Doppler effect equation

In order to dissipate the recoil energy Mossbauer was the first to use atoms in solid crystal lattices as emitters and also to cool both emitter and absorber. In this way it could be shown that the 7-ray emission from radioactive cobalt metal was absorbed by metallic iron. However, it was also found that if the iron sample were in any other chemical state, the different chemical surroundings of the iron nucleus produce a sufficient effect on the nuclear energy levels for absorption no longer to occur. To enable a search for the precisely required absorption frequency, a scan based on the Doppler effect was developed. It was noted that a velocity of 102 ms-1 produced an enormous Doppler shift and using the same equation (7) it follows that a readily attainable displacement of the source at a velocity of 1 cms-1 produces a shift of 108 Hz. This shift corresponds to about 100 line-widths and provides a reasonable scan width. 

Explain what is meant by the Doppler effect. Rationalize why Doppler broadening increases with increasing temperature and decreasing mass in Equation 21-5. 

THEORY OF ELECTROMAGNETIC WAVE PROPAGATION, Charles Her-ach Papas. Graduate-level study discusses the Maxwell field equations, radiation from wire antennas, the Doppler effect and more, xiii + 244pp. 5b x 8b. 

The relativistic equation [8] for the Doppler effect on an emitted photon gives the observed frequency v for a closing velocity v as... 

In a QELS experiment, a monochromatic beam of light from a laser is focused on to a dilute suspension of particles and the scattering intensity is measured at some angle 0 by a detector. The phase and the polarization of the scattered light depend on the position and orientation of each scatterer. Because molecules or particles in solution are in constant Brownian motion, scattered light will result that is spectrally broadened by the Doppler effect. The key parameter determined by QELS is the diffusion coefficient, D, or particle di sivity which can be related to particle diameter, d, via the Stokes-Einstein equation ... 

Since the integration of the kinetics equations [Eqs. (A2.1)and(A2.2)] yields energy density, a relation between energy density and temperature is needed to determine the Doppler effect. This relation (given in Appendix B for UO2) can be conveniently curve-fitted by an expression of the form... 

Note Equations (3.38) and (3.39) describe the linear Doppler shift. For higher accuracies, the quadratic Doppler effect must also be considered (Sect. 14.1). 

Dynamic light-scattering, sometimes called quasi-elastic light scattering or photon correlation spectroscopy, can be used to measure the diffusion coefficients of polymer chains in solution and colloids, a kind of Doppler effect see Section 3.6.6. In a dilute dispersion of spherical particles, the diffusion coefficient D is related to the particle radius, a, through the Stokes-Einstein equation. 

To facilitate modeling of the metal fuel used in KALIMER, several reactivity models are modified in SSC-K code. For neutronic calculations, SSC-K uses point kinetic equations with detailed reactivity feedback from each channel. Reactivity effects are required both for transient safety analysis and for control requirements during normal operation. Reactivity changes are calculated for control rod scram, the Doppler effect in the fuel, sodium voiding or density changes, fuel thermal expansion, core radial expansion, thermal expansion of control rod drives, and vessel wall thermal expansion. Figure 5 shows the components of reactivity feedback considered in the KALIMER core. The effect of fuel expansion becomes more significant when metallic fuel is used. 

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