Chapter 31 - Nuclear Physics and Radioactivity PDF

Physics Cutnell & Johnson Chapter 31 Nuclear Physics and Radioactivity Copyright ©2022 John Wiley & Sons, Inc. EdPuzzle Introduction Do the video Quiz to learn about different types of decay Copyright ©2022 John Wiley & Sons, Inc. 2 EdPuzzle In...

Physics Cutnell & Johnson Chapter 31 Nuclear Physics and Radioactivity Copyright ©2022 John Wiley & Sons, Inc. EdPuzzle Introduction Do the video Quiz to learn about different types of decay Copyright ©2022 John Wiley & Sons, Inc. 2 EdPuzzle Introduction Do the video Quiz to learn about half-life and radioactive dating Copyright ©2022 John Wiley & Sons, Inc. 3 As far as we know, everything in that has ever happened in the universe is due to 4 forces. If you find a 5th force you can win a Nobel prize… Copyright ©2022 John Wiley & Sons, Inc. 4 1. Gravity we experience every day and allows all objects with mass to attract one another 2. Electromagnetism is responsible for all Chemistry, electricity, magnetism, light and contact forces (essentially everything we did FSKS in 123…) Copyright ©2022 John Wiley & Sons, Inc. 5 We will introduce the other two forces today: 3. Strong Force: Binds Protons and Neutrons in nucleus (Binds all particles made of quarks) – Very short range! Don’t notice in everyday life Copyright ©2022 John Wiley & Sons, Inc. 6 We will introduce the other two forces today: 4. Weak Force: Causes radioactive decay, decay (Transforms neutrons into protrons & vice versa!) – Very short range also! Don’t notice in everyday life Copyright ©2022 John Wiley & Sons, Inc. 7 31.1 Nuclear Structure (1 of 6) All matter around us, is made of atoms. Atoms have electrons outside, and a nucleus inside The atomic nucleus consists of positively charged protons and neutral neutrons. Proton’s and Neutrons are made of quarks (don’t need to know) Copyright ©2022 John Wiley & Sons, Inc. 8 31.1 Nuclear Structure (2 of 6) Table 31.1 Properties of Select Particles Mass Mass Particle Electric Charge (C) Kilograms (kg) Atomic Mass Units (u) Electron negative 1.60 times 10 to the power negative 19 9.109382 times 10 to the power negative 31 5.485799 times 10 to the power negative 14  1.60 10  19 9.109 382 10  31 5.485 799 10  14 Proton positive 1.60 times 10 to the power negative 19 1.672622 times 10 to the power negative 27 1.007 276 1.60 10  19 1.672 622 10  27 Neutron 0 1.674927 times 10 to the power negative 27 1.008 665 1.674 927 10  27 Hydrogen atom 0 1.673534 times 10 to the power negative 27 1.007 825 1.673 534 10  27 Copyright ©2022 John Wiley & Sons, Inc. 9 31.1 Nuclear Structure (3 of 6) Atomic number = Type of element -Number of protons = number of electrons -Number of electrons = Chemical properties - Chemical properties = Type of element Copyright ©2022 John Wiley & Sons, Inc. 10 31.1 Nuclear Structure (4 of 6) Nuclei that contain the same number of protons but a different number of neutrons are known as isotopes. Same Atomic number (protons) = Type of element Chemical properties Copyright ©2022 John Wiley & Sons, Inc. 11 31.1 Nuclear Structure (3 of 6) Test your knowledge with this game! Copyright ©2022 John Wiley & Sons, Inc. 12 31.1 Nuclear Structure (5 of 6) Nuclei aren’t 100% spherical, their radius is instead given by 1 r 1.2 10  15 m  A 3 ` Copyright ©2022 John Wiley & Sons, Inc. 13  Conceptual Example 1 Nuclear Density It is well known that lead and oxygen contain different atoms and that the density of solid lead is much greater than gaseous oxygen. Using the equation, decide whether the density of the nucleus in a lead atom is greater than, approximately equal to, or less than that in an oxygen atom. 