Question 32: NCERT Solutions for 12th Class Physics: Chapter 11-Dual Nature of Radiation and Matter
(a) Obtain the de Broglie wavelength of a neutron of kinetic energy 150 eV. An electron beam of this energy is suitable for crystal diffraction experiments. Would a neutron beam of the same energy be equally suitable? Explain. (mn = 1.675 × 10-27 kg)
(b) Obtain the de Broglie wavelength associated with thermal neutrons at room temperature (27°C). Hence explain why a fast neutron beam needs to be thermalised with the environment before it can be used for neutron diffraction experiments.
Solution:
(a) Let us first calculate the wavelength of matter wave associated with neutron of kinetic energy 150 eV.
As the inter atomic spacing (1 A= 10-10 m) is about hundred times greater than this wavelength, so a neutron beam of 150 eV energy is not suitable for diffraction experiments.
(b) Average kinetic energy of a neutron at absolute temperature T is
As this wavelength is comparable to inter atomic spacing (= 1 A) in a crystal, so thermal neutrons can be used for diffraction experiments. So high energy neutron beam should be first thermalised before using it for diffraction.
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NCERT Solutions for 12th Class Physics: Chapter 11-Dual Nature of Radiation and Matter