Obtain the de-Broglie wavelength associated with thermal neutrons at room temperature (27o C). hence explain why a fast neutron beam needs to be thermalised with the environment before it can be used for neutron diffraction experiments. The mass of neutron is and the Boltzmann constant .
The kinetic energy of a thermal neutron at absolute temperature T is given by
Here T = 27o C = 300 K.
The de-Broglie wavelength of these neutrons is given by
= 1.45 Å.
Thus, ‘thermal’ neutron have wavelength of the order of interatomic spacing and hence are suitable for diffraction experiments. Fast neutrons will possess wavelength quite small as compared to interatomic spacing and hence will not be suitable for diffraction experiments. Thus, for neutron diffraction experimants, fast neutron beam needs to be thermalised.
The distance of the closest approach of an alpha particle fired at a nucleus with kinetic energy K is r0. The distance of the closest approach when the alpha particle is fired at the same nucleus with kinetic energy 2K will be
Calculate de-Broglie wavelength for electron and proton moving with same speed of 105 ms–1.
Calculate the de-Broglie wavelength of a proton of kinetic energy 500 eV. The mass of proton is .
For what kinetic energy of a neutron will the associated de-Broglie wavelength be ? The mass of neutron is .
A particle is moving three times as fast as an electron. The ratio of the de-Broglie wavelength of the particle to that of the electron is . Calculate the particle’s mass and identify the particle.
An electron and a photon each has a wavelength 1.00 nm. Find their momenta. Given,
Crystal diffraction experiments can be performed using X-rays or electron accelerated through appropriate voltage. Which probe, an X-ray photon or the electron, has greater energy? Take the wavelength of either probe equal to 1 Å, which is of the order of interatomic spacing in the crystal lattice. Mass of electron is .
Obtain de-Broglie wavelength of a neutron of kinetic energy 150 eV. As we have seen in last example, an electron beam of 150 eV energy is suitable for crystal diffraction experiments. Would a neutron beam of the same energy by equally? Explain. The mass of neutron is .
X-rays of wavelength 0.82 Å fall on a metal plate. Find the smallest wavelength associated with the emitted photoelectrons. The work function of the metal is zero.
Calculate the de-Broglie wavelength of an electronic energy 100 eV.