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Transcript
By C K Cheung Radioactivity Radioactivity is the spontaneous disintegration (= decay) of the nucleus of an atom, from which may be emitted some or all of the followings: 1/ -particle 2/ -particle 3/ rays This spontaneous process is not affected by: a/ chemical combination (e.g. ________________) b/ physical environment (e.g. _____________________) Experiment 1000 identical cubes with one marked surface Marked face uppermost ‘decayed’ and will be taken away. away Repeat the experiment until only a few cubes have not ‘decayed’ number of undecayed cubes number of throw 1 By C K Cheung Law of Radioactive Decay The rate of disintegration of a given nuclide at any time is directly proportional to the number of nuclei, N, of the nuclide present at that time. dN decayed dt No. of radioactive nuclei = No Hence, dN N dt dN (cons tan t )( dt ) N dN ( )dt N If at t = 0, N = No 1/ 2/ dN = change in number of undecayed nuclei called decay constant > 0 at t = t, N = N N N0 ln( t dN dt N 0 N )=-t N0 N = N0 e t number of undecayed nuclei 2 By C K Cheung N ~e t t 0 Note: dN dN N probability for a nucleus to decay per unit time is constant 1/ = Ndt dt ..\powerpoint\meaning of decay constant.ppt 1st 2nd 2/ dN N Activity (A) dt A = A 0 e t e.g. A radioactive sample has T = 5600 yrs. Find the time taken for 1 of 16 the sample to decay. 521 yrs. 3 By C K Cheung Half-life ( T ) Time required for half of the sample to decay. λt ∵ N = N0 e N e t ∴ N0 1 e2 λT - T = lne( 1 ) 2 T = lne( 2 ) ∴ λ = ln( 2) T Background Radiation. A /counts s-1 A0 AT Ab T time AT = A0 Ab Ab 2 4 By C K Cheung Properties of 3 radiations Property Nature Mass (atomic mass unit /amu) Effect on photographic plate number of ion-pairs per mm in air (ionization power) Absorption (stopped by up to) (penetration power) Helium nuclei electrons EM radiation with very short wavelength 4u u 1840 0 Yes Yes Yes ~104 ~102 ~1 ~cm air ~10 – 2 mm Al ~mm Al foil ~ sheet of paper or skin ~ cm Pb Speed (ms – 1) ~107 ~107 - 108 Effect of B & E Bent slightly Bent strongly No effect Disperse considerably (varies) 3x108 Some uses of radioactive isotopes: 1/ Cobalt – 60 emits - rays which are used for treating cancer, and for sterilization 2/ As tracer elements: a radioisotope will experience the same chemical treatment as its non-active isotope, but its activity enables it to be detected even in minute quantities. 5 By C K Cheung 3/ To measure the thickness of a material: I = I0e - kx Incident intensity = I0 X 4/ Dating methods atmosphere radioactive 14 7N 01n146C * 11H N: atmospheric nitrogen n : ejected from nuclei in atmosphere by cosmic ray C: radioactive with T1/2 = 5700 yrs. 6 By C K Cheung 14 * 6C O2 C *O2 C*O2 taken by plants & trees for manufacturer of carbohydrates in photosynthesis. The normal activity of living plants ~ 15.3 counts per minute per gram of carbon. But when the organism dies no intake of C*, but decay process goes on with T1/2 ~ 5700 years. By measuring the activity of some furniture from an ancient village age of the furniture can be estimated within the range of 1000 to 5000 years. 7 By C K Cheung Nuclear Fission When a heavy nuclide is split into 2 large fragments, the process is called fission. Usually, a fission process requires a neutron ( uncharged ) to initiate it. Note: we don’t interest in which the atomic nucleus changes only slightly after disintegration because the mass defect is small. But, if the nucleus split into 2 large nuclei, the mass decrease is appreciable. Consider: 236 ( U 92 ) … 235 U 92 + n 10 236 1 1/ U 92 Xe 140 + Sr 94 54 38 + 2 n 0 + 200MeV 236 1 2/ U 92 Ba 144 + Kr 90 56 36 + 2 n 0 + energy a variety of further decay a variety of further decay Called fission neutron Chain reaction n U235 n U235 n U235 8 By C K Cheung Fission Reactor Inside reactor, about 1 fission neutron ( out of produce 1 another new fission. 2 ) from each fission process can n U235 n n U235 U235 U235 > 99 % U 238 Natural Uranium < 1% U 235 U-238: Only fission with very fast neutrons Capture medium-speed neutrons without fissioning. ( undergo -decay ) U-235: Fissions with slow neutrons. 9 By C K Cheung Nuclear Fusion Two light nuclei combine together to yield a heavier nucleus, with release of energy e.g. Synthesis of He 42 from 4 H 11 : H 11 + H 11 H 12 + e + 0.4 Mev H 11 + H 12 He 32 + 5.5 Mev He 32 +He 32 He 42 + 2 H 11 + 12.9 Mev chain reaction Conditions for fusion process: 1/ high density ( to increase the collision chances ) 2/ high temperature ~ 108 – 109 K ( the initial light nuclei have enough K.E. to overcome their mutual repulsion and come close enough to react). Note: How to keep the hot reacting plasma from touching the vessel holding it , still an unsolved problem. 10 By C K Cheung Mass & Energy Def.: 1 atomic mass unit ( amu ) = ( 1 amu = ( 1 ) of the mass of a C12 atom. 12 1 12 1 x )( ) = 1.66 x 10 – 27 kg 12 1000 6.02 x10 23 E = mc2 1 amu = (1.66 x 10 – 27 kg )(3x108 )2 = 1.494 x 10 – 10 J Also, 1 eV = 1.6 x 10 –19 J 1 amu = 931.478 MeV Binding Energy Mass of neutron = mn Mass of proton = mp Mass of nucleus = m It is found that : mass of nucleus < sum of mass of individual nucleon Phenomenon called mass defect Note: 1/ 2/ 3/ m binding energy of nucleus < 0 dU F= short-range nuclear attractive force. dr Ionization energy = - binding energy 11 By C K Cheung Binding Fraction ( B.F. ) B.F. = B. E . = binding energy per nucleon A B.F. increases nucleus more stable B.F./MeV 8.5 fission fusion Fe-55 A ( mass number) 12