( ) (note: substitution is essential) = s 1 ; 1 (d) (i) N 0 exp( N 0 10 exp( 0.462t) t) = ; exp(0.462t) = ; t = 30.3 s; 3 activity of the strontium will be much greater than that of the xenon; and extent of health hazard depends on activity; 2 [26] 11

6 3. (a) the nuclei of different isotopes of an element have the same number of protons; but different numbers of neutrons; 2 Look for a little more detail than say just same atomic (proton) number, different mass (nucleon) number. (b) Z for iodine = 53; + antineutrino; (accept symbol) 2 Do not accept neutrino or gamma or energy, etc. (c) (d) λ = time / days shown on graph at least the 0, 8 and 16 day data points; exponential shape; scale on y-axis / goes through 24 day point; ; (accept ln 2 for 0.69) T = d 1 / 0.87 d 1 / s 1 ; 2 (e) 0.5 = 6.4e 0.086t ; to give t = 30d / s / 29d / s; 2 4. (a) (i) an atom or nucleus that is characterized by the constituents of its nucleus / a particular type of atom or nucleus / OWTTE; (in particular) by its proton (atomic) number and its nucleon number / number of protons and number of neutrons; 2 [11] nuclides that have the same proton number but different nucleon number / same number of protons different number of neutrons; 1 (b) (i) Na 12 Mg β v / e 0 / 1 e ; v ; MeV is equivalent to u; = rest mass of particle; rest mass= u; 3 No credit given for bald correct answer. (c) sodium-24 has more nucleons; and more nucleons (usually) means greater (magnitude of) binding energy; or sodium-23 has less nucleons; and less nucleons (usually) means less (magnitude of) binding energy; 2 12

7 5. (a) (i) there is more uranium-238 present than uranium-235; neutron capture is more likely in U-238 with high energy neutrons; if the neutrons are slowed they are more likely to produce fission in U-235 than neutron capture in U-238; 3 control rate at which reactions take place; by absorbing neutrons; 2 (b) (i) fuel enrichment means that the amount of uranium-235 present in the fuel is increased / OWTTE; this means that more U-235 available for fission; therefore the reaction can be sustained; 3 enriched fuel can be used in the manufacture of nuclear weapons; so possibly threatening World peace; 2 (c) (i) (energy released) = ( ) 10 5 ; = MeV 1 kinetic; 1 (d) (i) number of atoms in 1 kg of carbon = kg of U-235 = ; N A energy per kg carbon = kev; N A N A 124 kev and per kg U-235 = and number in N A 8 therefore ratio = ; 3 a much higher energy density implies that uranium will produce more energy per kg / smaller quantity of uranium needed to produce same amount of energy / OWTTE; 1 (e) (i) half-life: time for the activity to decrease by half / OWTTE; isotope: isotopes of elements are chemically identical but have different atomic masses / OWTTE / same number of protons in the nucleus but different number of neutrons / OWTTE; U 239 Np 93 v Np ; ; (iii) v ; 3 advantage: plutonium is another fissionable element / may be used as nuclear fuel; and is readily produced in reactors that use uranium as a fuel; disadvantage: -particles are harmful to living organisms / OWTTE; and the plutonium lasts for a very long-time / OWTTE; 4 [25] 13

8 6. (a) (i) fission 1 max kinetic energy 1 max (b) the two neutrons can cause fission in two more uranium nuclei producing four neutrons so producing eight etc; OWTTE; 1 max 7. (a) (i) activity = ()N; λ s ; Allow yr 1. ln 2 17 T s; = years; 2 (b) eg activity would change during analysis to find N / rate of change of activity is too great to allow N(t) to be determined / OWTTE; 1 [5] 14

9 MARK SCHEME! 1. D 2. D 3. B 4. B 5. C 6. B 7. A 8. A 9. B 10. B 11. A 12. C 13. C 14. B 15. D 16. D 17. C 18. B 10

10 19. B 20. A 21. D 22. B 23. C 24. C 25. B 26. C 27. C 28. D 29. A 30. C 31. A 11

11 MARK SCHEME! 2. D 6. A 11. D 14. B 15. D 19. B 24. A 25. A 38. C