From last time… Hydrogen atom Multi-electron atoms This week’s honors lecture: Prof. Brad Christian, “Positron Emission Tomography” Course evaluations next week Tues. Prof Montaruli Thurs. Prof. Rzchowski Thur. Dec 6, 2007 Phy208 Lecture 27

Atomic Quantum number summary Hydrogen atom states n: principle quantum number Determines energy (n=1, 2, 3…) ℓ: orbital quantum number Magnitude of orbital angular momentum ℓ=0, 1, 2, … n-1 mℓ: orbital magnetic quantum number Orientation of mℓ = - ℓ, - ℓ + 1, … 0, … ℓ - 1, + ℓ ms: spin quantum number ms=-1/2, +1/2 Thur. Dec 6, 2007 Phy208 Lecture 27

Elements in same column have similar chemical properties Play Lehrer song Thur. Dec 6, 2007 Phy208 Lecture 27

Na Optical spectrum 11 electrons Ne core = 1s2 2s2 2p6 (closed shell) 1 electron outside closed shell Na = [Ne]3s1 Outside (11th) electron easily excited to other states. Na 589 nm, 3p -> 3s Thur. Dec 6, 2007 Phy208 Lecture 27

How do atomic transitions occur? How does electron in excited state decide to make a transition? One possibility: spontaneous emission Electron ‘spontaneously’ drops from excited state Photon is emitted ‘lifetime’ characterizes average time for emitting photon. Thur. Dec 6, 2007 Phy208 Lecture 27

Another possibility: Stimulated emission Atom in excited state. Photon of energy hf=E ‘stimulates’ electron to drop. Additional photon is emitted, Same frequency, in-phase with stimulating photon One photon in, two photons out: light has been amplified E hf=E Before After If excited state is ‘metastable’ (long lifetime for spontaneous emission) stimulated emission dominates Thur. Dec 6, 2007 Phy208 Lecture 27

: Light Amplification by Stimulated Emission of Radiation LASER : Light Amplification by Stimulated Emission of Radiation Atoms ‘prepared’ in metastable excited states …waiting for stimulated emission Called ‘population inversion’ (atoms normally in ground state) Excited states stimulated to emit photon from a spontaneous emission. Two photons out, these stimulate other atoms to emit. Thur. Dec 6, 2007 Phy208 Lecture 27

Ruby Laser Ruby crystal has the atoms which will emit photons Flashtube provides energy to put atoms in excited state. Spontaneous emission creates photon of correct frequency, amplified by stimulated emission of excited atoms. Thur. Dec 6, 2007 Phy208 Lecture 27

Ruby laser operation Relaxation to metastable state (no photon emission) 3 eV 2 eV Metastable state Transition by stimulated emission of photon 1 eV PUMP Ground state Thur. Dec 6, 2007 Phy208 Lecture 27

Good description of atom Hydrogen atom: single electron orbiting around single positively-charged proton Hydrogen atom can be in different quantum states, corresponding classically to different orbits. Can also have more than one electron orbiting around the nucleus. # of electrons determines the chemical properties, and hence the element. Thur. Dec 6, 2007 Phy208 Lecture 27

Chap 42: Nuclear Physics Nucleus consists of protons and neutrons densely combined in a small space (~10-14 m) Protons have a positive electrical charge Neutrons have zero electrical charge (are neutral) Neutrons & protons generically called ‘nucleons’ Spacing between these nucleons is ~ 10-15 m Size of electron orbit is 5x10-11 m Nucleus is 5,000 times smaller than the atom! Neutron Proton Thur. Dec 6, 2007 Phy208 Lecture 27

Neutrons and Protons Neutron: zero charge (neutral) Proton: positive charge (equal and opposite to electron) Zero net charge -> # protons in nucleus = # electrons orbiting. The number of electrons determines which element. 1 electron  Hydrogen 2 electrons  Helium 6 electrons  Carbon How many neutrons? Thur. Dec 6, 2007 Phy208 Lecture 27

Carbon # protons Total # nucleons C 12 6 Carbon has 6 protons, 6 electrons (Z=6): this is what makes it carbon. Most common form of carbon has 6 neutrons in the nucleus. Called 12C Another form of carbon has 6 protons, 8 neutrons in the nucleus. This is 14C. This is a different ‘isotope’ of carbon Thur. Dec 6, 2007 Phy208 Lecture 27

Question Hydrogen is the element with one electron. Which of the following is NOT the nucleus of an isotope of hydrogen? One proton One proton and one neutron Two protons and one neutron Hydrogen Deuterium Trituium One proton One proton one neutron One proton two neutrons Isotopes of hydrogen Thur. Dec 6, 2007 Phy208 Lecture 27

