THEORETICAL PHYSICS - 1

PHOTO-ELECTRIC. A NOBEL AWARD ARTICLE [1921]

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The discovery of the ionization of gases by ultra-violet light was made by Philipp Lenard in 1900. As the effect was produced across several centimeters of air and made very great positive and small negative ions, it was natural to interpret the phenomenon, as did J. J. Thomson, as a Hertz effect upon the solid or liquid particles present in the gas.
Hungarian physicist Philipp Lenard

In 1902, Lenard observed that the energy of individual emitted electrons increased with the frequency (which is related to the color) of the light.
This appeared to be at odds with Maxwell’s wave theory of light, which predicted that the electron energy would be proportional to the intensity of the radiation.

Lenard observed the variation in electron energy with light frequency using a powerful electric arc lamp which enabled him to investigate large changes in intensity, and that had sufficient power to enable him to investigate the variation of potential with light frequency. His experiment directly measured potentials, not electron kinetic energy: he found the electron energy by relating it to the maximum stopping potential (voltage) in a phototube. He found that the calculated maximum electron kinetic energy is determined by the frequency of the light.

For example, an increase in frequency results in an increase in the maximum kinetic energy calculated for an electron upon liberation – ultraviolet radiation would require a higher applied stopping potential to stop current in a phototube than blue light. However Lenard’s results were qualitative rather than quantitative because of the difficulty in performing the experiments: the experiments needed to be done on freshly cut metal so that the pure metal was observed, but it oxidised in a matter of minutes even in the partial vacuums he used. The current emitted by the surface was determined by the light’s intensity, or brightness: doubling the intensity of the light doubled the number of electrons emitted from the surface.

The researches of Langevin and those of Eugene Bloch have shown that the greater part of the Lenard effect is certainly due to this ‘Hertz effect’. The Lenard effect upon the gas itself nevertheless does exist. Refound by J. J. Thomson and then more decisively by Frederic Palmer, Jr., it was studied and showed very different characteristics than those at first attributed to it by Lenard.

In 1905, Albert Einstein solved this apparent paradox by describing light as composed of discrete quanta, now called photons, rather than continuous waves. Based upon Max Planck’s theory of black-body radiation, Einstein theorized that the energy in each quantum of light was equal to the frequency multiplied by a constant, later called Planck’s constant. A photon above a threshold frequency has the required energy to eject a single electron, creating the observed effect. This discovery led to the quantum revolution in physics and earned Einstein the Nobel Prize in Physics in 1921. By wave-particle duality the effect can be analyzed purely in terms of waves though not as conveniently.
Einstein, in 1905, when he wrote the Annus Mirabilis papers

Albert Einstein’s mathematical description of how the photoelectric effect was caused by absorption of quanta of light was in one of his 1905 papers, named “On a Heuristic Viewpoint Concerning the Production and Transformation of Light”. This paper proposed the simple description of “light quanta”, or photons, and showed how they explained such phenomena as the photoelectric effect. His simple explanation in terms of absorption of discrete quanta of light explained the features of the phenomenon and the characteristic frequency.

The idea of light quanta began with Max Planck’s published law of black-body radiation (“On the Law of Distribution of Energy in the Normal Spectrum”) by assuming that Hertzian oscillators could only exist at energies E proportional to the frequency f of the oscillator by E = hf, where h is Planck’s constant. By assuming that light actually consisted of discrete energy packets, Einstein wrote an equation for the photoelectric effect that agreed with experimental results. It explained why the energy of photoelectrons was dependent only on the frequency of the incident light and not on its intensity: a low-intensity, high-frequency source could supply a few high energy photons, whereas a high-intensity, low-frequency source would supply no photons of sufficient individual energy to dislodge any electrons. This was an enormous theoretical leap, but the concept was strongly resisted at first because it contradicted the wave theory of light that followed naturally from James Clerk Maxwell’s equations for electromagnetic behavior, and more generally, the assumption of infinite divisibility of energy in physical systems. Even after experiments showed that Einstein’s equations for the photoelectric effect were accurate, resistance to the idea of photons continued, since it appeared to contradict Maxwell’s equations, which were well-understood and verified.

Einstein’s work predicted that the energy of individual ejected electrons increases linearly with the frequency of the light. Perhaps surprisingly, the precise relationship had not at that time been tested. By 1905 it was known that the energy of photoelectrons increases with increasing frequency of incident light and is independent of the intensity of the light. However, the manner of the increase was not experimentally determined until 1914 when Robert Andrews Millikan showed that Einstein’s prediction was correct.
The photoelectric effect helped to propel the then-emerging concept of wave–particle duality in the nature of light. Light simultaneously possesses the characteristics of both waves and particles, each being manifested according to the circumstances. The effect was impossible to understand in terms of the classical wave description of light,as the energy of the emitted electrons did not depend on the intensity of the incident radiation. Classical theory predicted that the electrons would ‘gather up’ energy over a period of time, and then be emitted.

