Solucionario

Chapter 39. Nuclear Physics and the Nucleus

The Elements

39-1. How many neutrons are in the nucleus of [pic]? How many protons? What is the ratio N/Z? (N is the number of neutrons and Z is the number of protons.)
A = N + Z; N = A – Z = 126 neutrons; Z = 82 protons; [pic]

39-2. The nucleus of a certain isotope contains 143 neutrons and 92 protons. Write the symbol forthis nucleus.
A = N + Z = 143 + 92 = 235; Z = 92: [pic]

39-3. From a stability curve it is determined that the ratio of neutrons to protons for a cesium nucleus is 1.49. What is the mass number for this isotope of cesium?
Z = 55; [pic] A = 137

39-4. Most nuclei are nearly spherical in shape and have a radius that may be approximated by
[pic]
What is the approximateradius of the nucleus of a gold atom [pic]?
[pic]; r = 6.98 x 10-15 m

39-5. Study Table 39-4 for information on the several nuclides. Determine the ratio of N/Z for the following nuclides: Beryllium-9, Copper-64, and Radium 224.
Beryllium: A = 9; Z = 4; N = 9 – 4 = 5; [pic]
39-5. (Cont.) Copper: A = 64; Z = 29; N = 64 – 29 = 35; [pic]
Radium: A =224; Z = 88; N = 224 – 88 = 136; [pic]

The Atomic Mass Unit
39-6. Find the mass in grams of a gold particle containing two million atomic mass units?
[pic] m = 3.32 x 10-21 kg
39-7. Find the mass of a 2-kg copper cylinder in atomic mass units? In Mev? In joules?
[pic] m = 1.20 x 1027 u
[pic] m = 1.12 x 1030 MeV
[pic] m = 1.79 x 1017 J

39-8. A certain nuclearreaction releases an energy of 5.5 MeV. How much mass (in atomic mass units) is required to produce this energy?
[pic] m = 0.00591 u

39-9. The periodic table gives the average mass of a silver atom as 107.842 u. What is the average mass of the silver nucleus? (Recall that me = 0.00055 u )
For silver, Z = 47. Thus, the nuclear mass is reduced by the mass of 47 electrons.
m = 107.842 u– 47(0.00055 u); m = 107.816 u
*39-10. Consider the mass spectrometer as illustrated by Fig. 39-3. A uniform magnetic field of 0.6 T is placed across both upper and lower sections of the spectrometer., and the electric field in the velocity selector is 120 V/m. A singly charged neon atom (+1.6 x 10-19 C) of mass 19.992 u passes through the velocity selector and into the spectrometer. Whatis the velocity of the neon atom as it emerges from the velocity selector?
[pic] v = 2 x 105 m/s

*39-11. What is the radius of the circular path followed by the
neon atom of Problem 19-10?
[pic]
[pic]; [pic] R = 6.92 cm

Mass Defects and Binding Energy
(Refer to Table 39-4 for Nuclidic Masses.)

*39-12. Calculate the mass defect andbinding energy for the neon-20 atom [pic].
[pic]
mD = 20.016490 u –19.99244 u ; mD = 0.17246 u
[pic]; E = 161 MeV
*39-13. Calculate the binding energy and the binding energy per nucleon for tritium [pic]. How much energy in joules is required to tear the nucleus apart into its constituent nucleons?
[pic]
39-13. (Cont.) mD = 0.009106 u; [pic]
E = 8.48 MeV; [pic];[pic]
Energy to tear apart: EB = 8.48 MeV(1.6 x 10-13 J/MeV) = 1.36 x 10-12 J

*39-14. Calculate the mass defect of [pic]. What is the binding energy per nucleon?
[pic]
mD = 7.058135 u –7.016930 u ; mD = 0.041205 u
[pic]; E = 38.4 MeV
[pic] [pic]

*39-15. Determine the binding energy per nucleon for carbon-12 ( [pic]).
[pic]
[pic] [pic]= 7.68 MeV/nucleon

*39-16.What is the mass defect and the binding energy for a gold atom [pic]?
[pic]
[pic]
[pic]= 7.91 MeV/nucleon

*39-17. Determine the binding energy per nucleon for tin-120 ( [pic]).
[pic]
[pic] [pic] 8.50 MeV/nucleon

Radioactivity and Nuclear Decay
39-18. The activity of a certain sample is rated as 2.8 Ci. How many nuclei will have disintegrated in a time of one minute?
[pic]...