𝑟 ≈ ( 1.2 × 10− 15 𝑚 ) 𝐴 1 1 𝑟 𝑃𝑏 ≈ ( 1.2 × 10 ≈ ( 1.2 × 10− 15 𝑚 ) (15.999) 3 − 15 𝑚 ) (207.2) 3 − 15 3. 02 × 10 𝑟 𝑚≈ 7.1 × 10 𝑚 − 15 𝑃𝑏 Lead (Pb) nuclei has a radius which is more than double that of Oxygen (O) Copyright ©2022 John Wiley & Sons, Inc. 14 31.2 The Strong Nuclear Force and the Stability of the Nucleus (1 of 2) Strong Nuclear force The mutual electromagnetic repulsion (Coulomb Force) of the protons tends to push the nucleus apart. What then, holds the nucleus together? Strong Nuclear Force: Very strong! Binds Protons and Neutrons in nucleus (Binds all particles made of quarks) – Very short range! Don’t notice in everyday life Copyright ©2022 John Wiley & Sons, Inc. 15  Strong Nuclear force Strong Nuclear force 137 times stronger than Electromagnetic repulsion ONLY at VERY Short distances Electromagnetic force works at large scales If nucleus too big, electromagnetic force dominates This makes nucleus unstable! Particle decays! Copyright ©2022 John Wiley & Sons, Inc. 16  Strong Nuclear force etic n ag o m tr l ec e E rc fo Strong Nuclear force etic a gn m ctro e El rce fo During nuclear decay, the nucleus will split into smaller pieces Since the nucleus is smaller, there will be a balance of forces and nucleus will be more stable. Copyright ©2022 John Wiley & Sons, Inc. 17 31.2 The Strong Nuclear Force and the Stability of the Nucleus (2 of 2) As for stability. The neutrons act like glue Add additional Strong Force , No extra repulsive electromagnetic force. Strong Nuclear force Copyright ©2022 John Wiley & Sons, Inc. 18  Example: Where’d all the mass go? Uranium-238 undergoes alpha decay to form Thorium-234 by emitting an alpha particle (which consists of 2 protons and 2 neutrons). The mass of Uranium-238 is 238.0508 atomic mass units (u), the mass of Thorium-234 is 234.0436 u, and the mass of the alpha particle is 4.0026 u. (a) Calculate the mass before and after of this nuclear reaction. 𝑚𝑖 =𝑚𝑈 =238.0508 𝑢 𝑚 𝑓 =𝑚 𝑇h + 𝑚𝐻𝑒 ¿ 234.0436 𝑢+4.0026 𝑢 ¿238.0462 𝑢 𝑚 𝑓 ≠ 𝑚𝑖 … Δ 𝑚=𝑚 𝑓 − 𝑚𝑖 ¿ −0.0046 𝑢 Where did the mass go? Is mass not conserved in nature?! Copyright ©2022 John Wiley & Sons, Inc. 19  2 𝐸=𝑚 𝑐 Copyright ©2022 John Wiley & Sons, Inc. 20  2 2 𝐸=𝑚 𝑐 Copyright ©2022 John Wiley & Sons, Inc. 21  Einstein and 1905, Einstein showed that mass (m) can be converted into pure energy (E)! Since m/s, a little bit of mass can turn into a LOT of energy This happens when big nuclei split by radioactive decay (Nuclear fission) Ex. Nuclear power + Atomic bombs! This happens when small nuclei fuse, like 2 hydrogens making helium (Nuclear fusion) Ex. THE POWER OF THE SUN! Copyright ©2022 John Wiley & Sons, Inc. 22 Sunshine and starlight is Hydrogen fuses into helium in the core of the sun (and all stars) Helium has LESS mass than hydrogen it is made of Missing mass = SUNLIGHT (and STARLIGHT!) Copyright ©2022 John Wiley & Sons, Inc. 23  Example: Where’d all the mass go? Uranium-238 undergoes alpha decay to form Thorium-234 by emitting an alpha particle (which consists of 2 protons and 2 neutrons). The mass of Uranium-238 is 238.0508 atomic mass units (u), the mass of Thorium-234 is 234.0436 u, and the mass of the alpha particle is 4.0026 u. (a) Calculate the mass before and after of this nuclear reaction. 