Isotopes Isotopes: Nuclei with same # protons, but different # neutrons 12C and 14C have same chemical properties. Both have 6 protons/6 electrons, same outer electron configuration So both called carbon But have different number of neutrons. 12C has 12-6 = 6 neutrons 14C has 14-6 = 8 neutrons Thur. Dec 6, 2007 Phy208 Lecture 27

Heavy Water: deuterium oxide D2O: two 2H, one 16O bonded together $15 / cube! How much heavier is D2O than H2O? 5 % 10% 15% 50% Thur. Dec 6, 2007 Phy208 Lecture 27

Thur. Dec 6, 2007 Phy208 Lecture 27

Thur. Dec 6, 2007 Phy208 Lecture 27

Nuclear Force So what holds the nucleus together? Coulomb force? Gravity? Coulomb force only acts on charged particles Repulsive between protons, and doesn’t affect neutrons at all. Gravitational force is much too weak. Showed before that gravitational force is much weaker than Coulomb force. Thur. Dec 6, 2007 Phy208 Lecture 27

The Strong Nuclear Force New attractive force. Dramatically stronger than Coulomb force at short distances. Doesn’t depend on sign of charge. This is the ‘strong interaction’, one of the four fundamental interactions: electromagnetic interaction strong interaction weak interaction gravitational interaction Thur. Dec 6, 2007 Phy208 Lecture 27

Estimating the strong force The Coulomb attraction energy (~10 eV) binds the hydrogen atom together. Protons in nucleus are 50,000 times closer together than electron and proton in hydrogen atom. (Hint: Coulomb energy ~ 1/separation) Attractive energy must be larger than the Coulomb repulsion, so nuclear binding energies are at least 5000 eV 500,000 eV 5,000,000 eV This is lower limit. Experimental binding energy ~ 8 MeV/nucleon Thur. Dec 6, 2007 Phy208 Lecture 27

Nuclear masses Nuclear masses very accurately measured. New unit of measurement Atomic Mass Unit: 1 u = 1.6605x10-27kg Defined so that mass of 12C is exactly 1 u. Proton mass mp=(1.6726x10-27kg)(1u/1.6605x10-27kg) mp =1.0073u Neutron mass mN=(1.6749x10-27kg) )(1u/1.6605x10-27kg mN =1.0087u Thur. Dec 6, 2007 Phy208 Lecture 27

Nuclear masses Isolated protons & neutrons Protons & neutrons bound in He nucleus 1.0073 u 1.0073 u 1.0087 u 1.0087 u 4.0320 u 4.0015 u 0.0305 u difference! Thur. Dec 6, 2007 Phy208 Lecture 27

Binding energy Only difference is interaction (strong force) Work required to separate the nucleons Thur. Dec 6, 2007 Phy208 Lecture 27

Binding energy Calculate binding energy from masses Mass of Hydrogen atom (1.0078 u) Mass of atom with Z protons, N neutrons Atomic masses well-known-> easier to use Thur. Dec 6, 2007 Phy208 Lecture 27

Binding energy/nucleon Ebinding/nucleon ( MeV ) Thur. Dec 6, 2007 Phy208 Lecture 27

Fission and fusion Schematic view of previous diagram 56Fe is most stable Move toward lower energies by fission or fusion. Energy released related to difference in binding energy. Thur. Dec 6, 2007 Phy208 Lecture 27

Nuclear fusion 5.06x10-29 kg of mass released as energy when protons & neutrons combined to form Helium nucleus. This is the ‘binding’ energy of the nucleus. E = mc2 = (5.06x10-29 kg)x(3x108 m/s)2 = 4.55x10-12 J = 28 MeV = 28 million electron volts! Binding energy/nucleon = 28 MeV / 4 = 7 MeV Principle of nuclear fusion: Energy released when ‘manufacturing’ light elements. Thur. Dec 6, 2007 Phy208 Lecture 27

What about different isotopes? Thur. Dec 6, 2007 Phy208 Lecture 27

Stability of nuclei Dots are naturally occurring isotopes. Blue shaded region is isotopes created in the laboratory. Observed nuclei have ~ N=Z Slightly fewer protons because they cost Coulomb repulsion energy. Thur. Dec 6, 2007 Phy208 Lecture 27

Radioactive nuclei ~ equal # neutrons and protons Thur. Dec 6, 2007 Phy208 Lecture 27

Nuclear spin Since nucleus is made of protons and neutrons, and each has spin, the nucleus also has a spin (magnetic moment). Can be very large. Turns out to have a biological application. Water is ubiquitous in body, and hydrogen is major element of water (H2O) Nucleus of hydrogen is a single proton. Proton has spin 1/2 Thur. Dec 6, 2007 Phy208 Lecture 27

