LECTURE 23 NUCLEI. Instructor: Kazumi Tolich

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1 LECTURE 23 NUCLEI Instructor: Kazumi Tolich

2 Lecture 23 2 Reading chapter 32.1 to 32.2 Nucleus Radioactivity

3 Mass and energy 3 The famous equation by Einstein tells us that mass is a form of energy. E = mc % In nuclear bomb, nuclear power plants, or the sun, nuclear reactions cause mass to disappear releasing a huge amount of energy. Only disappearance of ~1.6 g of mass is responsible for %, MeV of energy released by the nuclear bomb that destroyed Hiroshima.

Nucleus 4 The atomic number, Z, is the number of protons, the neutron number, N, is the number of neutrons, and the mass number, A, is the number of nucleons of the nucleus.

4 Nucleus 4 The atomic number, Z, is the number of protons, the neutron number, N, is the number of neutrons, and the mass number, A, is the number of nucleons of the nucleus. A = Z + N The notation for a particular nucleus of element X is written as 3 2X Two or more nuclei that have the same number of protons but have different number of neutrons are called isotopes. The atomic mass unit is defined to be u = %7 kg = MeV c %, is defined so that the mass of A% is exactly 12u. C,

5 Quiz: 1 5 There are 82 protons in a lead nucleus. Why doesn t the lead nucleus burst apart due to their mutual repulsion? A. Coulomb repulsive force doesn t act inside the nucleus. B. Gravity overpowers the Coulomb repulsive force inside the nucleus. C. The negatively charged neutrons balance the positively charged protons. D. The negatively charged electrons balance the positively charged protons. E. Protons lose their positive charge inside the nucleus. F. None of the above

6 Quiz: 23-1 answer 6 None of the above Strong nuclear force binds them together. Its range is observed to be about m or fermi. It is attractive and acts with nearly equal strength between protons and protons, protons and neutrons, and neutrons and neutrons. Most nuclei are spherical with radii approximated by r = AD m A A F By contrast, the radius of an atom is on the order of m. This means that the density of the nucleus is extremely high.

7 Quiz: 2 7 Which of the following is/are correct regarding the stability of nuclei? Choose all that apply. A. For light nuclei, the greatest stability is achieved when N Z. B. For light nuclei, the greatest stability is achieved when N > Z. C. For light nuclei, the greatest stability is achieved when N < Z. D. For heavy nuclei, the greatest stability is achieved when N Z. E. For heavy nuclei, the greatest stability is achieved when N > Z. F. For heavy nuclei, the greatest stability is achieved when N < Z.

8 Quiz: 23-2 answer 8 For light nuclei, the greatest stability is achieved when N Z. For heavy nuclei, the greatest stability is achieved when N > Z. %FL For heavier nuclei such as K% U, instability caused by the electrostatic repulsion between the protons is minimized when there are more neutrons than protons. Every isotope with A 84 is radioactive. There are many radioactive isotopes of lighter AP elements as well such as and H C, A F.

9 Three types of radiation 9 A unstable nucleus can decay into a stable nucleus. Any of three different types of particles may be emitted: 1. Alpha particles, which consist of two neutrons and two P protons, and are nuclei of % He. α rays can barely penetrate a sheet of paper. 2. Electrons (or positrons), also called beta rays. Positrons is an antiparticle of electron and have the same mass as electrons but are positively charged. β rays (both β 6 and β T ) can penetrate a few millimeters of aluminum. 3. Gamma rays are high-energy photons. γ rays can penetrate several centimeters of lead. 3 2

10 Quiz: 3 10 A uranium nucleus decay product(s)? A. %FL K% U B. %FP KVU C. %FP KVTh D. P % He E. %P% KPPu F. %F, LLTh P + % He P + He % P + He % P % P + He + He % %FL K% U undergoes an alpha decay. What is/are its

11 Quiz: 23-3 answer 11 %FP KVTh P + % He When a nucleus decays by emitting an alpha particle, it loses two protons and two neutrons: 3 2X 36P P 26% Y + % He. Here, X is the parent nucleus and Y is the daughter nucleus. %FL %FP P Th + % He U K% KV

12 Quiz: 4 12 %FL K% U A uranium nucleus (initially at rest) decays into a thorium nucleus %FP KVTh and an alpha particle. Which one has the greater momentum? A. %FP KVTh nucleus B. alpha particle C. The magnitudes of the momenta for both particles are the same.