𝑚𝑖 =𝑚𝑈 =238.0508 𝑢 𝑚 𝑓 =𝑚 𝑇h + 𝑚𝐻𝑒 ¿ 234.0436 𝑢+4.0026 𝑢 ¿238.0462 𝑢 𝑚 𝑓 ≠ 𝑚𝑖 … Δ 𝑚=𝑚 𝑓 − 𝑚𝑖 ¿ −0.0046 𝑢 Where did the mass go? Is mass not conserved in nature?! Copyright ©2022 John Wiley & Sons, Inc. 24  Example: Where’d all the mass go? Uranium-238 undergoes alpha decay to form Thorium-234 by emitting an alpha particle (which consists of 2 protons and 2 neutrons). The mass of Uranium-238 is 238.0508 atomic mass units (u), the mass of Thorium-234 is 234.0436 u, and the mass of the alpha particle is 4.0026 u. (a) Calculate the mass before and after of this nuclear reaction. What is the energy released in this alpha decay process, in MeV? Note: 1 u = 931.5 MeV ( when using mass in u ) 𝑚=0.0046 𝑢 Binding energy = Energy released 𝐸=𝐵𝑖𝑛𝑑𝑖𝑛𝑔 𝑒𝑛𝑒𝑟𝑔𝑦 ¿ E = ((ΔΔ 𝑚) 𝑐 ¿ (2 𝑚0.0046 ) )𝑢(931.5 MeV ≈4.29 𝑀𝑒𝑉 ) Copyright ©2022 John Wiley & Sons, Inc. 25 31.3 The Mass Deficit of the Nucleus and Nuclear Binding Energy (1 of 4) This energy released is called Binding energy We need to put energy in to break nuclear bonds! If the bonds are made, this energy is released Similar to sound energy released from potential energy when a ball hits the floor Binding energy Mass deficit c 2 m c 2 Copyright ©2022 John Wiley & Sons, Inc. 26  Example 3: The Binding Energy of the Helium Nucleus Revisited The atomic mass of helium is 4.0026u and the atomic mass of hydrogen is 1.0078 u and neutrons have mass 1.0087 u. Using atomic mass units, instead of kilograms, obtain the binding energy of the helium nucleus. Note: 1 u = 931.5 MeV ( when using mass in u ) 𝑖𝑛𝑑𝑖𝑛𝑔 ¿ 𝑒𝑛𝑒𝑟𝑔𝑦 =¿ ¿ ¿ ( 0.0304 𝑢 ) (931.5 MeV ) m𝑖 =𝑚 𝐻𝑒=4.0026 𝑢 ¿ 28. 32 MeV m 𝑓 =2 𝑚 𝐻 +2 𝑚𝑛= 2( 1.0078𝑢¿+2(1.008 7𝑢¿ u Δ 𝑚=𝑚 𝑓 − 𝑚𝑖 ¿ 4.03 3 u − 4.0026 ¿ 0.0304 𝑢 u Copyright ©2022 John Wiley & Sons, Inc. 27 31.3 The Mass Deficit of the Nucleus and Nuclear Binding Energy (4 of 4) heavy elements undergo fission Nuclear fission Nuclear fusion Light elements undergo fusion Copyright ©2022 John Wiley & Sons, Inc. 28 The elements from the periodic table (and in you) are created in stars… Supernovae explosions! Nuclear fusion All elements heavier than iron Fe are created when stars die… Supernovae explosions! All elements from He to iron Fe are created by nuclear fusion in stars! Copyright ©2022 John Wiley & Sons, Inc. 29 The elements from the periodic table (and in you) are created in stars… Copyright ©2022 John Wiley & Sons, Inc. 30  31.4 Radioactivity (1 of 6) The three types of particles emitted by radioactive nuclei have different piercing power NEED TO UNDERSTAND FOR EXAM Copyright ©2022 John Wiley & Sons, Inc. 31 31.4 Radioactivity (1 of 6) Positive charge Neutral (Zero charge) Negative charge A magnetic field separates the three types of particles emitted by radioactive nuclei. Copyright ©2022 John Wiley & Sons, Inc. 32 31.4 Radioactivity (2 of 6) α Decay When an unstable nucleus emits two protons and two neutrons A Z P A 4 Z 2 D  2 2 He Copyright ©2022 John Wiley & Sons, Inc. 33  31.4 Radioactivity (3 of 6) particles smoke detector Smoke detectors contain a small radioactive source This constantly emits particles particles hits electrons out of molecules in air This creates a constant current. When smoke blocks the path of particles, no current is created ALARM IS TRIGGERED! Copyright ©2022 John Wiley & Sons, Inc. 34 31.4 Radioactivity (4 of 6) β Decay When an unstable nucleus: 1. Emits an electron 2. Neutron becomes a proton A Z P A Z 1 D  0 1 e Copyright ©2022 John Wiley & Sons, Inc. 35 31.4 Radioactivity (5 of 6) γ Decay When an unstable nucleus emits a (high energy electromagnetic wave) Element, mass and atomic number stay constant Copyright ©2022 