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(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 experment. Would a neutron beam of the same energy be equally suitable? Explain (m_(n)=1.675xx10^(-27)kg) (b) Obtain the de-Broglie wavelength associated with thermal neutrons at room temperatuer (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. |
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Answer» Solution :(a) We know the mass of NEUTRON `m=1.675xx10^(-27)KG` and kinetic energy of given neutron `K=150eV=150xx1.6xx10^(-19)J=2.4xx10^(-17)J` `therefore`de-Broglie WAVELENGTH `lamda=(h)/(sqrt(2mK))=(6.63xx10^(-34))/(sqrt(2xx1.675xx10^(-27)xx2.4xx10^(-17)))=2.34xx10^(-12)m` The neutron beam of energy `150eV` (i.e., of wavelength `2.34xx10^(-12)m`) is not SUITABLE for crystal diffraction experiment because this wavelength is nearly `(1)/(100)th` time the inter atomic distance in the crystal (which is of the order of `10^(-10)m`). (b) As room temperature `T=27^(@)C=300K`, hence, kinetic energy of thermal neutrons `K=(3)/(2)k_(B)T=(3)/(2)xx1.38xx10^(-23)xx300J` `therefore`de-Broglie wavelength of neutrons `lamda=(h)/(sqrt(2mK))=(6.63xx10^(-34))/(sqrt(2xx1.675xx10^(-27)xx(3)/(2)xx1.38xx10^(-23)xx300))=1.45xx10^(-10)m`. As this wavelength is comparable to the inter-atomc spacing in crystals, neutron beam of thermal energy can be successfully used for crystal diffraction experiments. hence, for neutron diffraction experiments we would first thermalise neutrons with the environment. |
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