A Deuterium nucleus is accelerated to a velocity v = 0,9c on a trajectory described by the equation y = 0,49 x2 m. Determine the radiated power and the periodic loss of energy suffered by the accelerated particle.
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- When an alpha particle collides elastically with a nucleus, the nucleus recoils. Suppose a 6.00 MeV alpha particle has a head-on elastic collision with a silver-108 nucleus that is initially at rest. (a) What is the kinetic energy of the recoiling nucleus? MeV (b) What is the kinetic energy of the rebounding alpha particle? MeVWhat is the energy of H2 trapped in a zeolite, which can be modeled by a particle in a cube given nX = 10, nY = 10, nZ = 10 and LX = LY = LZ = 10−9 m.One of the bound states of positronium has a lifetime given in natural units by T = 2/mas where m is the mass of the electron and a is the fine structure con- stant. Using dimensional arguments introduce the factors ħ and c and determine T in seconds.
- (a) Show that the speed of an electron in the nth Bohr orbit of hydrogen is αc/n, where α is the fine structure constant, equal to e2/4πε0ħc. (b) What would be the speed in a hydrogen like atom with a nuclear charge of Ze?Alpha particles of kinetic energy 5.4 MeV are incident at a rate of 3.2 x 107 per second on a copper foil of thickness 3.2 x 10-6 m. A circular detector of diameter 1.0 cm is placed 13 cm from the foil at an angle of 30° with the direction of the incident alpha particles. At what rate does the detector measure scattered alpha particles? (The molar mass of copper is 63.5 g/mol and its density is 8.9 g/cm³.) Additional Materials BookFind the fraction of 7.7-MeV α particles that is deflected at an angle of 90° or more from a gold foil of 10 -6 m thickness.
- The speed of the alpha particles in Rutherford experiment was 0.01c, the scattering material was gold. What was the impact parameter of the alpha particle scattered by 60°?An electron is in the ground state of the tritium atom for which the nucleus consists of one proton and two neutrons. Suppose the nucleus instantaneously changes into He”, consisting of two protons and a neutron due to a nuclear reaction. What is the probability that the electron is found in the ground state of the Heion? The is sometimes called the “sudden approximation”In a Rutherford scattering experiment, an a-particle (charge = +2e) heads directly toward a gold nucleus (charge = +79e). The α-particle had a kinetic energy of 5.0 MeV when very far (r→ ∞) from the nucleus. Assuming the gold nucleus to be fixed in space, determine the distance of closest approach. Hint: Use conservation of energy with PE =kq1q2/r.
- A beam of α particles of kinetic energy E = 10 MeV and intensity I = 1 μ A hits a lead target [A = 207, Z = 82, ρ = 1.14 x 104 kg m-3] of thickness t = 0.2 mm. We locate a counter of area S = 1 cm2 at a distance of l = 0.5 m beyond the target at the angle θ = 40°. Neglecting, when necessary, the variation of the angle on the detector find: (a) the number of incident particles per second Ri, (b) the solid angle ΔΩ under which the target sees the detector, (c) the differential cross-section at the detector, and (d) how many hits the detector counts per second.J 5 Question 2 (1) Assume that the average energy of β-rays (electrons) emitted from the S-ray source is 0.8 MeV, and the average ionization energy of gas molecules (atoms) in the GM counter tube is about 30 eV. Find the number of gas molecules ionized when one electron enters the GM tube (1MeV = 10°eV). (2) Assuming that the electrons and cations thus generated are attracted to the electrode as they are, what is the total amount of negative charge generated by ionization in C (coulombs)? (3) If this ionization takes 10-4s, what is the current flowing through the anode?Find the relation between spontaneous emission lifetime and cross section for a simple atomic transition.