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Three-step model(PHOTOELCTRIC EFFECT)

In the X-ray regime, the photoelectric effect in crystalline material is often decomposed into three steps:
 1)Inner photoelectric effect . The hole left behind can give rise to auger effect, which is visible even when the electron does not leave the material. In molecular solids phonons are excited in this step and may be visible as lines in the final electron energy. The inner photoeffect has to be dipole allowed. The transition rules for atoms translate via the tight-binding model onto the crystal. They are similar in geometry to plasma oscillations in that they have to be transversal.
 2)Ballistic transport of half of the electrons to the surface. Some electrons are scattered.
 3)Electrons escape from the material at the surface.

In the three-step model, an electron can take multiple paths through these three steps. All paths can interfere in the sense of the path integral formulation. For surface states and molecules the three-step model does still make some sense as even most atoms have multiple electrons which can scatter the one electron leaving.

FOR more information read the book:Hügner, S. (2003). Photoelectron Spectroscopy: Principles and Applications. Springer. ISBN 3-540-41802-4.

THEORETICAL PHYSICS - 1

Neutrino – What is it?

A neutrino electrically neutral, weakly interacting elementary subatomic particle with half-integer spin. The neutrino (meaning “small neutral one” in Italian) is denoted by the Greek letter ν (nu). All evidence suggests that neutrinos have mass but that their mass is tiny even by the standards of subatomic particles. Their mass has never been measured accurately.

Neutrinos do not carry electric charge, which means that they are not affected by the electromagnetic forces that act on charged particles such as electrons and protons. Neutrinos are affected only by the weak sub-atomic force, of much shorter range than electromagnetism, and gravity, which is relatively weak on the subatomic scale. Therefore a typical neutrino passes through normal matter unimpeded.

Neutrinos are created as a result of certain types of radioactive decay, or nuclear reactions such as those that take place in the Sun, in nuclear reactors, or when cosmic rays hit atoms. There are three types, or “flavors”, of neutrinos: electron neutrinos, muon neutrinos and tau neutrinos. Each type is associated with an antiparticle, called an “anti-neutrino”, which also has neutral electric charge and half-integer spin. Whether or not the neutrino and its corresponding anti-neutrino are identical particles has not yet been resolved, even though the anti neutrino has an opposite chirality to the neutrino.

Most neutrinos passing through the Earth emanate from the Sun. About 65 billion (6.5×1010) solar neutrinos per second pass through every square centimeter perpendicular to the direction of the Sun in the region of the Earth.

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important role of supersymmetry in Unification of forces (grand unified theory)

The unification of forces is possible due to the energy scale dependence of force coupling parameters in quantum field theory called renormalization group running, which allows parameters with vastly different values at usual energies to converge to a single value at a much higher energy scale.

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It is commonly believed that this matching is unlikely to be a coincidence, and is often quoted as one of the main motivations to further investigate supersymmetric theories despite the fact that no supersymmetric partner particles have been experimentally observed (March 2011). Also, most model builders simply assume supersymmetry because it solves the hierarchy problem—i.e., it stabilizes the electroweak Higgs mass against radiative corrections.

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The Einstein field equations (EFE)

i never tried these equations untill i make my own mathematical approaches to the level of mathematical physics.

i never suggest readers of my blog to not read einstiens field equations,the field equations needs higher mathematics…guys once think about the photoelectric effect ,that was greatest discovery which einstien got nobel prize,but now school childrens learn that and they understand the fundamentals.same way the field equation needs fundemantals(those we won’t study in school)

learning einstiens certain theories give more imagination to the mind,i my self got understand when i tried to learn about einstien special theory of relativity.

The Einstein field equations (EFE) or Einstein’s equations are a set of 10 equations in Albert Einstein’s general theory of relativity which describe the fundamental interaction of gravitation as a result of spacetime being curved by matter and energy. First published by Einstein in 1915 as a tensor equation, the EFE equate local spacetime curvature (expressed by the Einstein tensor) with the local energy and momentum within that spacetime (expressed by the stress–energy tensor).

Similar to the way that electromagnetic fields are determined using charges and currents via Maxwell’s equations, the EFE are used to determine the spacetime geometry resulting from the presence of mass-energy and linear momentum, that is, they determine the metric tensor of spacetime for a given arrangement of stress–energy in the spacetime. The relationship between the metric tensor and the Einstein tensor allows the EFE to be written as a set of non-linear partial differential equations when used in this way. The solutions of the EFE are the components of the metric tensor. The inertial trajectories of particles and radiation (geodesics) in the resulting geometry are then calculated using the geodesic equation.

As well as obeying local energy-momentum conservation, the EFE reduce to Newton’s law of gravitation where the gravitational field is weak and velocities are much less than the speed of light.

Exact solutions for the EFE can only be found under simplifying assumptions such as symmetry. Special classes of exact solutions are most often studied as they model many gravitational phenomena, such as rotating black holes and the expanding universe. Further simplification is achieved in approximating the actual spacetime as flat spacetime with a small deviation, leading to the linearised EFE. These equations are used to study phenomena such as gravitational waves.

