Planck Einstein relationship

The formation of ions in a mass spectrometer ion source can be accomplished by a variety of ionization methods. Photoionization of a molecule or atom involves the absorption of a vacuum ultraviolet (VUV) or soft X-ray photon. Depending on the wavelength ( l) of the photon, whose energy E is given by the Planck-Einstein relationship,... 

At a quantum-mechanical level, there is a simple relationship that ties together the twin modes by which we visualize photons we say that the energy of a photon particle is E and the frequency of a light wave is v. The Planck-Einstein equation, Equation (9.3), says... 

Generally, ions can be transported by three mechanisms diffusion, conduction and convection. To / z F these transport components contribute by -DVc, -D z Fc Vyf /RT and c v, respectively, where according to the Nernst-Einstein relationship, see 14.3.55), the ion mobility is written as I z l FD / FT. In Volume I we derived the Nemst-Planck equation for the corresponding fluxes, see 11.6,7.1 and 2] and 13.13.12). In the present context we write the Nemst-Planck equation as... 

The general form of this relationship agrees with the well-known Nernst-Planck-Einstein formula, according to which the diffusion coefficient is given by the relation... 

Notice the similarity of this relationship with the Planck-Einstein formula for the energy of a photon, Eq. (14.4-8) ... 

The energy of a photon of light is related to its frequency v by the relationship E = hv, where h is Planck s constant. Blue light has an energy of about 250 kJ (60 kcal) per einstein (an einstein is a mole of photons). 

The photoelectron effect was first discovered by Henrich Hertz [11] in early 1887 in order to verify the implications of Maxwell s theory and relations. Hertz noticed a spark of light on metal contacts in electrical units when exposed to light. The dawn of a new era actually came in 1905. Albert Einstein brilliantly utilized Planck s new quantum energy concept to explain how low radiation intensity and high frequency can actually eject electrons from a metal piece. The converse failed to produce any electrons. Max Planck received the Nobel Prize on quantization of energy [12] in 1918 and Einstein received the Nobel Prize on photoelectric effect in 1921. The single relationship proposed so long ago by Einstein is still today the fundamental basis of photoelectron spectroscopy,... 

In order for a photochemical reaction to occur the radiation must be absorbed, and with the advent of the quantum theory it became possible to understand the relationship between the amount of radiation absorbed and the extent of the chemical change that occurs. It was first realized by A. Einstein (1879-1955) that electromagnetic radiation can be regarded as a beam of particles, which G. N. Lewis (1875-1940) later called photons each of these particles has an energy equal to /iv, where v is the frequency of the radiation and h is the Planck constant. In 1911 J. Stark (1874-1957) and independently in 1912 Einstein proposed that one photon of radiation is absorbed by one molecule. This relationship, usually referred to as Einstein s Law of Photochemical Equivalence, applies satisfactorily to electromagnetic radiation of ordinary intensities but fails for lasers of very high intensity. The lifetime of a moleeule that has absorbed a photon is usually less than about 10 sec, and with ordinary radiation it is unlikely for a molecule that has absorbed one photon to absorb another before it has become deactivated. In these circumstances there is therefore a one-to-one relationship between the number of photons absorbed and the number of excited molecules produced. Because of the high intensity of lasers, however, a molecule sometimes absorbs two or more photons, and one then speaks of multiphoton excitation. 

Since we are interested mainly in the roots of spontaneous emission, we shall quantize the electromagnetic field because we know that the semi-classical description where the atom is quantized and the field is classical, does not provide aity spontaneous emission it is introduced phenomenologically by a detailed balance of the population of the two-states atom and comparison with Planck s law. This procedure introduced by Einstein gave the well-known relationship between induced absorption (or emission), and spontaneous emission probabilities, the B12, B21 and A21 coefficients, respectively, but caimot produce the coherent aspect and its link with spontaneous emission. 

In this equation, the slope h is Planck s constant, which is equal to 6.6254 x joule second, and the intercept -w is the work function, a con.stant that is characteristic of the surface material and represents the minimum energy binding electron in the metal. Approximately a decade before Millikan s work that led to Equation 6-16, Einstein had proposed the relationship between frequency v of light and energy E as embodied by the now famous equation... 

Alternatively, Einstein s relationship relates the wavelength of light A to the linear momentum p according to X = h/p (where h = 6.626 x 10 [Ls] is the Planck constant). De Broglie applied this to the material wave of the mass m to obtain... 

By 1925 it was realized that the classical ideas that described matter didn t work at the atomic level. Some progress—Planck s quantum theory, Einstein s application of quantum theory to light, Bohr s theory of hydrogen, de Broglie s relationship—had been made, but it was all very specific and not generally applied to atoms and molecules. 

Forcing B21/B12 = 1 (which has some basis when the temperature-dependent terms are considered to cancel) [36] brings Equation 3.38 in line with Planck s formula given in Equation 3.33 (but multiplied with (hv) since in Equation 3.33 (pv) is defined as number of modes with energy (hv). Equating Equations 3.33 and 3.38 leads to a relationship between the Einstein s A21 (associated with spontaneous emission) and B21 (associated with stimulated emission) coefficients as... 

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