Magnetic resonance imaging 80% of the body's atoms are hydrogen atoms, Once excited by the RF signal, the hydrogens will tend to return to their lower state in a process called "relaxation" and will re-emit RF radiation at their Larmor frequency. This signal is detected as a function of time, and then is converted to signal strength as a function of frequency by means of a Fourier transformation. Thur. Dec 6, 2007 Phy208 Lecture 27

Magnetic resonance imaging MRI detects photon resonance emission and absorption by the proton spins. Thur. Dec 6, 2007 Phy208 Lecture 27

Radioactivity Most stable nuclei have about same number of protons as neutrons. If the energy gets too high, nucleus will spontaneously try to change to lower energy configuration. Does this by changing nucleons inside the nucleus. These nuclear are unstable, and are said to decay. They are called radioactive nuclei. Thur. Dec 6, 2007 Phy208 Lecture 27

Particles in the nucleus Can still, however, get an approximate description of nucleus with protons and neutrons. Proton Charge +e Mass 1.6726x10-27 kg Spin 1/2 Neutron Charge 0 Mass 1.6749x10-27 kg Both are spin 1/2 particles -> obey Pauli exclusion principle One particle per quantum state Thur. Dec 6, 2007 Phy208 Lecture 27

Putting nucleons in the nucleus proton and neutron states in the nucleus are quantized. Certain discrete energy levels available (particle in box) Neutrons and protons are Fermions 2 protons cannot be in same quantum state 2 neutrons cannot be in same quantum state But neutron and proton are distinguishable, so proton and neutron can be in same quantum state. Thur. Dec 6, 2007 Phy208 Lecture 27

Proton and Neutron states Quantum states for nucleons in the nucleus Particles in a box Proton and neutron can be in the same state protons neutrons Nucleon quantum states in the nucleus Schematic indicating neutron & proton can occupy same state Thur. Dec 6, 2007 Phy208 Lecture 27

Populating nucleon states Various quantum states for nucleons in the nucleus Similar to the hydrogen atom: one electron in each quantum state. Two states at each energy (spin up & spin down) protons neutrons Helium This is 4He, with 2 neutrons and 2 protons in the nucleus Thur. Dec 6, 2007 Phy208 Lecture 27

Other helium isotopes Too few neutrons, -> protons too close together. High Coulomb repulsion energy Too many neutrons, requires higher energy states. neutrons protons neutrons protons Thur. Dec 6, 2007 Phy208 Lecture 27

Radioactive decay Decay usually involves emitting some particle from the nucleus. Generically refer to this as radiation. Not necessarily electromagnetic radiation, but in some cases it can be. The radiation often has enough energy to strip electrons from atoms, or to sometimes break apart chemical bonds in living cells. Thur. Dec 6, 2007 Phy208 Lecture 27

Discovery of radioactivity Accidental discovery in 1896 Henri Becquerel was trying to investigate x-rays (discovered in 1895 by Roentgen). Exposed uranium compound to sunlight, then placed it on photographic plates Believed uranium absorbed sun’s energy and then emitted it as x-rays. On the 26th-27th February, experiment "failed" because it was overcast in Paris. Becquerel developed plates anyway, finding strong images, Proved uranium emitted radiation without an external source of energy. Thur. Dec 6, 2007 Phy208 Lecture 27

Detecting radiation A Geiger counter Radiation ionizes (removes electrons) atoms in the counter Leaves negative electrons and positive ions. Ions attracted to anode/cathode, current flow is measured Thur. Dec 6, 2007 Phy208 Lecture 27

Radioactive tracers George de Hevesy Worked on radioactivity as student with Ernest Rutherford. Lodged in nearby boarding home. Suspected his landlady was serving meals later in the week ‘recycled’ from the Sunday meat pie. His landlady denied this! deHevesy described his first foray into nuclear medicine: “The coming Sunday in an unguarded moment I added some radioactive deposit [lead-212] to the freshly prepared pie and on the following Wednesday, with the aid of an electroscope, I demonstrated to the landlady the presence of the active deposit in the soufflé.” George de Hevesy Thur. Dec 6, 2007 Phy208 Lecture 27

Energy of nucleus Nucleons attracted by nuclear force, so more nucleons give more attractive force. This lowers the energy. But more nucleons mean occupying higher quantum states, so higher energy required. Tradeoff gives observed nuclear configurations Thur. Dec 6, 2007 Phy208 Lecture 27

Stable and Unstable Isotopes Thur. Dec 6, 2007 Phy208 Lecture 27

Question The nucleus of a helium atom consists of two protons and two neutrons. Thur. Dec 6, 2007 Phy208 Lecture 27

