Worked examples—calculating momentum transfer

Here we work through two straightforward examples of the calculation of momentum transfer. The first refers to a t3q)ical problem 

Incident neutrons, of fixed energy 1000 cm, are used to excite a vibrational transition at 560 cm and the detector is at a scattering angle, 6, of 30° to the incident beam direction. The final energy is  

Here we have used the well-known Bragg s Law [1] to calculate the final wavelength. 

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The approximation works very well within the limits originally set for its use [1]. However, in the molecular spectroscopy of hydrogenous molecules a further version of the approximation is made. Here the cross section used in the calculation of the observed intensities is the total bound scattering cross section of each atom and the dynamics are always treated as incoherent, irrespective of the momentum transferred. This is discussed further with specific examples in 11.1. 

Equation (2.7) is often encountered in thermodynamics the work described by this equation will be referred to as Pv work. On a molecular scale, the energy transfer by Pv work can be understood in terms of momentum transfer of the molecules in the system when they bounce off the moving boundary, as discussed in Section 1.3. A piston-cylinder assembly is a common system that is used to obtain work (e.g., in your automobile). Example 2.3 illustrates how work is calculated for such a system. 

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