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Atoms and Nuclei

Atoms and Nuclei. Professor Jasmina Vujic Lecture 1 Nuclear Engineering 162 Department of Nuclear Engineering University of California, Berkeley. ATOMS AND NUCLEI. ATOMS – “Greek: indivisible” – the smallest parts of matter that retain their physical and chemical properties.

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Atoms and Nuclei

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  1. Atoms and Nuclei Professor Jasmina Vujic Lecture 1 Nuclear Engineering 162 Department of Nuclear Engineering University of California, Berkeley

  2. ATOMS AND NUCLEI ATOMS – “Greek: indivisible” – the smallest parts of matter that retain their physical and chemical properties

  3. INSIDE THE ATOM The center consists of a heavy NUCLEUS with a POSITIVE electric charge, which is surrounded by a swarm of much lighter particles, the NEGATIVELY charged ELECTRONS. A crudeapproximation of the hydrogen atom is a MARBLE (the nucleus) in the center of a FOOTBALL STATIUM and PINHEAD (the electron) orbiting over the benches.

  4. The NUCLEUS consists of NUCLEONS with are of two types: • PROTONS, with a positive charge • NEUTRONS, which have no electric charge In a free atom, the number of electrons EQUALS the number of protons, and the atom is electrically NEUTRAL.

  5. ELEMENTS • There are more than 120 chemical ELEMENTS (92 elements present in nature). ATOMIC NUMBER, Z. All atoms of a given element have the same number of protons (electrons), which is called the atomic number. MASS NUMBER, A. The total number of nucleons (protons and neutrons) inside the nucleus is called the atomic mass number.

  6. ISOTOPES • The nuclei with the same number of protons and different number of neutrons are called ISOTOPES. They pertain to the same element, they have the same chemical properties, but different physical properties (different mass numbers)

  7. ATOMIC MASS, M. The mass in grams of 6.02x1023 atoms. • M= 1.008 g for hydrogen, • M= 4.003 g for helium, • M= 16.00 g for oxygen, • M= 238.0 g for uranium • AVOGADRO’S Number, • Nav = 6.022142x1023 atoms/mole

  8. The Atomic Mass Unit Is defined to be 1/12 the mass of a neutral ground-state atom of 12C Avogadro’s number (Nav) = 6.022142x1023 molecules/mole 1 gram mole (12C) = 12.0000 g/mole The mass of one (12C) atom (12.0000 g/mole)/ Nav = 1.9926x10-23 g 1 amu = 1.9926x10-23 g/12 1 amu = 1.660538x10-24 g The energy equivalent of 1 amu : E(1 amu) = 931.494 MeV

  9. The Atomic Mass Unit NUMBER DENSITY, N. Number of atom per cubic centimeter. EXAMPLE: Uranium with mass density of 19 g/cm3, has the number density of

  10. Energy and Matter • The equivalence of MATTER and ENERGY • Einstein’s Formula • E = mc2 • The speed of light, • c =3×108 m/s • Matter can be converted into ENERGY, and ENERGY can be converted into MATTER • Conversion of 1 kg of matter into energy releases: E =mc2 =(1 kg)(3×108 m/s)2= 9×1016 J

  11. Conversion of Energy and Matter • Proton rest mass 1.672 621 6×10-27 kg or 938.272 MeV 1.007 276 amu • Neutron rest mass 1.674 927 2×10-27 kg or 939.565 MeV 1.008 664 amu • Electron rest mass 9.109 381 9 ×10-31 kg or 0.511 MeV

  12. Conversion of Energy and Matter • In “burning” of 1 kg of uranium, 0.87 g of matter is converted into energy: EU=(0.87)×(9×1016 J)=7.8×1013 J • Combustion of 1 kg of gasoline releases: Eg=5×107 J • The energy yield from one kilogram of uranium is more than a MILLION times that from fossil fuel.

  13. Models of Atom • Thomson’s “plum pudding” model • Rutherford’s model - the first planetary model • Bohr’s model • Pauli’s exclusion principle (1925)

  14. Thomson: The Plum Pudding Model + - - - + + -

  15. The Rutherford Atomic Model - 1911 • 1900: Alpha, beta and gamma rays were discovered • 1909 Rutherford bombarded thin gold foils with alpha particles (Po(214-84)): • Large angle deflection seen in 1/8000 alpha particles suggests the existence of a very small and massive nucleus • Proposed the planetary model • We now know: • Rnuc ~ 1.3 A1/3 x 10-15 m • Ratom ~ 1.5 x 10-10 m

  16. Bohr’s hydrogen atom - 1913 • Bohr was not satisfied with the Rutherford’s model - • classical mechanics did not work for the planetary model - it violated classical laws of electromagnetism • Unstable model, since an accelerated charge will emit light and therefore lose E - • Bohr postulates the first semi-classical model • Angular momentum of electron is quantized: • mvr = nħ • Then energy and orbital radii are also quantized (derive radius on the board) • rn = 0.529 n2/Z (Å) • En = -13.6 Z2/n2 (eV)

