Question

1. (a) Consider a thermal neutron, that is, a neutron with speed v corresponding to the average thermal energy at the temperature T = 300K. Is it possible to observe a diffraction pattern when a beam of such neutrons falls on a crystal? Justify your answer with a calculation. (b) In a large accelerator, an electron can be provided with an energy over 1GeV = 109eV. What it is the de Broglie wavelength corresponding to such electrons?

Answer 1

a) energy of thermal neutron = KT,

where K=boltzmann constant = 1.38x10^-23 m²kgs^-2K^-1

and T=300K

so E= 1.38x10^-23m²kgs^-2K^-1 x 300K =4.14x10^-21 J

wavelength, =hc/E= 6.626x10^-34kgm²s^-1x3x10⁸ms^-1/(4.14x10^-21J)=4.8x10^-5 m.

size of a crystal is generally in microns. Since wavelength is greater than size of crystal, hence diffraction is not possible.

b) Given, energy E= 10⁹eV= 10⁹ x 1.6x10^-19J (since 1eV= 1.6x10^-19J)

=1.6x10^-10 J

wavelength, =hc/E=6.626x10^-34kgm²/s x 3x10⁸m/s /(1.6x10^-10J) =1.24x10^-15 m

answered by: anonymous