FUND.OF PHYSICS
11th Edition
ISBN: 9781119306887
Author: Halliday
Publisher: WILEY
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Chapter 42, Problem 70P
To determine
To calculate:
the effective nuclear temperature of a nucleon in a middle-mass nucleus (with a typical kinetic energy of 5 MeV).
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A typical kinetic energy for a nucleon in a middle-mass nucleus may be taken as 5.00 MeV.To what effective nuclear temperature does this correspond, based on the assumptions of the collective model of nuclear structure?
One of the major observations of the nuclear line of stability is that heavy nuclei (Z > 16) that are stable have more neutrons than protons; this is in contrast to light nuclei where the proton and neutron number are the same. Explain why this is the case.
The liquid drop model may be used to determine the nuclear binding energy for an isotope. This model uses the semiempirical binding energy formula, which takes into consideration four major effects (one term per effect) that contribute to the nuclear binding energy. The semiempirical binding energy formula may be expressed as:
Z(Z - 1)
C3
A1/3
(N – z)2
E, = C;A – C,A?/3
A
The first term is the volume term, the second is the surface term, the third is the Coulomb term, and the fourth is the symmetry term. For nuclei having A 2 15, the constants have the following values:
= 15.7 MeV, C, = 17.8 MeV, C3
= 0.71 MeV, and C.
= 23.6 MeV
56
(a) Use the semiempirical binding energy formula to determine the nuclear binding energy (in MeV) for the isotope
Fe.
26
MeV
(b) Determine the percentage contribution to the binding energy by each of the four terms. (You should expect positive and negative values, but the sum should be 100%. Due to the nature of this problem, do not use rounded intermediate…
Chapter 42 Solutions
FUND.OF PHYSICS
Ch. 42 - Prob. 1QCh. 42 - Prob. 2QCh. 42 - Prob. 3QCh. 42 - Prob. 4QCh. 42 - Prob. 5QCh. 42 - Prob. 6QCh. 42 - Prob. 7QCh. 42 - Prob. 8QCh. 42 - Prob. 9QCh. 42 - Prob. 10Q
Ch. 42 - Prob. 11QCh. 42 - Prob. 12QCh. 42 - a Which of the following nuclides are magic:...Ch. 42 - Prob. 14QCh. 42 - Prob. 15QCh. 42 - Prob. 1PCh. 42 - Prob. 2PCh. 42 - A 10.2 MeV Li nucleus is shot directly at the...Ch. 42 - Prob. 4PCh. 42 - Prob. 5PCh. 42 - Prob. 6PCh. 42 - Prob. 7PCh. 42 - Prob. 8PCh. 42 - Prob. 9PCh. 42 - Prob. 10PCh. 42 - Prob. 11PCh. 42 - Prob. 12PCh. 42 - Prob. 13PCh. 42 - Prob. 14PCh. 42 - Prob. 15PCh. 42 - Prob. 16PCh. 42 - Prob. 17PCh. 42 - Prob. 18PCh. 42 - Prob. 19PCh. 42 - Prob. 20PCh. 42 - Prob. 21PCh. 42 - Prob. 22PCh. 42 - Prob. 23PCh. 42 - A penny has a mass of 3.0 g. Calculate the energy...Ch. 42 - Prob. 25PCh. 42 - Prob. 26PCh. 42 - Prob. 27PCh. 42 - Prob. 28PCh. 42 - Prob. 29PCh. 42 - The half-life of a particular radioactive isotope...Ch. 42 - Prob. 31PCh. 42 - Prob. 32PCh. 42 - Prob. 33PCh. 42 - Calculate the mass of a sample of initially pure...Ch. 42 - Prob. 35PCh. 42 - Prob. 36PCh. 42 - Prob. 37PCh. 42 - A dose of 8.60 Ci of a radioactive isotope is...Ch. 42 - Prob. 39PCh. 42 - Prob. 40PCh. 42 - Prob. 41PCh. 42 - Prob. 42PCh. 42 - Prob. 43PCh. 42 - Prob. 44PCh. 42 - Prob. 45PCh. 42 - Prob. 46PCh. 42 - Prob. 47PCh. 42 - Prob. 48PCh. 42 - Prob. 49PCh. 42 - Prob. 50PCh. 42 - Prob. 51PCh. 42 - Prob. 52PCh. 42 - Prob. 53PCh. 42 - Prob. 54PCh. 42 - Prob. 55PCh. 42 - Prob. 56PCh. 42 - Prob. 57PCh. 42 - Prob. 58PCh. 42 - Prob. 59PCh. 42 - Prob. 60PCh. 42 - Prob. 61PCh. 42 - Prob. 62PCh. 42 - Prob. 63PCh. 42 - Prob. 64PCh. 42 - Prob. 65PCh. 42 - Prob. 66PCh. 42 - Prob. 67PCh. 42 - Prob. 68PCh. 42 - Prob. 69PCh. 42 - Prob. 70PCh. 42 - Prob. 71PCh. 42 - Prob. 72PCh. 42 - Prob. 73PCh. 42 - Prob. 74PCh. 42 - Prob. 75PCh. 42 - Prob. 76PCh. 42 - Prob. 77PCh. 42 - Prob. 78PCh. 42 - Prob. 79PCh. 42 - Prob. 80PCh. 42 - Prob. 81PCh. 42 - Prob. 82PCh. 42 - Prob. 83PCh. 42 - Prob. 84PCh. 42 - Prob. 85PCh. 42 - Prob. 86PCh. 42 - Prob. 87PCh. 42 - Characteristic nuclear time is a useful but...Ch. 42 - Prob. 89PCh. 42 - Using a nuclidic chart, write the symbols for a...Ch. 42 - If the unit for atomic mass were defined so that...Ch. 42 - Prob. 92PCh. 42 - Prob. 93PCh. 42 - Prob. 94PCh. 42 - Prob. 95PCh. 42 - Prob. 96PCh. 42 - Prob. 97P
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- (a) Calculate the energy released in the neutron- Induced fission reaction n+235U92Kr+142Ba+2n , given m(92Kr) = 91.926269 u and m(142Ba)= 141.916361 u. (b) Confirm that the total number of nucleons and total charge are conserved in this reaction.arrow_forward(a) How many 239Pu nuclei must fission to produce a 20.0kT yield, assuming 200 MeV per fission? (b) What is the mass of this much 239Pu?arrow_forward(a) Calculate the energy released in the neutron- induced fission n+238U96Sr+140Xe+3n , given m(96Sr)=95.921750uand m(140Xe)=139.92164 . This result is about 6 MeV greater than the result for spontaneous fission. Why? Confirm that the total number of nucleons and total charge are conserved in this reaction.arrow_forward