Similar to the way that electromagnetic fields are determined using charges and currents via Maxwell’s equations, the EFE are used to determine the spacetime geometry resulting from the presence of mass-energy and linear momentum, that is, they determine the metric tensor of spacetime for a given arrangement of stress–energy in the spacetime. The relationship between the metric tensor and the Einstein tensor allows the EFE to be written as a set of non-linear partial differential equations when used in this way. The solutions of the EFE are the components of the metric tensor. The inertial trajectories of particles and radiation (geodesics) in the resulting geometry are then calculated using the geodesic equation.

As well as obeying local energy-momentum conservation, the EFE reduce to Newton’s law of gravitation where the gravitational field is weak and velocities are much less than the speed of light.

Exact solutions for the EFE can only be found under simplifying assumptions such as symmetry. Special classes of exact solutions are most often studied as they model many gravitational phenomena, such as rotating black holes and the expanding universe. Further simplification is achieved in approximating the actual spacetime as flat spacetime with a small deviation, leading to the linearised EFE. These equations are used to study phenomena such as gravitational waves.

 

The EFE is a tensor equation relating a set of symmetric 4×4 tensors. Each tensor has 10 independent components. The four Bianchi identities reduce the number of independent equations from 10 to 6, leaving the metric with four gauge fixing degrees of freedom, which correspond to the freedom to choose a coordinate system.

Although the Einstein field equations were initially formulated in the context of a four-dimensional theory, some theorists have explored their consequences in n dimensions. The equations in contexts outside of general relativity are still referred to as the Einstein field equations. The vacuum field equations (obtained when T is identically zero) define Einstein manifolds.

Despite the simple appearance of the equations they are actually quite complicated. Given a specified distribution of matter and energy in the form of a stress–energy tensor, the EFE are understood to be equations for the metric tensor g_{\mu \nu}, as both the Ricci tensor and scalar curvature depend on the metric in a complicated nonlinear manner. In fact, when fully written out, the EFE are a system of 10 coupled, nonlinear, hyperbolic-elliptic partial differential equations.

One can write the EFE in a more compact form by defining the Einstein tensor

  • The nonlinearity of the EFE makes finding exact solutions difficult. One way of solving the field equations is to make an approximation, namely, that far from the source(s) of gravitating matter, the gravitational field is very weak and the spacetime approximates that of Minkowski space. The metric is then written as the sum of the Minkowski metric and a term representing the deviation of the true metric from the Minkowski metric, with terms that are quadratic in or higher powers of the deviation being ignored. This linearisation procedure can be used to investigate the phenomena of gravitational radiation.

 

 

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Gravitational singularity(simple way understanding)

  • is gravitational singularity and space time singularity are same?
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  • simple its same,guys the time and space sometimes makes an whirlpool like pattern(i personaly understand like this) this patern is no longer uniform,it may be a swirl type or water pool type,it may be affected by mass.
    how singularity works?
    what is singularity?
    A gravitational singularity or spacetime singularity is a location where the quantities that are used to measure the gravitational field become infinite in a way that does not depend on the coordinate system. These quantities are the scalar invariant curvatures of spacetime, which includes a measure of the density of matter.
    For the purposes of proving the Penrose–Hawking singularity theorems, a spacetime with a singularity is defined to be one that contains geodesics that cannot be extended in a smooth manner.
  • The end of such a geodesic is considered to be the singularity. This is a different definition, useful for proving theorems.
    • The two most important types of spacetime singularities are curvature singularities and conical singularities. Singularities can also be divided according to whether they are covered by an event horizon or not (naked singularities).
    •  According to general relativity, the initial state of the universe, at the beginning of the Big Bang, was a singularity. Both general relativity and quantum mechanics break down in describing the Big Bang, but in general, quantum mechanics does not permit particles to inhabit a space smaller than their wavelengths.
    • Another type of singularity predicted by general relativity is inside a black hole: any star collapsing beyond a certain point (the Schwarzschild radius) would form a black hole, inside which a singularity (covered by an event horizon) would be formed, as all the matter would flow into a certain point (or a circular line, if the black hole is rotating).
    • This is again according to general relativity without quantum mechanics, which forbids wavelike particles entering a space smaller than their wavelength. These hypothetical singularities are also known as curvature singularities.
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worm hole (short cut to space time)

the idea behind this worm hole is given by albert einstien.when einstien publishes his general theory of relativity,it contains the space-time,gravity-time wrap,gravity curve.etc.A wormhole, also known as an Einstein–Rosen bridge,is a hypothetical topological feature of spacetime that would be fundamentally a “shortcut” through spacetime. A wormhole is much like a tunnel with two ends each in separate points in spacetime. A wormhole would be an unvisualisable structure of 4 or more dimensions.The mouths of a wormhole are analogous to holes in a 2D plane; a real wormhole’s mouths could be spheres in 3D space.theory of general relativity have valid solutions which contain wormholesWormholes which could actually be crossed in both directions, known as traversable wormholes, would onImagely be possible if exotic matter with negative energy density could be used to stabilize them.