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Nuclear Physics

Nuclear Physics. Protons and neutrons react inside the nucleus Elements transmute into other elements Isotopes react differently Independent of chemical combination Energy changes ~ 10 8 kJ Mass Changes are detectable. Electrons react outside the nucleus

justina-perkins
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Nuclear Physics

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  1. Nuclear Physics

  2. Protons and neutrons react inside the nucleus Elements transmute into other elements Isotopes react differently Independent of chemical combination Energy changes ~ 108 kJ Mass Changes are detectable Electrons react outside the nucleus The same number of each kind of atom appear in the reactants and products Isotopes react the same Depend on chemical combination Energy Changes ~ 103 Kj Mass reactants = mass products Six Differences Between Nuclear Reactions and Chemical Reactions

  3. Radioactivity • Much of our understanding of atomic structure came from studies of radioactive elements. • Radioactivity - The process by which atoms spontaneously emit high energy particles or rays from their nucleus. • First observed by Henri Becquerel in 1896.

  4. Cloud chamber • A simple device for the detection of radiation. • A ‘vapor trail’ is produced as radioactive particles pass through it.

  5. Survey meter (Geiger counter) thin window anode cathode Argon filled tube under high voltage ratemeter - tells number of counts/minute Good for area monitoring or locating ‘hot spots’.

  6. La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Ac Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Radioactive elements H He Li Be B C N O F Ne Na Mg Al Si P S Cl Ar K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr I Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te Xe Cs Ba Lu Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn Fr Ra Lr Rf Db Sg Bh Hs Mt 110 111 112

  7. The common types ofradioactive emissions • The three most common forms of radioactive emission, are • alpha particles, α, which are helium ions • beta particles, ß , which are electrons, and • gamma rays, γ, which are pure energy similar to x-rays • Also should know positrons ß+, which are positive electons.

  8. Radioactivity • Major types of radioactive decay • alpha emission, α, attracted tonegative plate • beta emission, ß, attracted topositive plate • gamma radiation, γ, not affected

  9. Magic numbers • Some combinations of protons and neutrons appear to be more stable than others. • Proton magic numbers • 2, 8, 20, 28, 40, 50, and 82 • Neutron magic numbers • 2, 8, 20, 28, 40, 50, 82, and 126. • This indicates the existence of energy levels in the nucleus, similar to those observed for electrons outside the nucleus.

  10. Predicting the type of decay • The chart of the nuclides provides a convenient map of the types of isotopes. • It shows how each type of radioisotope will decay. It does not give you the reasons why. • There are a few rules that can be used to predict how a nuclide will decay.

  11. Proton : neutron ratio Stable isotopes run at ~ 45o slope then slope down at Z = 20 (Ca). A band of stability is observed. Radioactive nuclides will attempt to find the shortest path to ‘get back’ to the band of stability. 20 40 60 80 100 120 N - neutrons 20 40 60 80 Z - protons

  12. Proton : neutron ratio neutron rich region 1 : 1 ratio line 20 40 60 80 100 120 N - neutrons proton rich region 20 40 60 80 Z - protons

  13. Decay tendencies ß- decay αdecay, elements with Z > 82 20 40 60 80 100 120 N - neutrons ß+ decay or electron capture 20 40 60 80 Z - protons

  14. Alpha Decay • Stripped helium atom 4He • Nucleii contain 2 less protons and 2 less neutrons 238U → 234Th + 4He How many protons in uranium? How many protons in Thorium? Notice the mass numbers add up 238 = 234 + 4

  15. Beta Decay0-1e • A beta particle is an electron • A neutron turns into a proton and an electron • The decay produces another proton in the nucleus • 210Pb → 210Bi + β • How many protons in Pb, Bi?

  16. Gamma emission • All nuclear decays release gamma radiation. • The nucleus is unstable and oscillates until it releases the particle, but it is left in a high energy state that requires the release of excess electromagnetic radiation in the form of gamma radiation. • Alpha, beta, and positron emitters give off alpha particles with little gamma radiation. • Gamma emitters give off lots of gamma rays with each particle emitted.

  17. 0 -1 1 1 1 0 p e n +  Electron Capture • Addition of an electron to a proton in the nucleus is known as electron capture or K-capture. • The result of this process is that a proton is transformed into a neutron.

