J. Robert Oppenheimer

Matthew A. QuigleyDepartment of Physics, MSC125

West Chester University of PAWest Chester, PA 19383

MQ667557@wcupa.edu

Taken from a Los Alamos publication (Los Alamos: Beginning of an era, 1943-1945, Los Alamos Scientific Laboratory, 1986.)

A Brief History

Born: April 22, 1904

Died: February 18, 1967

Alma mater: -Harvard University-University of Cambridge-University of Göttingen

Director of the Institute for Advanced Study in Princeton, New Jersey.[1]

Director of the Manhattan Project and “Father of the Atomic Bomb.”[1]

Awarded:-1946 Presidential Medal of Merit and-1963 Enrico Fermi Prize -Never awarded a Nobel Prize

“He never wrote a long paper or did a calculation of any kind; he didn’t have the patience for that, but he inspired other people to do things, and his influence was fantastic.”

-Murray Gell-Mann [1]

Notable Scientific Contributions

-Born-Oppenheimer Approximation[2]

-Oppenheimer-Phillips Process[4]

-Tolman-Oppenhiemer-Volkoff Limit[5]

-Physical calculations behind the propagation of a fast neutron chain reaction, structural design and construction for the first weaponize artificial nuclear explosion.[6]

-His work predicated the existence of quantum tunneling, neutrons, mesons, neutron stars, positrons, and black holes.[1][6]

The fundamental equation for quantum mechanics is the Schrödinger Equation:

The Schrödinger Equation describes how the quantum state of a system changes with position and time by relating the Hamiltonian operator and total energy to the probability amplitude of a quantum state.

Because the Hamiltonian operator is a second order differential equation for the spatial coordinates of the electrons and nuclei, computation for the wavefunction of molecules greater than hydrogen becomes impossibly difficult.

Born-Oppenheimer ApproximationThe Hamiltonian of a molecule depends on:-Electronic Kinetic Energy-Nuclear Kinetic Energy-Electron-Nuclei Coulomb Potential Energy-Electron-Electron Coulomb Potential Energy-Nuclei-Nuclei Coulomb Potential Energy-Any External Electric or Magnetic Fields

A molecule consisting of n electrons and m nuclei would have a 3(n + m) variable second order differential equation to solve for the Hamiltonian!

Born-Oppenheimer Approximation

The mass of the nucleus is significantly larger than the mass of the surrounding electrons but the average kinetic energy of an electron is significantly larger than that of the nucleus. Max Born and J. Robert Oppenheimer, suggested that because the electrons are moving so much faster than the nuclei, we could approximate the kinetic energy to be zero and any nuclear motion to be independent of electron configuration.[2]

Born-Oppenheimer ApproximationNow the electronic wavefunction can be separated and solved by assuming the nuclei are at fixed points with zero kinetic energy.[3]

The electronic wave function and the energy related to the electronic structure of the molecule to that of atoms can then be inserted in the wave equation describing the nuclear motion.[3]

Solution of the nuclear part gives the eigenfunctions and eigenvalues for the total energy.

A problem with the Born-Oppenheimer Approximation is that the nuclei are treated with no definite size and a uniform radius. As a consequence, isotopes have the same potential energy. All coupling between electronic and rotational motion are neglected which give rise to significant error as the electron/nucleus mass ratio approaches 1.[3]

Oppenheimer-Phillips ProcessFor a nuclear reaction to occur, the two nuclei need to overcome the Coulomb barrier. The coulomb barrier is the name given to the electrostatic interaction caused by electric potential energy:

In 1935, J. Robert Oppenheimer and Melba Phillips proposed an explanation to the results of radioactive decay observed in stable atoms after being to bombarded with deuterons. The idea being that if the deuteron was able to overcome the coulomb barrier, it would fuse with the nucleus and produce a heavy isotope while ejecting its original proton.[4]

2D + AX → 1H + A+1X

This explanation would allow for nuclear interactions to occur at lower energies than predicated using the electric potential energy due to the polarization of the deuteron atom. As it approaches the positively charged nucleus, the proton faces away and the neutron faces towards the intended target. Fusion begins to occur when the binding energy of the neutron and the target nucleus is greater than the binding energy of the deuteron, causing the proton to be repelled from the newly formed heavier nucleus.[4]

Tolman-Oppenheimer-Volkoff Limit

Visual interpretation of a neutron star. http://www.nasa.gov/centers/goddard/images/content/96714main_DiskPreBurst_lg_web.jpg

Tolman-Oppenheimer-Volkoff LimitIn any stable body, the force of gravity pushing into an object is at equilibrium; a force of equal magnitude and opposite direction to counteract it.

