Because electron is lighter that the nuclei by a factor of 2000 and there are different timescales for nuclear and electron motions, based on Born-Oppenheimer approximation the two motions can be decoupled. Then nuclei may be treated as stationary while electrons move around them. Select one: True False
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Because electron is lighter that the nuclei by a factor of 2000 and there are different timescales for nuclear and electron motions, based on Born-Oppenheimer approximation the two motions can be decoupled. Then nuclei may be treated as stationary while electrons move around them.
Answer: The given statement is True.
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- 2. Protons with energy 1.0MeV scatter off a fixed spherical potential whose range is known to be a = 10-¹3 cm. The total elastic scattering cross section o and the differential cross section do/d are measured to a precision of about one percent. (a) Assuming that the energy is not near any resonance of the potential, show that the only phase shifts that can be reliably determined from the data are do and 6₁. (b) Given the experimental value o = = (10.5 ± 0.1) × 10-26 cm² and the values for do/dn listed in the table (one percent accuracy), determine do and 8₁. (Do not worry about the errors in your values for do or $₁. (deg) | dold_2 (10-26 cm²) O 1.232 45 90 135 180 1.103 0.823 0.585 0.49914:56 Sun 19 May 2 of 8 SECTION A qmplus.qmul.ac.uk Answer ALL questions in Section A Expect to use about half a page for each section A solution. Question A1 Give the term used in condensed matter physics for each of the following: a) The centre of the Brillouin zone [1 mark] b) A method for generating a neutron beam by bombarding a heavy metal target with protons [1 mark] c) The group of atoms associated with each lattice point in a crystal structure d) The Fourier transform of the lattice of a crystal [1 mark] [1 mark] e) A vibrational mode whose frequency tends to zero as the wavevector approaches zero [1 mark] f) A model of electronic structure in which electrons move in a weak, periodic potential and do not interact with each other by the Coulomb force [1 mark] Question A2 The body-centred cubic structure is common among metals. a) How many nearest neighbours has each atom in this structure? Give the nearest-neighbour distance in terms of the unit cell parameter a. [2 marks] b)…An isotope of beryllium (atomic mass of 7.017 u) emits a y ray and recoils with a speed of 1.54 × 104 m/s. Assuming that the isotope is stationary to begin with, find the wavelength of the y ray. min Before emission VBe After emission
- If an average of 10000 photons are detected per mm2 the probability of detecting between 9800 and 10200 counts in any exposed mm2 is approximately: a) 59 b) 75 c) 89 d) 95 e) 99Whilst the vast majority of alpha particles passed through the gold foil with little or no deviation, a small fraction of them were scattered through larger angles, some even backwards. Commenting on these findings Rutherford wrote “It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you.” Explain the implications of Rutherford’s results for models of atomic structureProve using the uncertainty principle that an electron cannot exist inside a nucleus.
- 121. (a) Estimate the ground state energy of an electron in an atom by treating it as if it were in an infinite square well (1D) of width equal to an atomic diameter of 10-10 m. (b) Estimate the ground state energy of an a particle in a nucleus by treating it as if it were in an infinite square well (1D) of width equal to a nuclear diameter of 10-14 Estimate the ground state energy of an electron in a nucleus by treating it as if it were in an infinite square well (1D) of width equal to a nuclear diameter of 10¬14 m. m. (c)L: 3. What would have happened if neutrons had been used in Rutherford experiment? Explain your answer.During nuclear decay a^238 U atom can break apart into a helium -4 atom and one other atomAssuming that no subatomic particles are destroyed during this decay process, what the other element produced ?