13 Quiz: 23-4 answer 13 The magnitudes of the momenta for both particles are the same. By momentum conservation, they must have the same magnitude of momentum since the initial momentum was zero. This follows that the decay products are emitted in the opposite directions.

14 Quiz: 5 14 What is the daughter nucleus when a potassium nucleus undergoes a β 6 -decay? A. PV %VCa B. PV %VK C. F, A7Cl D. FP %ASc E. PV ALAr F. PV ALK PV AKK

15 Quiz: 23-5 answer 15 PV %VCa In a β 6 -decay, a neutron is converted into a proton, A an electron and an antineutrino: V n A A p + e 6 + ν i The charge is conserved. A nucleus that undergoes a β 6 -decay loses a neutron 3 and gains a proton: 2 X 2TA 3 Y + e 6 + ν i PV PV AKK %VCa + e 6 + ν i If a nucleus undergoes a β T -decay, a proton has become a neutron emitting a positron and a neutrino, : 3 2X 26A 3 Y + e T + ν i

16 Quiz: 6 16 Suppose that the radii of two nuclei X and Y are about the same. X undergoes an alpha decay, and Y undergoes a beta decay. How do the radii of the daughters of X and Y compare? A. The radius of X s daughter is smaller than that of Y s daughter. B. The radius of X s daughter is larger than that of Y s daughter. C. The radius of X s daughter is about the same as that of Y s daughter.

17 Quiz: 23-6 answer 17 The radius of X s daughter is smaller than that of Y s daughter. The radius of a nucleus is approximated by r = AD m A A F. The radius of X s daughter is smaller than that of X because the atomic number A went down by 4: 3 2 X 36P P 26% Y + % He But the radius of Y s daughter is same as that of Y because the atomic number A remains the same: 3 2 X 2TA 3 Y + e 6 + ν i

18 Beta decay and discovery of neutrinos 18 During a β 6 -decay, a parent nucleus 3 2 X decays into a daughter nucleus Y by emitting an electron. If this were a two body decay ( 2TA 3 Y and e 6 ), the kinetic energy of e 6 can only be one value (from conservations of energy and momentum). But experiments showed that the kinetic energy of e 6 is a continuous spectrum. This lead to a discovery of another particle emitted in the decay, called neutrinos. 2TA 3

19 Quiz: 7 19 An excited nucleus undergoes a gamma decay. How do the atomic number and neutron number change? A. The atomic number increases by 1, and the neutron number remains the same. B. The atomic number remains the same, and the neutron increases by 1. C. The atomic number decreases by 1, and the neutron number remains the same. D. The atomic number remains the same, and the neutron decreases by 1. E. The atomic and neutrons numbers both remain the same.

20 Quiz: The atomic and neutrons numbers both remain the same. Alpha and beta decays are often followed by a gamma decay. A gamma ray is a photon emitted by a nucleus as it returns to its ground state.

21 Demo: 1 21 Cloud Chamber Tracks of alpha particles. Geiger counter Comparison between β decays and γ decays. n γ rays are more penetrating. Salt substitute is radioactive! (and so are many others, like a banana)

22 Radioactive decay series 22 Heavy nuclei decaying via alpha emission may very well decay to a daughter nucleus which is also unstable. The decays will continue until a stable nucleus is reached. An original parent nucleus producing a series of decays is called a radioactive decay series.

23 Activity 23 Some nuclei decay more rapidly than others. The time rate of decay is called the activity. The units of activity are either curie (Ci) or becquerel (Bq). 1 Ci = AV decays s 1 Bq = 1 decay s

LECTURE 26 RADIATION AND RADIOACTIVITY. Instructor: Kazumi Tolich

LECTURE 26 RADIATION AND RADIOACTIVITY Instructor: Kazumi Tolich Lecture 26 2 30.4 Radiation and radioactivity Alpha decay Beta decay Gamma decay Decay series Nuclear radiation is a form of ionizing radiation