With J. J. Thomson's discovery of the electron in 1897, it became clear that atoms were not the smallest building blocks of nature, but were rather composite particles.

With de Broglie's suggestion of the existence of electron matter waves in 1924, and for a short time before the full 1926 Schrödinger equation treatment of hydrogen like atom, a Bohr electron " wavelength " could be seen to be a function of its momentum, and thus a Bohr orbiting electron was seen to orbit in a circle at a multiple of its half-wavelength ( this historically incorrect Bohr model is still occasionally taught to students ).

With covalent bonds, an electron moves by hopping to a neighboring bond.

With sufficient compression, electrons are forced into nuclei in the process of electron capture, relieving the pressure.

With the advent of quantum mechanics this picture was given more formal interpretation in the form of the free electron model and its further extension, the nearly free electron model.

With covalent bonds, an electron moves by hopping to a neighboring bond.

With its description of the electron wave functions in molecules as delocalized molecular orbitals that possess the same symmetry as the molecule, Hund and Mulliken's molecular-orbital method, including contributions by John Lennard-Jones, proved to be more flexible and applicable to a vast variety of types of molecules and molecular fragments, and has totally eclipsed the valence-bond method.

With each collision, though, the electron is deflected in a random direction with a velocity that is much larger than the velocity gained by the electric field.

With the rise of electronics in the 1930s, electronics engineers usually became members of the IRE, but the applications of electron tube technology became so extensive that the technical boundaries differentiating the IRE and the AIEE became difficult to distinguish.

With this expression we can write the electron contribution to the current to the probe in terms of the ion saturation current as

With only three valence electrons, simple covalent bonding will be electron deficient with respect to the octet rule.

With one unpaired electron, the superoxide ion is a free radical, and, like dioxygen, it is paramagnetic.

With better understanding of atomic physics, however, it was later determined that the green spectra was caused by a low-probability electron transition in doubly ionized oxygen, a so-called " forbidden transition ".

With the electrical field calculated, he could measure the droplet's charge, the charge on a single electron being ().

With this theory, the properties of a many-electron system can be determined by using functionals, i. e. functions of another function, which in this case is the spatially dependent electron density.

With the development of TEM, the associated technique of scanning transmission electron microscopy ( STEM ) was re-investigated and did not become developed until the 1970s, with Albert Crewe at the University of Chicago developing the field emission gun and adding a high quality objective lens to create the modern STEM.

With the development of sensitive electron energy analyzers in the 1960s, it became possible to measure fine details of the total energy distribution.

With the loss of all its acquired kinetic energy in this way, the free electron can no longer overcome the slight negative potential at the ground electrode, and the measured current drops sharply.

With F-mixing, once a single electron wave function is calculated it is not used directly.

With an electron multiplier an impact of a single ion starts off an electron cascade, resulting in a pulse of 10 < sup > 8 </ sup > electrons which is recorded directly.

With increasing beam power the net gain ( gain minus loss ) reduces to unity and the gain medium is said to be saturated.

With beamed propulsion one can leave the power-source stationary on the ground, and directly ( or via a heat exchanger ) heat propellant on the spacecraft with a maser or a laser beam from a fixed installation.

With the motion of the beam this revolved around, and turned, the ' sun ' a second rotating cog fixed to and which turned the drive shaft.

With some care, and looking at a wide range of energy losses, one can determine the types of atoms, and the numbers of atoms of each type, being struck by the beam.

With a somewhat higher tension than used before clipping the beam yielded a deflected profile for the wire which could be easily handled at by a pneumatic servo pantograph with only 3 G accelerations.

With the help of Victor W. Cohen, Rabi built a molecular beam apparatus at Columbia.

With a hull length of and a beam of she appeared as a typical representative of the North American sidewheelers around the second half of the century and was the largest steamer on the lake at that time.

With IMRT, radiation oncologists are able to break up the radiation beam into many " beamlets.

With furnace atomization, a microliter-sized portion of sample is pipette into a small, open-ended graphite cylinder, which is located in the light beam of the instrument, and the cylinder is then heated by applying a high electrical potential across the cylinder.

With acousto-optic deflectors or galvanometer-driven mirrors, a single laser beam can be shared among hundreds of optical tweezers in the focal plane, or else spread into an extended one-dimensional trap.

With this beam the components of Cygnus A, spaced 100 ", were put directly in evidence without the need for repeated observations with variable spacing aperture synthesis interferometry.

With Kaufmann ’ s approval, the consulting engineers arranged for the contractor to install a supporting wall under the main supporting beam for the west terrace.

With an appropriate choice of beam species and velocity and of geometry, this effect can be used to determine the magnetic field in the plasma.

With p = l = 0, the TEM < sub > 00 </ sub > mode is the lowest order, or fundamental transverse mode of the laser resonator and has the same form as a Gaussian beam.

With each weaving operation, the newly constructed fabric must be wound on a cloth beam.

With nothing to stop Hendrick, the villagers were brainwashed by the beam of light, one by one, until only a visiting professor and his son remained.

With an additional Kerr lens the beam width gets smaller.

With the hope of selling kits to the larger readership ; Roberts and Mims designed a device that would transmit voice over a beam of light, the Opticom.

With Raytheon the U. S. Air Force has developed a nonlethal weapon system called Active Denial System ( ADS ) which emits a beam of radiation with a wavelength of 3 mm.

With tungsten cathodes, emission current densities about 100 mA / mm < sup > 2 </ sup > can be achieved, but only a small portion of emitted electrons takes part in beam formation, depending on the electric field produced by anode and control electrode voltages.

With a baseline of 8 percent, the subjects were able to successfully increase the reflection of the beam by. 05 percent, and showed a similar success when asked to mentally decrease the amount of reflected light.

With the tractor beam deactivated, the Starspeeder escapes the Star Destroyer.

With the force field down, Spock, McCoy and a security team beam to the planet.

With the standard beam systems clearly no longer of any use, some sort of entirely new system would have to be developed.