Modern Physics, 3rd Edition
3rd Edition
ISBN: 9780534493394
Author: Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher: Cengage Learning
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Chapter 7, Problem 16P
To determine
The smallest values of energy and velocity particle permitted for the
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Consider a proton confined within typical nuclear dimensions of 5×10^(−15) m. Estimate the minimum kinetic energy of the proton. Repeat this calculation for an electron confined within typical nuclear dimensions. Comment briefly on the physical significance of your results, given that the nuclear binding energy for a proton is typically in the range 1−10 MeV
1. Consider an electron confined in a region of nuclear dimensions (about 5 fm). Find its minimum
possible kinetic energy in MeV. Treat this problem as one-dimensional, and use the relativistic relation
between E and p. Give your answer to 2 significant figures. (The large value you will find is a strong
argument against the presence of electrons inside nuclei, since no known mechanism could contain an
electron with this much energy.)
Let u,= 0.02 cm 1 and u, = 0.04 cm be the partial linear attenuation
coefficients in the slab shown in the figure below. Let L = 5 cm and
No = 106 particles. How many particles N, are transmitted, and how
%3D
many are absorbed by each interaction process in the slab?
dt
Uncharged partleles
No
N,
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Modern Physics, 3rd Edition
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- The Yukawa potential adds an exponential term to the long-range Coulomb potential, which greatly shortens the range of the Coulomb potential. It has great usefulness in atomic and nuclear calculations. Voro .To = k еа r r V(r) e ro Find a particle's trajectory in a bound orbit of the Yukawa potential to first order inr/a.arrow_forwardA neutron of mass m of energy E a,V(x) = +V ) II. Estimate the kinetic energy of the nucleons when they reach region II.arrow_forwardPROBLEM 2: Consider neutrons slowing down by elastic scattering from 1.0 MeV to 0.025 eV in large spatially homogeneous regions. (a) Estimate the number of scattering events required for these neutrons to slow down in large regions of hydrogen (A = 1), iron (A = 56), and uranium (A = 238). (b) Suppose that in each neutron-nucleus collision, the probability that a neutron is captured is 0.001 (independent of energy). Estimate the probability that these neutrons in regions 238) will not be captured while of hydrogen (A 1), iron (A 56), and uranium (A slowing down from 1.0 MeV to 0.025 e V. Note: In practice, the probability that a neutron with energy E will be captured depends on E. This makes realistic calculations of the non-capture probability considerably more difficult.arrow_forward
- A proton is in a box of width L. What must the width of the box be for the ground-level energy to be 5.0 MeV, a typical value for the energy with which the particles in a nucleus are bound? Compare your result to the size of a nucleus—that is, on the order of 10-14 m.arrow_forwardAn alpha particle with kinetic energy 11.0 MeV makes a collision with lead nucleus, but it is not "aimed" at the center of the lead nucleus, and has an initial nonzero angular momentum (with respect to the stationary lead nucleus) of magnitude L=pob, where po is the magnitude of the initial momentum of the alpha particle and Part A What is the distance of closest approach? m. (Assume that the lead nucleus Express your answer in meters. remains stationary and that it may be treated as a point charge. The atomic number of lead is 82. The alpha particle is a helium nucleus, with atomic number 2.) να ΑΣφarrow_forwardA typical diameter of a nucleus is about 10-14 m. Use the infinite square-well potential to calculate the transition energy from the first excited state to the ground state for a proton confined to the nucleus. Of course, this is only a rough calculation for a proton in a nucleus.arrow_forward
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- Consider a particle of mass m confined in a three-dimensional cube of length L so small that the motion of the particle is relativistic. Obtain an expression for the allowable energies of the particle in this case. Calculate the ground state energy for an electron if L = 10 fm (10 ^ -5 nm, a typical nuclear dimension)arrow_forwardPROBLEM 3. Using the variational method, calculate the ground state en- ergy Eo of a particle in the triangular potential: U(r) = 0 r 0. Use the trial function v(x) = Cx exp(-ar), where a is a variational parameter and C is a normalization constant to be found. Compare your result for Eo with the exact solution, Eo 1.856(h? F/m)/3.arrow_forwardDraw the Multi Cavity Klystron Functi onal Diagram and explain its operation, advantages and disadvantages. ) A one cavity Klystron is operated at 45 GHz with a D.C beam voltage of 650V for 4.75 mode, repeller space length of 0.8cm, and a D.C beam current of 50mA. The beeam coupling coefficient is assumed to be 1. a) calculate the repeller voltage b) electronic efficiency and output power.arrow_forward
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