John Wiley & Sons, Inc. 36 31.4 Radioactivity (5 of 6) γ Decay Gamma rays are ionizing radiation, which can cause mutations in DNA (why Chernobyl is dangerous…) Copyright ©2022 John Wiley & Sons, Inc. 37 31.4 Radioactivity (6 of 6) Gamma knife Radioactive materials provides gamma rays targeted at tumors in the brain, brain surgery without a knife! Copyright ©2022 John Wiley & Sons, Inc. 38 Radioactive materials can be injected into patients to detect cancerous tumors Copyright ©2022 John Wiley & Sons, Inc. 39 31.9 Radiation Detectors (1 of 2) Radioactivity is measured with devices that convert the radiation into currents, creating a signal A Geiger counter A scintillation counter Copyright ©2022 John Wiley & Sons, Inc. 40 Example: Identifying decay products Copyright ©2022 John Wiley & Sons, Inc. 41 Example: Identifying decay products What products would be formed if could undergo: Use conservation of charge and atomic mass number! a) 22 2284−4 4 9 942 −2 𝑃𝑢+ 𝑈 2 𝐻𝑒 b) 228 0 95 𝐴𝑚 +¿ −1 𝑒 ¿ neutron becomes Charge:94 → 95 +¿ − 1 proton c) 228 94 𝑃𝑢 +𝛾 Copyright ©2022 John Wiley & Sons, Inc. 42 Example: Identifying decay products What products would be formed if could undergo: Use conservation of charge and atomic mass number! a) 1 83 4 187− 4 73 75− 2 𝑅𝑒+ 𝑇𝑎 2 𝐻𝑒 b) 187 0 76 𝑂𝑠 +¿ −1 𝑒 ¿ neutron becomes Charge:94 → 95 +¿ − 1 proton c) 187 75 𝑅𝑒 +𝛾 Copyright ©2022 John Wiley & Sons, Inc. 43 31.8 Radioactive Decay Series (1 of 2) The sequential decay of one nucleus after another is called a radioactive decay series. Copyright ©2022 John Wiley & Sons, Inc. 44 Example: Nuclear decay series A single atom of Thorium-238 undergoes six different decays Complete the chain below, writing the element formed with its atomic mass number and proton number clearly labeled, Use the periodic table to identify the elements. 2 28 2 28 2 24 2 20 2 20 88 𝑅𝑎 89 𝐴𝑐 87 𝐹𝑟 85 𝐴𝑡 86 𝑅𝑛 - - - - - - decay deca deca deca deca deca y y y y y Copyright ©2022 John Wiley & Sons, Inc. 45 Don’t need to add in decay questions for exam 31.5 The Neutrino During beta decay, energy is released. However, it is found that most beta particles do not have enough kinetic energy to account for all of the energy released. The additional energy is carried away a neutrino. N 234 90 Th 234 91 Pa  0 1 e  Neutrino: Italian for little neutral one Copyright ©2022 John Wiley & Sons, Inc. 46  LAST SECTION OF FSKS 123 31.6 Radioactive Decay and Activity (1 of 2) As particles decay, they decrease. We measure in ½ life. Half life : The time it takes for half of the radioactive nuclei to disintegrate Your energy levels at this point in the semester Copyright ©2022 John Wiley & Sons, Inc. 47  LAST SECTION OF FSKS 123 31.6 Radioactive Decay and Activity (1 of 2) As particles decay, they decrease. We measure in ½ life. Half life : The time it takes for half of the radioactive nuclei to disintegrate This process is governed by two equations 𝑙𝑛 2 𝑁 =𝑁 0 𝑒 − 𝜆𝑡 ; 𝜆= 𝑇 1/ 2 Number of Nuclei after time Number of Nuclei at the start ` decay constant (related to ½ life) time passed (AGE OF OBJECT!) Copyright ©2022 John Wiley & Sons, Inc. 48 31.6 Radioactive Decay and Activity (2 of 2) Half life can range from less than a second to billions of years. Different half lives are useful for dating different objects. Isotope Half-Life Polonium 214 84 Po P o left superscript 214 subscript 84 1.64 times 10 to the power negative 4 s 1.64 10  4 s Krypton K r left superscript 89 subscript 36 89 Kr 3.16 min 36 Radon Rn R n left superscript 222 