00 - Basics of optical traps The optical trap is based on the concept of photon momentum transfer. Photon momentum was proposed by Planck and used by Einstein to explain the photo-electric effect. A photon of wavelength ? carries momentum h? where h is the Planck constant. The existence of photon momentum transfer can be proved by firing a camera flash onto a reflecting plate. The faint "ping" heard are vibrations in the plate that spring from the momentum transfer of the reflected photons. So far we know that reflected photons transfer momentum. This is due to their change of direction of propagation. The same holds then of course for refracted light, since light is refracted in a lens, the direction is changed for the photons. Normally we wouldn't notice this since the forces exerted are very small, about femtoNewton (fN), but for sufficiently small particles, such forces can be large. For a particle of 1 µm diameter and unit density, the gravitational force mg is of the order of 10 fN. With laser light of sufficiently high intensity, this can be balanced with a light pressure force. Optical trapping works for small transparent particles. The phenomena can be explained using simple ray-optics arguments. First we consider what happens when a ray passes through a spherical transparent particle (see figure at left). This ray is first refracted in a powerful lens before it enters the sphere, hence momentum is transferred to the sphere. As can be seen from this picture there is a resultant force F acting on the sphere. F has two components: one acting along the direction of the beam, the scattering force Fs, and one acting perpendicular, denoted Fg for the gradient force. The scattering force tries to push the particle along the ray and is somewhat counteracted by the gradient force. What does that mean? Well, let's say that we have a second ray more intense than the first entering the sphere from the left but at the same angle of incidence and relative position. The gradient force from the second beam would then be larger than the first. The sphere would then feel a net force pushing it towards the second beam. Now let us consider the focus of a laserbeam. If the beam has a Gaussian intensity distribution the intensity in the focus will be strongest along the beam axis and decay as we move outwards radially. The intensity would also decay if we moved away from the focus along the beam axis (after all, a focus is a place where the light intensity is collected in a minimised volume). A particle sitting moving away from the focus would then feel a gradient force pushing it back. This is an optical trap. If the gradient force dominates over the scattering force, the trapping is three dimensional. This is used in an optical tweezers and requires high power microscope objectives. Below is some pictures that qualitatively show how the 3-D trapping mechanism works. If the scattering force is larger than the gradient force optical trapping can still be performed. By directing the laserbeam vertically, the scattering force can be balanced by gravitational forces. This is used in optical levitation. Source: http://www.fy.chalmers.se/atom/research/tweezers/principles.xml 01 - Bohr radius From Wikipedia, the free encyclopedia Jump to: navigation, search 1 Bohr radius = SI units52.9177×10?12 m 52.9177×10?3 nmNatural units3.27441×1024 lP 18.7789×103 leUS customary / Imperial units173.615×10?12 ft 2.08337×10?9 inIn the Bohr model of the structure of an atom, put forward by Niels Bohr in 1913, electrons orbit a central nucleus. The model says that the electrons orbit only at certain distances from the nucleus, depending on their energy. In the simplest atom, hydrogen, a single electron orbits, and the smallest possible orbit for the electron, that with the lowest energy, is most likely to be found at a distance from the nucleus called the Bohr radius. According to 2006 CODATA the Bohr radius of hydrogen has a value of 5.2917720859(36)×10?11 m (i.e., approximately 53 pm or 0.53 ångströms).[1][2] This value can be computed in terms of other physical constants: where: is the permittivity of free space is the reduced Planck's constant is the electron rest mass is the elementary charge is the speed of light in vacuum is the fine structure constant While the Bohr model does not correctly describe an atom, the Bohr radius keeps its physical meaning as a characteristic size of the electron cloud in a full quantum-mechanical description. Thus the Bohr radius is often used as a unit in atomic physics, see atomic units. Note that the definition of Bohr radius does not include the effect of reduced mass, and so it is not precisely equal to the orbital radius of the electron in a hydrogen atom in the more physical model where reduced mass is included. This is done for convenience: the Bohr radius as defined above appears in equations relating to atoms other than hydrogen, where the reduced mass correction is different. If the definition of Bohr radius included the reduced mass of hydrogen, it would be necessary to include a more complex adjustment in equations relating to other atoms. The Bohr radius of the electron is one of a trio of related units of length, the other two being the Compton wavelength of the electron and the classical electron radius . The Bohr radius is built from the electron mass me, Planck's constant and the electron charge . The Compton wavelength is built from , and the speed of light . The classical electron radius is built from , and . Any one of these three lengths can be written in terms of any other using the fine structure constant : The Bohr radius including the effect of reduced mass can be given by the following equation: , where is the Compton wavelength of the proton. is the Compton wavelength of the electron. is the fine structure constant. In the above equation, the effect of the reduced mass is achieved by using the increased Compton wavelength, which is just the Compton wavelengths of the electron and the proton added together. [edit] Notes and references 1. ^ fundamental physical constants, NIST 2. ^ The number in parentheses (36) denotes the uncertainty of the last digits. 03 - Physics Today - Click here ^ to open PDF File 04 - On Truth & Reality The Spherical Standing Wave Structure of Matter (WSM) in Space If you may need these contents in other language, try our Translator Online