- Characteristic nuclear time is a useful but loosely defined quantity, taken to be the time required for a nucleon with a few million electron-volts of kinetic energy to travel a distance equal to the diameter of a middle-mass nuclide.What is the order of magnitude of this quantity? Consider 5 MeV neutrons traversing a nuclear diameter of 197Auarrow_forwardDraw a plot of the binding energy per nucleon as a function of mass number for a large number of nuclei, 2 ≤ A ≤ 240. How do you explain the constancy of binding energy per nucleon in the range 30 < A < 170 using the property that nuclear force is short-ranged?arrow_forwardAnother series of nuclear reactions that can produce energy in the interior of stars is the cycle described below. This cycle is most efficient when the central temperature in a star is above 1.6 x107 K. Because the temperature at the center of the Sun is only 1.5 x 107 K, the following cycle produces less than 10% of the Sun’s energy. (a) A high - energy proton is absorbed by 12C. Another nucleus, A, is produced in the reaction, along with a gamma ray. Identify nucleus A. (b) Nucleus A decays through positron emission to form nucleus B. Identify nucleus B. (c) Nucleus B absorbs a proton to produce nucleus C and a gamma ray. Identify nucleus C . (d) Nucleus C absorbs a proton to produce nucleus D and a gamma ray. Identify nucleus D. (e) Nucleus D decays through positron emission to produce nucleus E. Identify nucleus E. (f ) Nucleus E absorbs a proton to produce nucleus F plus an alpha particle. What is nucleus F? Note: If nucleus F is not 12C— that is, the nucleus you started with —…arrow_forward
- (a) In the liquid-drop model of nuclear structure, why does the surface-effect term -C2A2/3 have a negative sign? (b) What If? The binding energy of the nucleus increases as the volume-to-surface area ratio increases. Calculate this ratio for both spherical and cubical shapes and explain which is more plausible for nuclei.arrow_forwardThe nucleus of a fictitious element consists of 15 protons and 16 neutrons. The mass of the respective atom is 31.021 u. Calculate the nuclear binding energy per nucleon, in MeV. The mass of the hydrogen atom is 1.007825 u, the mass of the neutron is 1.008665 u.arrow_forward56Fe is among the most tightly bound of all nuclides. It makes up more than 90% of natural iron. Note that 56Fe has an even number of both protons and neutrons. Calculate BE/A, the binding energy per nucleon, for 56Fe in megaelectron volts per nucleon.arrow_forward
- The binding energy for a nucleus containing Z protons and N neutrons is defined as c²[ZM + Nm, - M] where M is the mass of the neutral atom containing the nucleus, the quantity in the parentheses is the mass defect, and c? = 931.5 MeV/u.The binding energy of a nuclide can also be written as E, = Am x 931.5 MeV/u where Am is the mass defect. The Figure below show the mass for neutral atom and the nucleons of a helium atom. SHe Binding energy Mass = 4.0026 u Mass = 4.0330 u Calculate the mass defect Am of a helium atomarrow_forwardUsing the graph given, estimate how much energy is released when a nucleus of mass number 200 fissions into two nuclei each of mass number 100.arrow_forwardAnother series of nuclear reactions that can produce energy in the interior of stars is the cycle described below. This cycle is most efficient when the central temperature in a star is above 1.6 × 107 K. Because the temperature at the center of the Sun is only 1.5 × 107 K, the following cycle produces less than 10% of the Sun’s energy. (a) A high-energy proton is absorbed by 12 C. Another nucleus, A , is produced in the reaction, along with a gamma ray. Identify nucleus A decays through positron emission to form nucleus B. (c) Nucleus B absorbs a proton to produce nucleus C and a gamma ray. Identify nucleus C absorbs a proton to produce nucleus D and a gamma ray. Identify nucleus D. (e) Nucleus D decays through positron emission to produce nucleus E. Identify nucleus E. (f) Nucleus E absorbs a proton to produce nucleus F plus an alpha particle. What is nucleus F ? Note: If nucleus F is not 12C—that is, the nucleus you started with—you have made an error and should review the sequence…arrow_forward
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