Planck relationship

As outlined in Chapter 5, radiant emission from atoms and molecules occurs when an electron in a higher energy orbital around the nucleus of an atom (or nuclei in the case of molecules), drops into a lower energy orbital, usually closer to the nucleus. The difference in energy between the two states of the electron appears as energy according to the Planck relationship (1900) given by equation (8.1),... 

For light to induce a transition between energy levels of an atom or molecule, it is necessary that the frequency of the hght and the energy difference between the levels satisfy, at least approximately, the Planck relationship ... 

LI The Planck Distribution of Black-body Radiation. The Planck relationship between the energy of the photon and the frequency of monochromatic light leads to the equation of distribution of the intensity of light as a function of frequency (or wavelength)... 

The numerical constant in Equation 5.28 is the same as h in the Planck relationship. So the assumption that electrons have circular orbits with angular momentum restricted to multiples of h gave the correct emission spectra for hydrogen. We could also start from the assumption L = nh, rearrange Equation 5.20, and derive R ... 

The energies necessary for electronic excitation of molecules are comparable to those necessary for the excitation of the valence electrons of atoms—that is, 1.5 to 8.0 electron volts. From the Planck relationship (p. 6), the student may verify (Exercise 10) the relationship between the energy change AE associated with a process and the wavelength, X, of the resulting photon ... 

Using the Planck relationship, show that the-energy change giving rise to a radiation is related to the wavelength of radiation ... 

In 1924, Louis de Broglie, as a young doctoral student, investigated some of the consequences of relativity theory. It was known that for electromagnetic radiation, the energy, E, is expressed by the Planck relationship,... 

Ail interpretations based on the assumptions with respect to use of the Nernst-Planck relationships are, however, subject to sizable uncertainty because the constancy attributed to the diffusion coefficients used in these relationships is susceptible to sizable variability. Bead volume variations are ignored. This leads to variations in ion mobilities which dictate changes in the diffusion coefficients of the Nemst-Planck relationships. Sizable divergence of measurements firom prediction can be expected on this basis. Even in rigid ion exchangers such as zeolites the difference in size of the counterions exchanged usually affects their mobility, and so leads to variations of the diffusivities [3]. 

As in other types of spectroscopy, transitions between energy states can be brought about by absorption or emission of electromagnetic radiation of a frequency i that corresponds in energy to AF. Thus, by substituting the Planck relationship E - /iv into Equation 19-4. we obtain the frequency of the radiation required to bring about the transition... 

We next use the Planck relationship, E = hv, (Equation 6.2) to calculate the fiequency v of a photon that has this amount of energy ... 

In the quantum theory of radiation [93], all electromagnetic radiation are considered to be beams of particles. As stated above, they are called photmis. Each photmi has an energy E that is defined by the Planck relationship,... 

We can write expressions for E and E +i, subtract them, and then substitute the values for h, m, and L. The ground state corresponds to n = 1, and the first excited state corresponds to = 2. Finally, we can calculate the wavelength of the photon from the Planck relationship and c = kv. 

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