subscript 86 222 86 3.83 d Strontium Sr S r left superscript 90 subscript 38 90 38 29.1 yr Radium 226 Ra R a left superscript 226 subscript 88 1.6 times 10 to the power 3 yr 1.6 10 3 yr 88 Carbon C left superscript 14 subscript 6 Age of dead trees, 5.73 10 3 yr 5.73 times 10 to the power 3 yr 14 C 6 animals, etc. Uranium 238 U U left superscript 238 subscript 92 4.47 times 10 to the power 9 yr 4.47 10 9 yr 92 Age of meteors, Indium 115 In I n left superscript 115 subscript 49 4.41 times 10 to the power 14 yr 4.411014 yr earth itself! 49 Table 31.2 Some Half-Lives Copyright for ©2022 John Wiley & Sons,Radioactive Inc. Decay 49 Conceptual Example 12 Dating a Bottle of Wine A bottle of red wine is thought to have been sealed about 5 years ago. The wine contains a number of different atoms, including carbon, oxygen, and hydrogen. The radioactive isotope of carbon is the familiar C-14 with half- life of 5730 yr. The radioactive isotope of oxygen is O-15 with a half life of 122.2 s. The radioactive isotope of hydrogen is called tritium and has a half life of 12.33 yr. The activity of each of these isotopes is known at the time the bottle was sealed. However, only one of the isotopes is useful for determining the age of the wine. Which is it? Tritium, as the half life is closer to the expected opening date of wine O-14 will experienced to many half-lives and will barely be detectable C-14 will barely have decayed in 5 years, difference not detectable. Copyright ©2022 John Wiley & Sons, Inc. 50  Make sure you can do this for exam! 31.7 Radioactive Dating (3 of 3) Living organisms absorb carbon-14 into their tissue. Once they die, the absorption stops, C-14 undergoes decay into N-14. The C-14 has a half life of 5730 years This is used to date fossils and other living objects. Copyright ©2022 John Wiley & Sons, Inc. 51 Example: Carbon-14 dating Scientists know that C-14 decays in N-14 when organisms die. C-14 has a half- life of 5730 years and is used to determine the age of fossils. (a) Determine the decay constant for carbon-14 (b) Determine the age of a Human skull containing 76.6% of its original amount of C-14 () 0.693 0.693 (a) 𝜆=? 𝜆= ¿ 𝑇 1/2 5730 𝑦𝑒𝑎𝑟𝑠 KEEP IN UNITS OF HALF-LIFE −4 −1 Age will then be give in years ¿ 1.21×10 𝑌𝑒𝑎𝑟 𝑠 (b)𝑁 =𝑁 0 𝑒 − 𝜆 𝑡 𝑁 =0.76.6 𝑁 0 − 𝜆𝑡 𝑁 𝑡 =? 𝑒 = 𝑁0 𝑁 − 𝜆 𝑡 =𝑙𝑛 𝑁0 ` Copyright ©2022 John Wiley & Sons, Inc. 52 31.7 Radioactive Dating (3 of 3) When certain igneous rocks are created they contain only Uranium-238 (U-238) These rocks decays into lead-206 (Pb-206) with a half life of 4.47 billion years () This is used to date meteors and the Earth itself! Copyright ©2022 John Wiley & Sons, Inc. 53 Example: U-238 dating Scientists know that U-238 decays in Pb-206 when rocks form. U-238 has a half- life of 4.47 billion years (a) Determine the decay constant for uranium-238 (b) Determine the age of the moon, using a moon rock containing 55.5% of its original amount of U-238 () 9 (a) 𝑇 1/ 2=4.47×10 𝑦𝑟𝑠 0.693¿ 0.693 𝜆= 9 ¿ 1.55 ×10 −10 𝑦𝑟 𝑠 −1 𝑇 1/2 4.47× 10 𝑦𝑟𝑠 (b)𝑁 =𝑁 0 𝑒 − 𝜆𝑡 𝑁 =0.555 𝑁 0 𝑡 =? The moon is 3.8 billion years old ` 9 ❑ ≈3.80× 10 𝑦𝑟𝑠 Copyright ©2022 John Wiley & Sons, Inc. 54 31.7 Radioactive Dating (3 of 3) See if you can calculate age of all objects in game below. (Takes long to load, but this will help for exam…) Copyright ©2022 John Wiley & Sons, Inc. 55 THE END Copyright ©2022 John Wiley & Sons, Inc. 56 Copyright Copyright © 2022 John Wiley & Sons, Inc. All rights reserved. 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