Different nuclear configurations Higher energy Lower energy Tendency toward equal # protons & neutrons Nucleus with only protons: high energy states must be occupied. Nucleus with protons and neutrons: don’t need to occupy higher energy states Thur. Dec 6, 2007 Phy208 Lecture 27

Comparing the ‘old’ and ‘new’ Thur. Dec 6, 2007 Phy208 Lecture 27

What is this nuclear force? Modern view is that all forces arise from an exchange of particles. Coulomb force is the exchange of photons that have zero mass Strong nuclear force is the exchange of a particle with mass. Thur. Dec 6, 2007 Phy208 Lecture 27

EM force and Strong Force Electromagnetic force Strong nuclear force (approximate view) Thur. Dec 6, 2007 Phy208 Lecture 27

Nucleons are not fundamental We now know that protons and neutrons are not fundamental particles. They are composed of quarks, which interact by exchanging gluons. Thur. Dec 6, 2007 Phy208 Lecture 27

The ‘new’ nuclear force Strong force is actually between quarks in the nucleons. Quarks exchange gluons. Most of the strong force glues quarks into protons and neutrons. But a fraction of this force leaks out, binding protons and neutrons into atomic nuclei Thur. Dec 6, 2007 Phy208 Lecture 27

What makes a nucleus stable? A nucleus with lower energy is more stable. This is a general physical principle, that systems tend to their lowest energy configurations e.g. water flows downhill Ball drops to the ground Hydrogen atom will be in its ground state Same is true of nucleus Observed internal configuration is that with the lowest energy. Thur. Dec 6, 2007 Phy208 Lecture 27

Marie Curie, Nobel prizes in physics, chemistry Radioactivity Stable nuclei have about the same number of protons and neutrons. Neutrons are somewhat favored because of the electric repulsion between protons. If the ratio of protons to neutrons gets too far off-balance, a nucleus will spontaneously transform itself into another nucleus with a better balanced ratio by emitting , ,  particles (2p2n, electrons, photons). Marie Curie, Nobel prizes in physics, chemistry

Stability of nuclei Dots are naturally occurring isotopes. Blue shaded region is isotopes created in the laboratory. Observed nuclei have ~ N=Z Slightly fewer protons because they cost Coulomb repulsion energy. Thur. Dec 6, 2007 Phy208 Lecture 27

Stable and Unstable Isotopes Thur. Dec 6, 2007 Phy208 Lecture 27

Binding energy of different nuclei

Fusion vs. fission 1) Schematic view of previous diagram 56Fe is most stable Move toward lower energies by fission or fusion.

Visualizing a nucleus A nucleon made up of interacting quarks. A nucleus of several nucleons, with their interacting quarks Visualizing a nucleus A nucleon made up of interacting quarks. Thur. Dec 6, 2007 Phy208 Lecture 27

Four fundamental forces Thur. Dec 6, 2007 Phy208 Lecture 27

Nucleus bound very tightly To change properties of nucleus, need much larger energies than to change electronic states. Properties of nucleus that might change are Exciting nucleus to higher internal energy state Breaking nuclei apart Fusing nuclei together. Required high energies provided by impact of high-energy… …protons, electrons, photons, other nuclei High energies produced in an accelerator facility Thur. Dec 6, 2007 Phy208 Lecture 27

Nuclear Binding Energy Mass of nucleus is less than mass of isolated constituents! Helium nucleus energy < energy isolated nucleons. Helium nucleus Energy difference is binding energy. 2 protons & 2 neutrons Thur. Dec 6, 2007 Phy208 Lecture 27

Nuclear binding energy 12C has a mass of 12.00000 u (1 u = 1.661x10-27 kg) ‘Missing mass’ in He case is = 5.06x10-29 kg The corresponding energy is Thur. Dec 6, 2007 Phy208 Lecture 27

Nucleus properties Experimentally, Nuclear matter is ~ incompressible radius of nucleus r = roA1/3 (A=mass # = # nucleons) says that volume V proportional to A. says that nucleon density is constant Nuclear matter is ~ incompressible More nucleons -> larger nucleus Nucleons ~ same distance apart in all nuclei Thur. Dec 6, 2007 Phy208 Lecture 27

Question Tritum is an isotope of hydrogen with three total nucleons: two neutrons and one proton. How many electrons does it have? One Two Three Trituium One proton two neutrons One electron Thur. Dec 6, 2007 Phy208 Lecture 27

Even stronger Electron / nucleus bound by Coulomb attraction. Strength ~10 eV. Protons in nucleus 50,000 times nearer. Coulomb repulsion ~500,000 eV = 0.5 MeV Nuclear force must be much stronger than this. Experimentally, nucleons bound by ~ 8 MeV / nucleon (8,000,000 eV / nucleon) Thur. Dec 6, 2007 Phy208 Lecture 27