  18. Decay Series • Most radioactive elements are too far from the zone of stability to reach it in one decay. • Multiple decays must occur. • This is called a decay series. • Uranium’s can be 13 to 15 steps long. • Can take different paths because there is a probability of the nucleus undergoing certain decays, sometimes the probability of alpha vs. beta are close that either are likely.

  19. Radioactive decay • Although we can predict the methods by which an isotope may undergo radioactive decay to become more stable, we can not predict how quickly these changes will occur. • The rate of decay is dependent on the stability of the specific radioactive species. • Half Life is defined as the time required for 50% of a specific radioactive species to decay. • We commonly use the symbol - t1/2

  20. Half-life 100 80 With each half-life, 50% of an isotope will decay. 60 % 40 20 0 0 2 4 6 8 10 half-lives

  21. Half-life examples • Name Half-life • Carbon-14 5720 years • Sodium-24 15 hours • Iron-59 45 days • Cobalt-60 5.3 years • Nickel-63 100 years • Uranium-235 704 million years

  22. Half-life example 1 • The t1/2 for 63Ni is 100 years. If you had 100g of 63Ni, how much would remain after 400years? • ……after 250years?

  23. Half-life • Amount remaining for 63Ni • (half-lives) amount (g) time(yrs) • 0 100 0 • 1 50 100 • 2 25 200 • 3 12.5 300 • 4 6.25 400 • Decay can take a long time! • Always take 1/2 amount and add t 1/2 • 63Ni is used in some smoke detectors.

  24. Half-life • Amount remaining for 63Ni • (half-lives) amount (g) time(yrs) • 0 100 0 • 1 50 100 • 2 25 200 • 3 12.5 300 • 4 6.25 400 • At 250 years, we need to interpolate to find the # g remaining half-way between 2 and 3 half-life cycles. • Half-way between 25 and 12.5 g is 18.75 g, but the decay rate is faster in the beginning of the cycle when more atoms are present, so the amount is a little less than 18.75 g. 250

  25. Half-life • Amount remaining for 63Ni • (half-lives) amount (g) ln (amount) time(yrs) • 0 100 4.61 0 • 1 50 3.91 100 • 2 25 3.22 200 • 3 12.5 2.53 300 • 4 6.25 1.83 400 • 5 3.12 1.14 500 • 6 1.56 0.44 600 • 7 0.78 -0.25 700 • 8 0.39 -0.94 800 • 9 0.20 -1.61 900 • 10 0.10 -2.30 1000 A linear relationship will exist between the natural log (ln) of undecayed atoms vs. time.

  26. Half-life 4.61 You can plot the ln (amount) vs. time to create a linear curve. 2.30 ln (amount, Nt) 0 0 800 400 Time, t in yrs -2.30 y = mx + b ln Nt = ∆ ln Ntt + ln N0 ∆ t

  27. Radioactive decay ln Nt = ∆ ln Ntt + ln N0 ∆ t • At a time equal to one half-life period • ∆ t = half-life, t1/2 and Nt= 1/2 N0 ∆ lnNt= lnN0-ln Nt = lnN0 = lnN0 lnNtln1/2 N0 ∆ ln Nt =ln 2= 0.693 lnNt = 0.693 t + ln N0 t1/2

  28. Radioactive decay • Upon further math manipulation lnNt = 0.693 t + ln N0 • t1/2 • lnNt - ln N0 = 0.693 t • t1/2 • lnNt = 0.693 t • lnN0 t1/2 Nt N0 = e-k t

  29. Radioactive decay • We can also recognize radioactive decay as a first order rate where the radiation decreases proportionately with the amount of atoms remaining. Mathematically: • -∆ N /∆ t = kN • By integration, we obtain: • ln N = - kt + a • When t = 0, a = ln N0 so: • ln (N /N0) = k t • N = N0 e - k t

  30. Radioactive decay • The rate constant (k) is dependent on the specific radioactive species. • It is one significant characteristic of a radioactive isotope. • We commonly use a modified form of this constant , t1/2 • The time required for 50% of a specific radioactive species to decay.

  31. Activity • In practice, we can’t directly evaluate N or even ∆N /∆t. • A useful approach is to determine activity (A). • Activity = disintegrations / unit time • or you can use • Activity = counts / unit time • If the detection method is not 100% but is proportional to the number of disintegrations.

