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 J E k = (1/2)m o v 2 = 1.6 x J v 2 = 2E k /m o = 2(1.6 x J)/(9.1 x kg) = 3.52 x m 2 /s 2 v = 5.93 x 10 6 m/s low speed: no need to use relativistic = h/p = h/m o v = (6.6 x Js)/(9.1 x kg x 5.93 x 10 6 m/s) = 1.23 x m = nm

The Atomic Nucleus Composed of nucleons: proton (+e) and neutrons (neutral) m p = x kg = MeV m n = x kg = MeV m e = 9.1 x kg = MeV Positively charged (# of protons = # of electrons) Heavy object: most of the atomic mass is concentrated in the nucleus Size ≈ m = 10 femtometer ( = femto) Considering the size of an atom ≈ 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 = mc 2 atomic number: Z

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

“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 Dmitri Ivanovich Mendeleev ( )

atomic mass number (A): total # of protons and neutrons A = Z + N (integer) X A Z element ElementSymbolZN Mass # Hydrogen101 Helium224 Lithium347 Uranium

Approximate radius, R, for the nucleus R = (1.2 x )A 1/3 m The actual mass of atom or nucleus is expressed in atomic mass units (U). 1 u = x kg = 931 MeV Exactly equal to one-twelfth of the mass of the most abundant form of the carbon atom m p = x kg = u m n = x kg = u m e = 9.1 x kg = u

The average atomic mass of mercury (Hg) is 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 u = u Nuclear mass = atomic mass – electron mass = u – u = u include everything (p, n, and e)

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

Helium Nucleus He 4 2 atomic mass = u 2 electrons: electron mass = 2 x u = u nucleus mass = u – u = u We know He nucleus is composed of 2 protons and 2 neutrons: 2 proton mass = 2 x u 2 neutron mass = 2 x u total mass = u > He nucleus mass  m = u – u = u

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. E = mc 2  E =  mc 2 binding energy of the nucleons in the nucleus  m for He = u = x (1.66 x kg) = 5.0 x kg  E =  mc 2 = (5.0 x kg)(3 x 10 8 m/s) 2 = 4.5 x J = 28 MeV 1 u = x kg = 931 MeV = x 931 MeV = 28.2 MeV binding energy per nucleon in He = 7 MeV

np He nucleus 28 MeV Ex How 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 kg) = 3.0 x MeV is released per nucleus: total energy released = 28 x 3.0 x MeV = 8.4 x MeV = 1.5 x J New York city needs W of electricity. This amount can run NY city for 2 days!!

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

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

T 1/2 : half-life

N(t) = N o e -pt # of unstable nuclei at time t Initial # of unstable nuclei at time t = 0 At T 1/2, N(T 1/2 ) = (0.5)N o If you know T 1/2, 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 decay constant

Carbon Dating By measuring the ratio of 14 C isotope to 12 C 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. should be dead! half-life: 5730 yrs ? bbc.co.uk A mummy found in Egypt

14 7 N n  14 6 C + ? 11p11p Ratio of 14 C to 12 C? Before 1900 (atomic bomb testing) 1.5 x C  14 7 N + ? 0 -1  beta decay

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

Ex Cobalt-60 has a half-life of 5.25 yrs (1.66 x 10 8 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 = u = 60 u = 60 x 1.66 x kg = 1.0 x kg N o = (1 x kg)/(1 x kg) = 1 x atoms p = 0.693/T 1/2 = 0.693/(1.66 x 10 8 s) = 4.2 x s -1 How long does it take to reach N/No = 0.99? ln(N/No) = -pt ln(0.99) = -(4.2 x )t t = 2.4 x 10 6 s about a month 1 yr =  x 10 7 s

Which of the following nuclear reaction is(are) impossible? (a) Pa   Ac (b) 14 6 C  14 7 N + +1  (c) U  -1  Np (a) 2. (b) 3. (c) 4. All 5. None

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 U n stable isotope T 1/2 ≈ 10 9 yrs U unstable Kr Ba n n n 200 MeV per fission In 1938, Otto Hahn, Lise Meitner, and Fritz Strassmann discovered:

235 U 236 U 92 Kr 141 Ba n Chain Reaction

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 "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."