On the quantum theory of radiation einstein pdf

Usually at thermal equilibrium, the number of atoms N 2 i. Conditions of Population inversion. There must be a source to supply the energy to the medium. The atoms must be continuously raised to the excited state. Meta stable States. An atom can be excited to a higher level by supplying energy to it. Normally, excited atoms have short life times and release their energy in a matter of nano seconds 10 -9 through spontaneous emission.

It means atoms do not stay long to be stimulated. As a result, they undergo spontaneous emission and rapidly return to the ground level; thereby population inversion could not be established. In other words, it is necessary that excited state have a longer lifetime. A Meta stable state is such a state. Metastable can be readily obtained in a crystal system containing impurity atoms. These levels lie in the forbidden gap of the host crystal.

Developed by Therithal info, Chennai. Toggle navigation BrainKart. Posted On : We know that, when light is absorbed by the atoms or molecules, then it goes from the lower energy level E1 to the higher energy level E2 and during the transition from higher energy level E2 to lower energy level E1 the light is emitted from the atoms or molecules.

Absorption b. Spontaneous emission c. Stimulated Emission Absorption: An atom in the lower energy level or ground state energy level E 1 absorbs the incident photon radiation of energy hv and goes to the higher energy level or excited level E 2 as shown in figure.

E-mail: carlos hbar. This physical picture suggests that Einstein gravity is an emergent low-energy long-distance phenomenon that is insensitive to the details of the high-energy short-distance physics. PACS: Jb; In this essay we will take a careful look at this idea, and highlight some of the possibilities, problems, and opportunities that such a situation entails. We were led to these notions via current research on analog models of gen- eral relativity [1].

Because of the extreme difficulty and inadvisability of working with intense gravitational fields in a laboratory setting, interest has now turned to investigating the possibility of simulating aspects of general relativity — though it is not a priori expected that all features of Einstein gravity can successfully be carried over to the analog models. Numerous rather different physical systems have now been seen to be useful for devel- oping analog models of general relativity.

A literature search as of March finds well over a hundred scientific articles devoted to one or another aspect of analog gravity and effective metric techniques. Typically these are models of general relativity, in the sense that they provide an effective metric and so generate the basic kinematical background in which general relativity resides; in the absence of any dynamics for that effective metric we cannot really speak about these systems as models for general relativity.

However, as we will discuss more fully bellow, quantum effects in these analog models might provide of some sort of dynamics resem- bling general relativity.

Remember that for mechanical systems with a finite number of degrees of freedom small oscillations can always be resolved into normal modes: a finite collection of uncoupled harmonic oscillators. For a classical field theory you would also expect similar behaviour: small deviations from a background solution of the field equations will be resolved into travelling waves; then these travelling waves can be viewed as an infinite collection of harmonic oscillators, or a finite number if the field theory is truncated in the infra-red and ultra-violet, to which you can then apply a normal mode analysis.

In many cases the answer is definitely yes: Linearization of a Lagrangian-based dynamics, or linearization of any hyperbolic second-order PDE, will automatically lead to an effective Lorentzian geometry that governs the propagation of the fluctuations. Above : Illustration of the observed black body radiation spectrum for two different temperatures. The dots indicate experimental measurements of the amount of energy, or intensity of radiation, emitted at a given wavelength, whereas the predictions from wave theory are shown by the green curves.

Wave theory made reasonably good predictions for long wavelengths, but utterly failed for short wavelengths, for which the theory predicted that energies should tend toward infinity as the wavelength approached zero. This clearly untenable prediction was known as the "ultraviolet catastrophe". Note that the visible range of EM radiation is at the far left of each graph, from 0.

Planck's hypothesis led to a satisfactory prediction of blackbody radiation intensities for all wavelengths. For certain materials, especially metals, an electric current can readily be measured upon illumination of its surface, under vacuum, with light of sufficiently short wavelength. What occurs here is that light provides the energy to ionize the material. The chemical equation representing this process is.

This helps clarify why the photoelectric effect was first observed for metals, as they have the lowest ionization energies , although, in principle it can be observed in any material as long as sufficiently short EM wavelengths are employed. The electrons produced and measured as current are essentially the same phenomena as Thomson's cathode rays, but the excess kinetic energy of the ejected electrons, or photoelectrons, showed an interesting dependence on the wavelength of the illuminating light.

First of all, no photoelectrons are observed until the frequency of light reaches a minimum, threshold value. Since energy is conserved, the energy from the incident light must be equal to the sum of the ionization energy of A plus the kinetic energy of the photoelectron. Note that in some accounts of the photoelectric effect e.

Skip to main content. Search SpringerLink Search. Abstract The stationary probability distribution of the one-step process corresponding to Einstein's theory of absorption and emission of radiation is derived. References Ehrenfest, P. Google Scholar Einstein, A. Google Scholar Gauss, K. Google Scholar Heitler, W. Google Scholar Keynes, J. Google Scholar Lavenda, B.

Google Scholar Planck, M. Google Scholar Van Kampen, N. Google Scholar Download references. Authors B.