Using the work done by Richard C. Tolman with spherical symmetry, J. Robert Oppenheimer and George Volkoff were able to derive a relativistic version of the hydrostatic equation used to find the equilibrium structure of a spherically symmetric body of isotropic material.[5]

This lead to the Tolman-Oppenheimer-Volkoff equation which sets the constraints for any structure of a spherically symmetric body of isotropic material which is in static gravitational equilibrium.[5]

Tolman-Oppenheimer-Volkoff Limit

The weight of a neutron star is balanced by a combination of short-range repulsive neutron-neutron strong force interactions to prevent itself from collapse, but there is a limit to how massive the neutron star can be. This is known as the Tolman-Oppenheimer-Volkoff limit. If exceeded, the star would not remain stable as a neutron star and undergo gravitational collapse. The outcome of such an event would be predicted by Oppenheimer in 1939 to be what we now call a black hole.[6]

The Manhattan Project

In September of 1942, Brigadier General Leslie R. Groves, Jr. selected J. Robert Oppenheimer to lead the Manhattan Project.[7]

In 1945 a uranium-235 fission based prototype had been successfully created using diffusion through a membrane of gasses Uranium Hexafluoride (UF6). Nuclear fission occurs when an incoming neutron is absorbed by uranium-235, briefly becoming and excited uranium-236 before splitting into krypton-92, barium-141 and three neutrons.[7] Photons are released in the form of gamma rays that superheats the air around it causing a tremendous change in heat and pressure that is used to destroy everything within the blast radius.

The Manhattan ProjectU + 2ClF3 → UF6 + Cl2

1n + 235U → 141Ba + 92Kr + 3 1n + 202.5 MeV

The first artificial nuclear explosion occurred on July 16, 1945 in the Jornada del Muerto desert near Socorro New Mexico. It produced an explosion equivalent to 20 kilotons of TNT and entered human beings into the atomic age.[7]

“We knew the world would not be the same. A few people laughed, a few people cried. Most people were silent. I remembered the line from the Hindu scripture, the Bhagavad Gita; Vishnu is trying to persuade the Prince that he should do his duty and, to impress him, takes on his multi-armed form and says, 'Now I am become Death, the destroyer of worlds.' I suppose we all thought that, one way or another.”

-J. Robert Oppenheimer on the Trinity test (1965). Atomic Archive. Retrieved May 5, 2013

The Manhattan Project

Trinity blast after 10 sec. July 16, 1945 at 5:30 am. Taken from Los Alamos national laboratory www.lanl.gov

References1. Bethe, Hans (1997). "J. Robert Oppenheimer 1904-1967". Biographical Memoirs

(Washington, D.C.: United States National Academy of Sciences) 71: 175–218.2. Born, Max; Oppenheimer, J. Robert (1927). "Zur Quantentheorie der Molekeln" [On

the Quantum Theory of Molecules]. Annalen der Physik (in German) 389 (20): 457–484.

3. Eckart, C. (1935). "The Kinetic Energy of Polyatomic Molecules". Physical Review 46: 383–387

4. Oppenheimer, 1995, page 192 cf. Note on the transmutation function for deuterons, J. Robert Oppenheimer and Melba Phillips, Phys. Rev. 48, September 15, 1935, 500-502.

5. R.C. Tolman (1939). "Static Solutions of Einstein's Field Equations for Spheres of Fluid". Physical Review 55 (4): 364–373.

6. J.R. Oppenheimer and G.M. Volkoff (1939). "On Massive Neutron Cores". Physical Review 55 (4): 374–381. Bombaci (1996). "The Maximum Mass of a Neutron Star". Astronomy and Astrophysics 305: 871–877.

7. Hoddeson, Lillian; Henriksen, Paul W.; Meade, Roger A.; Westfall, Catherine L. (1993). Critical Assembly: A Technical History of Los Alamos During the Oppenheimer Years, 1943–1945. New York, New York: Cambridge University Press.