(2) The neutrons produced in a reactor are known as thermal neutrons, because their kinetic energies have been reduced (by collisions) until K = 3kT, where T is room temperature (293 K). (a) What is the kinetic energy of such neutrons? (b) What is their de Broglie wavelength? Because this wavelength is of the same order as the lattice spacing of the atoms of a solid, neutron diffraction (like X-ray and electron diffraction) is a useful means of studying solid lattices.
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- (a) The lifetime of a highly unstable nucleus is 10−20 s . What is the smallest uncertainty in its decay energy? (b) Compare this with the rest energy of an electron.A thermal neutron has a speed v at temperature T = 300 K and kinetic energy m,v² m = 3KT. Calculate its deBroglie wavelength. State whether a beam of these neutrons could be diffracted by a crystal, and why? (b) Use Heisenberg's Uncertainty principle to estimate the kinetic energy (in MeV) of a nucleon bound within a nucleus of radius 10-15 m.(a) The lifetime of a highly unstable nucleus is 10-12 s. What is the smallest uncertainty (in ev) in its decay energy? ev (b) What is the ratio of this energy, AE, to the rest energy of an electron, Erest? ΔΕ Erest
- Nuclear radii may be measured by scattering high-energy electrons from nuclei. (a) What is the de Broglie wavelength for 172 MeV electrons? (b) Are these electrons suitable probes for this purpose? (a) Number i 9.37e-14 Units fm (b) yesNote that a thermal neutron is a neutron whose most probable kinetic energy is ~ 0.025 eV. What is the de Broglie wavelength of a thermal neutron? (Hint: Neutrons in a nuclear reactor are thermalized in order to enhance their probability of fissioning 235U.)T1
- What is the kinetic energy of each electron in a beam of electrons if the beam produces a diffraction pattern of a crystal which is similar to that of a beam of 1.00 eV neutrons? (knowing that electron mass is 9.11*10^-31 kg and neutron mass is 1.67*10^-26 kg). What are the specific equations that are being used in this problem?Rudolf Mössbauer discovered in 1957 that transitions from an excited nuclear state occur with negligible nuclear recoil when the nucleus is embedded in a large crystal lattice because the entire lattice absorbs the recoil. A transition like that in 191Ir from the 129- keV excited state to the ground state has a lifetime of 1.9 x 10-10 s. (a) Determine the energy width of the decay. (b) Similarly, if the photon is absorbed by 191Ir embedded in a crystal, the recoil is negligible. However, even a slight motion of the absorber will lead to a Doppler shift suffi cient to destroy the resonance absorption. Calculate the speed necessary to shift the energy absorption by 5Γ, where Γ is the nuclear decay width. This effect is called the Mössbauer effectc) Electrons of energy 1 GeV are scattered off the nuclei, 64Cu, 108Ag and 197 Au. The first diffraction minima are observed at scattering angles 7.4°, 6.2° and 5.00 for the three nuclei respectively. Write down the relation between the momentum transferred in the scattering process and the scattering angle. Hence make an estimate of the radii of the three nuclei and comment on the dependence of the radii on the atomic mass numbers. [ 11]
- Q#1 (a)(i)A thermal neutron has a speed v at temperature T= 300 K and kinetic energy m-: 3 KT Calculate its deBroglie wavelength. State whether a beam of these neutrons could be diffracted by a crystal, and why? (ii) Explain in detail two Heisenberg uncertainty principles. Apply Uncertainty principle to estimate the kinetic energy (in MeV) of a nucleon bound within a nucleus of radius 10 15 m. (b) A metal surface is illuminated by 8.5 x 10'* Hz light emits electrons whose maximum energy is 1.97 eV. The same surface is illuminated by 12 x 104H2 light emits electrons whose maximum energy is 0.53 eV. Find the Planck's constant and work function of the surface. idth nf one dimensional hox in which a proton has an energy of 400,000 eV in its first excitedThe distance between atoms in a crystal of NaCl is 418.5 nm. The crystal is being studied in a neutron diffraction experiment. At what speed (in m/s) must the neutrons be moving so that their de Broglie wavelength is the same length as the spacing between the atoms? (Assume the neutrons are non-relativistic.)a) Calculate the uncertainty in momentum for a proton confined to a nucleus of radius 6.0fm b) What is the kinetic energy of a photon with that momentum. c) Suppose a photon in that nucleus had a kinetic energy of 5.6MeV. If the photon were represented by a de Broglie wave, how many wavelengths could fit across the diameter of the nucleus?