PHYS 219 Spring semester 2014 Lecture 28: Radiactive Decay Rn Reifenberger Birck Nantechnlgy Center Purdue University PHYS 219 Test III Friday; May 9, 2014 1 PM-3 PM PHYS 1 Lecture 28 1 Radiactivity Early Histry Henri Becquerel In early 1896, fllwing Wilhelm Cnrad Röntgen's discvery f X-rays in 1895, Becquerel shwed that materials such as uranium salts emit penetrating X-raylike radiatin. He shared the Nble Prize in Physics (1903) with Marie Skłdwska-Curie and her husband Pierre Curie fr the discvery f spntaneus radiactivity. Marie Curie In 1898, Marie Curie islated tw radiactive chemical elements frm a dark-clred mineral called pitchblende (uranium xide): discvered the elements plnium and radium (frm the Latin wrd fr ray ). In 1903, became the first wman t receive a dctrate degree in France. In 1911, she received the Nbel Prize (again!) in Chemistry fr her discvery f radium and plnium. 2 1
Radiactivity Evidence fr Nuclear Parts Barely penetrate a sheet f paper Penetrate several cm s f lead Lrentz Frce: F =qvbsinθ; sign f q frm right-hand rule energetic particles nuclear rigin Penetrate few mm s f aluminum Because there are n external frces, mmentum and energy are cnserved in a radiactive decay prcess 3 Rate f Nuclear Decay The number f decays per secnd is called the activity (R) f a radiactive surce The unit f activity is the Curie (Ci): 1 curie = 1 Ci = 3.7 10 10 decays/s (This definitin is histrical. The activity f 1 gram f radium is rughly 1 Ci.) Anther unit f activity is the becquerel (Bq): 1 becquerel = 1 Bq = 1 decay/s 4 2
Representative Orders f Magnitude in Ci in Bq Radium watch dial 1x10-6 (μci) 3.7x10 4 1 kg beach sand; Guarapari, Brazil 2.2x10-6 (μci) 8.3x10 4 Typical lab surce ~1x10-3 (mci) ~3.7x10 7 Cell death ~10 Ci ~3.7x10 11 Radiatin therapy ~1000 Ci ~3.7x10 13 Oak Ridge, TN (released t envirnment) Tmask (FSU) (released t envirnment) Ttal man made radiatin released t envirnment ~1x10 6 Ci ~3.7x10 16 ~1.1x10 9 Ci ~4.1x10 19 ~1.7x10 9 Ci Ttal radiactivity in wrld s ceans ~4.3x10 11 Ci 1 Bq=1 decay/s; 1 Ci=3.7x10 10 Bq 5 Hanfrd (~ 0.7 x 10 6 Ci) Oak Ridge (~1x10 6 Ci) Savannah River (~0.9 x 10 6 Ci) Radiactive Ht Spts in the Wrld (estimated) Guarapari, Brazil: httest beach in the wrld Tmsk -7, Seversk (strage tank expldes in 1993 ) (~1130x10 6 Ci) Ekaterinburg, Cherylabinsk (strage tank expldes in 1957) (~130x10 6 Ci) Krasnyarsk (30 yrs. f discharge frm a factry making bmbgrade plutnium) (~460x10 6 Ci) 6 3
Radiactive decay is nature s way f returning unstable nuclei t the nuclear stability line Excess neutrns Mre than 2000 radiactive istpes have been identified 7 Alpha decay an example http://phet.clrad.edu/simulatins/sims.php?sim=alpha_decay Radium 226 88 Ra When nucleus has t many prtns cmpared t the number f neutrns, the repulsive electrstatic frce begins t dminate; nucleus becmes unstable and emits an α particle. Radn 4 He 222 Rn 2 86 (Helium nucleus) Stpped by paper Ra Rn He 226 222 4 88 86 2 8 4
Beta decay an example http://phet.clrad.edu/simulatins/sims.php?sim=beta_decay (132 neutrns) 214 82 Pb Sme nuclei are smewhat neutrn rich. As a result, a neutrn breaks apart and a prtn and an electrn appear in its place. (131 neutrns) (Beta-particle) Discvered in 1956 0 0 214 83 Bi 0 1 e Stpped by Al fil Nte that the mass number remains unchanged in beta decay Pb Bi e 214 214 0 82 83 1 9 It is interesting that a free neutrn is unstable n p + e - + neutrn prtn + electrn + antineutrin has zer mass and travels at the speed f light A free neutrn lives fr abut 10.6 minutes 10 5
Gamma decay an example 214 Bi * 83 A nucleus underging radiactive decay smetimes prduces a prtn r neutrn in a highly energetic state. The excess energy is given ff by a gamma decay (i.e. a high energy phtn). 214 83 Bi 0 0 Bi Bi 214 * 214 0 83 83 0 Stpped by lead 11 Half-Life f a Radiactive Nucleus When will this atm decay? I Xe e 131 131 0 53 54 1 Radiactive decay is prbabilistic 6
The Law f Radiactive Decay (applies t α, β, and γ decay) t 1 Nt () Nt ( 0) 2 Nt () Nt ( 0) : Number f radiactive nuclei at time t : Number f radiactive nuclei at time t=0 : half-life f radiactive istpe is nt affected by temperature, pressure, etc. It has a value that is characteristic f each unstable nucleus 13 Nt ( 0) Rn P He 222 218 4 86 84 2 3.8 d Nt () 14 7
0 The element 91 38Sr (Strntium) has a half-life f 9.7 hurs. If a sample cntains 91 0 grams f the radiactive istpe Sr at 38 t=0, hw much remains after 22.1 hurs? Mass in grams 60 t=22.1 hrs 1 N(t = 22.1 hrs) = 0 2 = 0 0.206 =24.7 grams 22.1/9.7 30 15 9.7 19.4 29.1 (in hurs) 15 The activity (R, decays/s) f a surce can als be calculated: Number f radiactive atms remaining after a time t Decays/secnd after a time t 1 N(t) = N 2 t/τ -0.693 e = 0.5 (just anther way t write 1 / 2) t/τ -0.693-0.693 N(t) = N e = Ne 0.693 λ decay cnstant; units [1 / s] τ N(t) =N e ΔN(t) R Δt -λt t/τ -λt -λt = λ N(t) =(λ N ) e =R e Nte that R is activity (decay rate) when t=0 16 8
Example: A radiactive surce with a half-life f 30 mins. is measured t have a decay rate f 80,000 s -1. Hw many radiactive nuclei are present? 0.693 decay cnstant; units [1/s] Nt () Ne Nt () t R N() t ( N) e Re t where R N t N 0.693N 60 s 30 min 80,000 s R min 0.693 0.693 8 2.0810 t 1 17 Suppse yu have a sample f 4.75 10 7 atms f Radn? Radn has a half-life f 3.82 days. What is the activity f this sample? R(t) = R e t N 1/2 4.7510 7 3.82 days 0.693 1day 1hr 1min 3.82 days 24 hr 60 min 60s 2.110 s 6 1 6 1 7 (2.1 10 )(4.75 10 ) 99.7 / R N s s 1Ci 3.710 decays/s 9 99.7 Bq 2.7 10 Ci 0.0027 μci 10 R(t) =[99.7 Bq] e 6 1 (2.110 s ) t 18 9