  17. Bohr’s Atomic Model The orbital electrons can revolve around the nucleus only in certain fixed radii, called stationary states such that the angular momentum of electrons must be integral multiplies of h/2π: mvr = n(h/2π) where n is the principal quantum number h is Plank’s constant A photon is emitted only when an electron falls from one orbit to another orbit of lower energy. The energy of photon is equal to the difference between the energy levels on the electron in the two orbits:

  18. Bohr’s Atomic Model The normal condition of the atom, or ground state, is the state with n=1. The atom is in it’s lowest possible energy state and it’s most stable condition.

  19. Energy Levels of the Hydrogen Atom Ionization Continuum 0 eV N=4 N=3 N=2 Balmer Series visible -13.6 eV N=1 Lyman Series (ultraviolet)

  20. Bohr’s Atomic Model Excitation of the Atom When a sufficient amount of energy is transferred to the atom, causing an electron to “jump” from the lower to higher energy levels, the atom is said to be “excited”. Ionization of the Atom When a sufficient amount of energy is transferred to the atom, causing an electron to be removed from the electric field of the nucleus, the is said to be ionized, and the negative electron together with the remaining positively charged atom, is called the ion pair. Excitation and ionization are the main mechanisms through which energy is transferred from radiation to matter

  21. Problem with Bohr’s model and classical mechanics • Could only predict correctly the energy levels of H. • The dual behavior of light (particle and wave) could not be explained by classical mechanics • The approach of Bohr of mixing classical mechanic with quantizing certain variables was suddenly heavily used • other accurate predictions were made with new semi-classical or relativistic models • Prelude to Quantum Mechanics

  22. Periodic Table of Elements and the Pauli Exclusion Principle To describe an atom completely, it is necessary to specify four quantum numbers, for each of the orbital electrons: n Principal quantum number 1,2,3... l Azimuthal quantum number 0 to (n-1) m Magnetic quantum number -1 to 0 to +1 s Spin quantum number ±1/2 The Pauli Exclusion Principle: no two electron in any atom may have the same set of four quantum numbers N = 2n2

  23. Pauli principle: No two electrons in an atom can be in the same state • Quantization came naturally out of quantum mechanics • Four quantum numbers fully described the electron energy levels • Principal quantum number : n • Describes the orbital shells • n=1, 2 and 3 for K, L and M shells respectively • Corresponds to Bohr’s angular momentum quantization • Azimuthal quantum number: l • Explains fine structure in spectrum (elliptic orbit) • l = 0, 1, 2, …, n • Magnetic quantum number: m • Explains splitting of spectral lines in magnetic field - Zeeman Effect • m = [-l, l] • Intrinsic spin (angular momentum) of electron: s • s = [-1/2, ½]

  24. Binding Energy • The nucleons (protons and neutrons) are bound together by a net force which NUCLEAR ATTRACTION forces exceed the ELECTROSTATIC (COULOMB) REPULSION forces. Associated with the net force is a POTENTIAL ENERGY of BINDING. • In order to separate the nucleus into its component nucleons, energy must be supplied from the outside. • Binding Energy(B)=total mass of separate particles - mass of the atom

  25. Binding Energy This is average binding energy per nucleon

  26. Binding Energy • Why energy is released in FISSION and FUSION processes?

  27. Binding energy Let’s revisit the fusion of four protons to form a 4He nucleus: *these masses come from the table of nuclides We have calculated the mass deficit --> i.e. the whole is less than sum of the parts The mass deficit is represented by a HUGE energy release, which can be calculated using Einstein’s famous equation, E=mc2, and is usually expressed in Mev 56Fe

  28. Contributions to Binding Energy EB = strong nuclear force binding -surface tension binding + spin pairing +shell binding-Coulomb repulsion 1) strong nuclear force -- the more nucleons the better 2) surface tension -- the less surface/volume the better (U better than He) 3) spin pairing -- neutrons and protons have + and - spins, paired spins better 4) shell binding -- nucleus has quantized shells which prefer to be filled (magic numbers) 5) Coulomb repulsion -- packing more protons into nucleus comes at a cost (although neutron addition will stabilize high Z nuclei)

  29. Binding Energy • Liquid Drop Model (Explains fission) • The nucleus is thought to be a homogenous mixture of nucleons in which all the nucleons interact strongly with each other. • Shell Model (Explains radioactive decay) • The various nucleons exist in certain energy levels within the nucleus, and interact weakly among themselves. • So-called magic numbers have been found:,2,8, 20, 50, 82, 126- isotopes containing these number of protons or neutrons have unusual stability in their structure. • Nucleons can be excited to higher energy levels. Gamma rays emitted.

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