Q. What is the de Broglie wavelength of an electron that has a kinetic energy of 100 eV?

1. Q. What is the de Broglie wavelength of an electron that has a kinetic energy of 100 eV? After an electron is accelerated in 100 V potential difference, its kinetic energy is 100 eV. eV unit has to be converted into SI unit, Joule. 1 eV = 1.6 x 10-19 J Ek = (1/2)mov2 = 1.6 x 10-17 J v2 = 2Ek/mo = 2(1.6 x 10-17 J)/(9.1 x 10-31 kg) = 3.52 x 1013 m2/s2 v = 5.93 x 106 m/s low speed: no need to use relativistic l = h/p = h/mov = (6.6 x 10-34 Js)/(9.1 x 10-31 kg x 5.93 x 106 m/s) = 1.23 x 10-10 m = 0.123 nm

2. atomic number: Z The Atomic Nucleus Composed of nucleons: proton (+e) and neutrons (neutral) mp = 1.673 x 10-27 kg = 938.28 MeV mn = 1.675 x 10-27 kg = 939.4 MeV me = 9.1 x 10-31 kg = 0.511 MeV Positively charged (# of protons = # of electrons) Heavy object: most of the atomic mass is concentrated in the nucleus Size ≈ 10-14 m = 10 femtometer (10-15 = femto) Considering the size of an atom ≈ 10-10 m, an atom is mostly empty. The force binding nucleons together should overcome Coulomb repulsion! Nuclear force is very strong and attractive. Each element has different # of protons  periodic table is arranged by the # of protons. E = mc2

3. 8 neutrons Z 146 neutrons = # of electrons: chemical property Missing information about the # of neutrons?

4. Dmitri Ivanovich Mendeleev (1834-1907) “I began to look about and write down the elements with their atomic weights and typical properties, analogous elements and like atomic weights on separate cards, and this soon convinced me that the properties of elements are in periodic dependence upon their atomic weights.” --Principles of Chemistry, 1905, Vol. II

5. atomic mass number (A): total # of protons and neutrons A = Z + N (integer) A X element Z

6. Approximate radius, R, for the nucleus R = (1.2 x 10-15)A1/3 m The actual mass of atom or nucleus is expressed in atomic mass units (U). 1 u = 1.6607 x 10-27 kg = 931 MeV Exactly equal to one-twelfth of the mass of the most abundant form of the carbon atom mp = 1.673 x 10-27 kg = 1.007276 u mn = 1.675 x 10-27 kg = 1.008665 u me = 9.1 x 10-31 kg = 0.00055 u

8. include everything (p, n, and e) The average atomic mass of mercury (Hg) is 200.59 u. What is the average nuclear mass for Hg atom? Z = 80 for Hg  there are 80 electrons. Mass of electrons in Hg atom = 80 x 0.00055 u = 0.044 u Nuclear mass = atomic mass – electron mass = 200.59 u – 0.044 u = 200.55 u

9. 6 A 7 60 58 Co Li Li X Co 27 27 3 3 Z Isotopes Atoms that have the same atomic number (Z) but different mass numbers (A). Natural abundance: 92% 8%

10. 4 He 2 Helium Nucleus atomic mass = 4.002602 u 2 electrons: electron mass = 2 x 0.00055 u = 0.0011 u nucleus mass = 4.002602 u – 0.0011 u = 4.001502 u We know He nucleus is composed of 2 protons and 2 neutrons: 2 proton mass = 2 x 1.007276 u 2 neutron mass = 2 x 1.008665 u total mass = 4.031882 u > He nucleus mass Dm = 4.031882 u – 4.001502 u = 0.030376 u

11. All nuclei have a mass that is smaller than the sum of the masses of its separated nucleons. This difference in mass is called the mass defect. DE = Dmc2 E = mc2 binding energy of the nucleons in the nucleus Dm for He = 0.030376 u = 0.030376 x (1.66 x 10-27 kg) = 5.0 x 10-29 kg 1 u = 1.6607 x 10-27 kg = 931 MeV = 0.030376 x 931 MeV = 28.2 MeV DE = Dmc2 = (5.0 x 10-29 kg)(3 x 108 m/s)2 = 4.5 x 10-12 J = 28 MeV binding energy per nucleon in He = 7 MeV

13. 28 MeV p n He nucleus Ex. 31.4How much energy is released as 1 kg of neutrons and 1 kg of protons are changed into 2 kg of helium 4 nuclei? # of He nuclei in 2 kg = 2 kg/(4 x 1.66 x 10-27 kg) = 3.0 x 1026 28 MeV is released per nucleus: total energy released = 28 x 3.0 x 1026 MeV = 8.4 x 1027 MeV = 1.5 x 1015 J New York city needs 1010 W of electricity. This amount can run NY city for 2 days!!

