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- 4. From van der Waals equation, using (3²0) T (2²) ₁ = 0 Ꭲ a = ²-RTcVmc 8 Show that = and Tc = b = 8a 27Rb ; Vmc 3 5. Show that the Lennard-Jones energy (i) Pc = a 276² ---(ii) has a minimum value equal to - at r = 2¹/66. Vmc = 3b 12 U₁₁ (r) = 4 € [¹ - (-)]30 DENAKER What three properties of the nucleus can be deduced from the Rutherford scattering experiment? Explain your answer. MA radioactive nucleus at rest decays into a second nucleus, an electron, and a neutrino. The electron and neutrino are emitted at right angles and have Part A momenta of 9.25×10-23 kg · m/s and , 6.35x10-23 kg m/s respectively. Determine the magnitude of the momentum of the second (recoiling) nucleus. ? Pnucleus = kg · m/s Submit Request Answer
- Q4. a) Alpha decay is a two body final state process, in which a nucleus 4 AXz →(A−4) Y(z−2) +¹ He₂ + Qa If the masses of the atoms of the parent and the daughter nuclei are (roughly) Au, and (A — 4)u and that of the a particle is 4u, determine the relation between the kinetic energy To of the a particle and Qa. b) Explain why in case of even A nuclei, it is possible to have two most stable isobars, where as for odd A nuclei, there can be only one most stable isobar. c) Construct the mass parabolas for A = 101, and identify the most stable isobars. d) Construct the mass parabolas for A = 106, and identify the two most stable isobars.In a Geiger tube, the total time taken to create a pulse and then let the electrons recombine with the ions to again form a neutral state is about how many µ s O 300 C 1 OO O 1000 303
- Q1a) Particles with MeV energy b) Find the maximum approach distances of 8 MeV energetic particles to the gold nucleusK:43) Assuming only maximum energy transfers occur for 12C ions with electrons in a material, determine the number of collisions required for a 100 MeV 12C ion to go to energy below 10 MeV.
- In a scattering experiment, an alpha particle A is projected with the velocity up = -(600 m/s)i + (750 m/s)j - (800 m/s)k into a stream of oxygen nuclei moving with a common velocity vo = (630 m/s)j. After colliding successively with nuclei B and C, particle A is observed to move along the path defined by the Points A₁(280, 240, 120) and A2(360, 320, 160), while nuclei B and Care observed to move along paths defined, respectively, by B₁(147, 220, 130), B2(114, 290, 120), and by C₁(240, 232, 90) and C₂(240, 280, 75). All paths are along straight lines and all coordinates are expressed in millimeters. Knowing that the mass of an oxygen nucleus is four times that of an alpha particle, determine the speed of each of the three particles after the collisions. The speed of particle A is The speed of particle B is The speed of particle Cis m/s. m/s. m/s.3. A beam of helium-3 atoms (m = 3.016 u) is incident on a target of nitrogen-14 atoms (m = 14.003 u) at rest. Dur- ing the collision, a proton from the helium-3 nucleus passes to the nitrogen nucleus, so that following the col- lision there are two atoms: an atom of "heavy hydro- gen" (deuterium, m = 2.014 u) and an atom of oxygen-15 15.003 u). The incident helium atoms are moving at (m a velocity of 6.346 × 10° m/s. After the collision, the deu- terium atoms are observed to be moving forward (in the same direction as the initial helium atoms) with a velocity of 1.531 x 10' m/s. (a) What is the final velocity of the oxygen-15 atoms? (b) Compare the total kinetic energies before and after the collision.14:56 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)…