  32. Activity • Since activity is proportional to N, we can use the following relationships: • At = A0 e-k t • or • At = A0 1/2t / t 1/2 • This assumes that we are only measuring a single species. Decays from multiple sources can result in counting errors

  33. Half-life example • The t1/2 for 63Ni is 100 years. If you had 100 g of 63Ni, how much would remain after 250 years? • At = A0 e -0.693 t / t1/2 • = 100 g e -0.693 (250 y)/(100 y) • = 17.7 g

  34. Energy changesin nuclear reactions. • Binding energy (mass defect) • Binding energy is positive (endothermic), taking apart • Mass defect is negative (exothermic), putting together • Measure of stability gained when protons and neutrons get together to form a nucleus. • The equation that shows the relationship between mass and energy is: • E= mc2 • We can use this relationship to determine how much energy is produced by a decrease in mass.

  35. Binding energy • A more useful version of the equation is: • ∆E = ∆mc2 • where: • ∆E = the binding energy • ∆m = mass difference between the nucleus and the separate nucleons. What would be the binding energy for a nuclear reaction that has a mass defect of 1 amu?

  36. Binding energy Binding energy = ∆m(amu) x 1.49 x 10-13 kJ / amu

  37. Example • Determine the binding energy of 16O. • We have accurate measurements of the masses for stable nuclides that can be used. • 16O 15.9949146 amu • n 1.0086649 amu • p 1.0078250 amu

  38. Example • To determine the binding energy, we simply need to look at the mass of the atom and the particles if taken separately. • 16O has 8 protons and 8 neutrons • 8 n 8 x 1.0086649 = 8.0693192 • 8 p 8 x 1.0078250 = 8.0620000 • Total 16.1319192

  39. Example • Finally, calculate the binding energy based on the mass difference. • ∆m = 16.1319192 - 15.9949146 • = 0.1370046 amu • BE = 0.1370046 amu * 1.49x 10-13 kJ / amu • = 2.05 x 10-14 kJ / amu Since 1 g = 6.02 x 1023 amu, this would be equivalent to 1.23 x 1010 kJ / gram.

  40. Binding energy • We can calculate the binding energy per nucleon for all of the stable isotopes to compare their relative stabilities. We end up with the following plot. Fe Most stable Relative binding Energy per nucleon Mass number 56

  41. Binding energy • As the total number of nucleons increases, we reach a point where the binding energy is at a maximum. • Higher mass nucleons are less stable. • This is why we can obtain energy from both fission and fusion and why alpha emission is common for heavier isotopes. Max. binding energy fusion fission Fe

  42. Nuclear power • Power can be obtained two ways. • Fission - Splitting atoms • Get energy if the nucleus is big. • The smaller ones are more stable. • What we do in nuclear reactors. • Fusion - Joining atoms • Get energy if the nuclei are small. • The larger one is more stable. • This is how the sun works.

  43. Chain reactions • Critical Reaction • When just enough fissions occur to keep the chain reaction going. • (neutrons formed = neutrons used) • Creates useful nuclear power. • Supercritical Reaction • When excess neutrons are produced and the rate of fission keeps increasing at an uncontrolled rate. • Creates nuclear bombs.

  44. 1 0 235 92 92 36 141 56 1 0 Energy from fission • Uranium-235 is used as a ‘fuel’ in a reactor. • One common reaction is • n + U Kr + Ba + 3 n + energy One thermal neutron at room temperature is absorbed, but 3 high speed neutrons are emitted. In order to continue the chain reaction, the emitted neutrons must be slowed down by a moderator, such as water or graphite.

  45. Binding energy The mass defect from splitting 1 mole of uranium-235 in a fission reactor is 0.186 grams. How many kJ of energy are released? The energy produced by splitting one mole of U-235 atoms is approximately 17 trillion kJ. 100 grams of 235U could produce as much energy as 80 trillion tons of TNT.

  46. US Nuclear reactors MOST IMPORTANT! REMOVE HEAT AS FAST AS IT IS PRODUCED! secondary coolant primary coolant reactor vessel turbine core heat exchanger Concrete & steel Containment building

  47. Nuclear Power Plant accidents • Three Mile Island –oops! • Chernobyl – OMG • Fukushima – Whoa! • Geopolitical issues? • New designs – breeder reactors, safer traditional reactors.

  48. Nuclear bombs A conventional explosive is used to drive two sections of U-235 together. This creates a supercritical mass.

  49. Energy from fusion • When you join small atoms together, you can also get energy. • The Sun fuses hydrogen to make helium.

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