14. all naturally occurring elements with Z > 83 Radioactivity Sometimes particles or photons are emitted from the nuclei of atoms: unstable nuclei radioactive unstable nuclei  stable nuclei

15. A A-4 A A A A X X X X X X Z Z Z-2 Z Z+1 Z Three major forms of radioactive emission: Alpha particle (a): nucleus of a He atom Beta particles (b): beta minus particle (electron) beta plus particle (positron) Gamma rays (g): high energy photons, short wavelength x-ray + + + AandZare conserved in nuclear reaction!!

16. T1/2: half-life

17. Initial # of unstable nuclei at time t = 0 N(t) = Noe-pt decay constant # of unstable nuclei at time t At T1/2, N(T1/2) = (0.5)No If you know T1/2, you can get p from this equation. Then, at any time you can calculate # of unstable nuclei. Or, with the knowledge of # of unstable nuclei, we can calculate how much time has passed.  Carbon dating

19. should be dead! ? half-life: 5730 yrs A mummy found in Egypt bbc.co.uk Carbon Dating By measuring the ratio of 14C isotope to 12C in a biological sample one can calculate the age of the object from which the sample came with the knowledge of the initial ratio when the biological activity ceased.

20. 147N + 10n  146C + ? 11p Ratio of 14C to 12C? Before 1900 (atomic bomb testing) 1.5 x 10-12 0-1b 146C  147N + ? beta decay

21. A mummy found in Egypt bbc.co.uk Measured the ratio of 14C to 12C r(t) = 1.05 x 10-12 ro = 1.5 x 10-12 T1/2 = 5730 yrs Let’s calculate decay const, p p = 0.693/T1/2 = 0.693/5730 = 1.21 x 10-4 (yr-1) Total # of 12C = N12 # of 14C = N14 = r(t)N12 r(t)N12 = roN12e-pt r(T)/ro = (1.05/1.5) = e-pT ln(0.7) = -pT T = -ln(0.7)/(1.21 x 10-4) = 2848 yr

22. Ex. 31.10 Cobalt-60 has a half-life of 5.25 yrs (1.66 x 108 s). Given 1 mg of the substance, find (a) the number of atoms in the sample, (b) the decay constant, (c) the time taken for 0.01 mg to decay. mass of Co-60 = 59.93381 u = 60 u = 60 x 1.66 x 10-27 kg = 1.0 x 10-25 kg No = (1 x 10-6 kg)/(1 x 10-25 kg) = 1 x 1019 atoms p = 0.693/T1/2 = 0.693/(1.66 x 108 s) = 4.2 x 10-9 s-1 How long does it take to reach N/No = 0.99? ln(N/No) = -pt ln(0.99) = -(4.2 x 10-9)t t = 2.4 x 106 s about a month 1 yr = p x 107 s

23. 45 Which of the following nuclear reaction is(are) impossible?(a) 23191Pa  a + 22789Ac(b) 146C  147N + +1b(c) 24092U  -1b + 24093Np • (a) • (b) • (c) • All • None

24. 138 235 236 U U Ba 56 92 92 unstable Nuclear Fission In a chemical reaction, changes in atoms are in their electron configuration. However, in a nuclear reaction, the configuration of nucleus changes by emitting or absorbing typically high energy photons, nucleons, alpha particles, and/or light charged particles. In this process, charge, nucleons, and mass-energy are conserved. Nuclear fission: Unstable heavy nucleus  multiple intermediate mass nuclei + large energy In 1938, Otto Hahn, Lise Meitner, and Fritz Strassmann discovered: stable isotope T1/2 ≈ 109 yrs n n 95 Kr n 36 200 MeV per fission n

25. 235U 236U 141Ba 92Kr n Chain Reaction

26. "When you sit with a nice girl for two hours, it seems like two minutes. When you sit on a hot stove for two minutes, it seems like two hours that's relativity." "Gravitation is not responsible for people falling in love." Through the release of atomic energy, our generation has brought into the world the most revolutionary force since prehistoric man's discovery of fire. This basic force of the universe cannot be fitted into the outmoded concept of narrow nationalisms. For there is no secret and there is no defense; there is no possibility of control except through the aroused understanding and insistence of the peoples of the world. We scientists recognise our inescapable responsibility to carry to our fellow citizens an understanding of atomic energy and its implication for society. In this lies our only security and our only hope - we believe that an informed citizenry will act for life and not for death. A. Einstein, 1947