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 1 Atomic Quantum number summary Hydrogen atom states ( ) n, l, m l, m s n: principle quantum number Determines energy (n=1, 2, 3 ) orbital quantum number Magnitude of orbital angular momentum 0, 1, 2, n-1 m : orbital magnetic r quantum number Orientation of L ( L z = m l h) m = - - + 1, 0, - 1, + m s : spin quantum r number Orientation of S ( S z = m s h) m s =-1/2, +1/2 L = h l( l +1) Thur. Dec 6, 2007 Phy208 Lecture 27 2 Na Optical spectrum Elements in same column have similar chemical properties 11 electrons Ne core = 1s 2 2s 2 2p 6 (closed shell) 1 electron outside closed shell Na = [Ne]3s 1 Outside (11 th ) electron easily excited to other states. 589 nm, 3p -> 3s Na Thur. Dec 6, 2007 Phy208 Lecture 27 3 Thur. Dec 6, 2007 Phy208 Lecture 27 4 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 5 Another possibility: Stimulated emission Atom in excited state. Photon of energy hf=δe 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 hf=δe Before Thur. Dec 6, 2007 Phy208 Lecture 27 6 ΔE After If excited state is metastable (long lifetime for spontaneous emission) stimulated emission dominates 1
LASER : Light Amplification by Stimulated Emission of Radiation Ruby Laser 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 7 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 8 Ruby laser operation Good description of atom 3 ev 2 ev 1 ev PUMP Relaxation to metastable state (no photon emission) Metastable state Transition by stimulated emission of photon 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. Ground state Thur. Dec 6, 2007 Phy208 Lecture 27 9 Thur. Dec 6, 2007 Phy208 Lecture 27 10 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 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 11 Thur. Dec 6, 2007 Phy208 Lecture 27 12 2
Carbon # protons Carbon has 6 protons, 6 electrons (Z=6): this is what makes it carbon. Total # nucleons Most common form of carbon has 6 neutrons in the nucleus. Called 12 C 12 C 6 Another form of carbon has 6 protons, 8 neutrons in the nucleus. This is 14 C. This is a different isotope of carbon Thur. Dec 6, 2007 Phy208 Lecture 27 13 Question Hydrogen is the element with one electron. Which of the following is NOT the nucleus of an isotope of hydrogen? A. One proton B. One proton and one neutron C. Two protons and one neutron Isotopes of hydrogen Hydrogen One proton Deuterium One proton one neutron Trituium One proton two neutrons Thur. Dec 6, 2007 Phy208 Lecture 27 14 Isotopes Heavy Water: deuterium oxide Isotopes: Nuclei with same # protons, but different # neutrons 12 C and 14 C have same chemical properties. Both have 6 protons/6 electrons, same outer electron configuration So both called carbon But have different number of neutrons. 12 C has 12-6 = 6 neutrons 14 C has 14-6 = 8 neutrons D 2 O: two 2 H, one 16 O bonded together How much heavier is D 2 O than H 2 O? A. 5 % B. 10% C. 15% D. 50% $15 / cube! Thur. Dec 6, 2007 Phy208 Lecture 27 15 Thur. Dec 6, 2007 Phy208 Lecture 27 16 Thur. Dec 6, 2007 Phy208 Lecture 27 17 Thur. Dec 6, 2007 Phy208 Lecture 27 18 3
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. 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 19 Thur. Dec 6, 2007 Phy208 Lecture 27 20 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 A. 5000 ev B. 500,000 ev C. 5,000,000 ev This is lower limit. Experimental binding energy ~ 8 MeV/nucleon Thur. Dec 6, 2007 Phy208 Lecture 27 21 Nuclear masses Nuclear masses very accurately measured. New unit of measurement Atomic Mass Unit: 1 u = 1.6605x10-27 kg Defined so that mass of 12 C is exactly 1 u. Proton mass m p =(1.6726x10-27 kg)(1u/1.6605x10-27 kg) m p =1.0073u Neutron mass m N =(1.6749x10-27 kg) )(1u/1.6605x10-27 kg m N =1.0087u Thur. Dec 6, 2007 Phy208 Lecture 27 22 Isolated protons & neutrons 1.0073 u Nuclear masses Protons & neutrons bound in He nucleus Binding energy Only difference is interaction (strong force) Work required to separate the nucleons 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 23 E = mc 2 ( ) 1.661"10 #27 kg /u ( )( 931.494 MeV /u) = 0.0305 u = 0.0305 u ( )( c 2 ) = 28.41 MeV $ 7.1 MeV /nucleon Thur. Dec 6, 2007 Phy208 Lecture 27 24 4
Binding energy Binding energy/nucleon Calculate binding energy from masses E binding = ( Zm p + Nm N " m nucleus )c 2 +Zm e "Zm e E binding = ( Zm H + Nm N " m atom )c 2 Mass of Hydrogen atom (1.0078 u) Atomic masses well-known-> easier to use Mass of atom with Z protons, N neutrons Thur. Dec 6, 2007 Phy208 Lecture 27 25 E binding /nucleon ( MeV ) Thur. Dec 6, 2007 Phy208 Lecture 27 26 Schematic view of previous diagram 56 Fe is most stable Move toward lower energies by fission or fusion. Energy released related to difference in binding energy. Fission and fusion 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 = mc 2 = (5.06x10-29 kg)x(3x10 8 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 27 Thur. Dec 6, 2007 Phy208 Lecture 27 28 What about different isotopes? 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 29 Thur. Dec 6, 2007 Phy208 Lecture 27 30 5
Radioactive nuclei ~ equal # neutrons and protons 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 (H 2 O) Nucleus of hydrogen is a single proton. Proton has spin 1/2 Thur. Dec 6, 2007 Phy208 Lecture 27 31 Thur. Dec 6, 2007 Phy208 Lecture 27 32 Magnetic resonance imaging 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 33 MRI detects photon resonance emission and absorption by the proton spins. Thur. Dec 6, 2007 Phy208 Lecture 27 34 6