Quantum Physics

968 Chapter 29 Nuclear Physicsforce on the alpha particle, (b) the acceleration of thealpha particle at this time, and (c) the potential energyof the alpha particle at the same time?6. Singly ionized carbon atoms are acceleratedthrough 1 000 V and passed into a mass spectrometerto determine the isotopes present. (See Chapter19.) The magnetic field strength in the spectrometeris 0.200 T. (a) Determine the orbital radii for the12 C and the 13 C isotopes as they pass through thefield. (b) Show that the ratio of the radii may bewritten in the formand verify that your radii in part (a) satisfy thisformula.7. (a) Find the speed an alpha particle requires tocome within 3.2 10 14 m of a gold nucleus.(b) Find the energy of the alpha particle in MeV.48. Find the radius of a nucleus of (a) 2 He and238(b) 92 U .Section 29.2 BindingEnergy9. Calculate the average binding energy per nucleon93197of and .10. Calculate the binding energy per nucleon for(a) 2 H, (b) 4 He, (c) 56 Fe, and (d) 238 U.11. A pair of nuclei for which Z 1 N 2 and Z 2 N 1 arecalled mirror isobars. (The atomic and neutron numbersare interchangeable.) Binding-energy measurementson such pairs can be used to obtain evidenceof the charge independence of nuclear forces.Charge independence means that the proton–proton, proton–neutron, and neutron–neutronforces are approximately equal. Calculate the differencein binding energy for the two mirror nucleiand .158 O41 Nb157 N79 Aur 1r 2 √m 1m 212. The peak of the stability curve occurs at 56 Fe. This iswhy iron is prominent in the spectrum of the Sunand stars. Show that56 Fe has a higher binding energyper nucleon than its neighbors 55 Mn and .Compare your results with Figure 29.4.13. Two nuclei having the same mass number areknown as isobars. Calculate the difference in binding2323energy per nucleon for the isobars and 12 Mg .How do you account for this difference?11 Na 59 Co14. Calculate the binding energy of the last neutron43in the 20 Ca nucleus. [Hint: You should compare the43mass of 20 Ca with the mass of 20 Ca plus the mass of a42neutron. The mass of 41.958 622 u.]20 Ca 42Section 29.3 Radioactivity15.The half-life of an isotope of phosphorusis 14 days. If a sample contains 3.0 10 16such nuclei, determine its activity. Express youranswer in curies.9916. A drug tagged with 43 Tc (half-life 6.05 h) is preparedfor a patient. If the original activity of the samplewas 1.1 10 4 Bq, what is its activity after it has sat onthe shelf for 2.0 h?17. The half-life of 131 I is 8.04 days. (a) Calculate the decayconstant for this isotope. (b) Find the number of131 I nuclei necessary to produce a sample with an activityof 0.50 Ci.18. After 2.00 days, the activity of a sample of an unknowntype of radioactive material has decreased to84.2% of the initial activity. (a) What is the half-lifeof this material? (b) Can you identify it by using thetable of isotopes in Appendix B?19. Suppose that you start with 1.00 10 3 g of a pureradioactive substance and 2.0 h later determine thatonly 0.25 10 3 g of the substance remains. Whatis the half-life of this substance?20. Radon gas has a half-life of 3.83 days. If 3.00 g ofradon gas is present at time t 0, what mass ofradon will remain after 1.50 days have passed?21. Many smoke detectors use small quantities of theisotope241 Am in their operation. The half-life of241 Am is 432 yr. How long will it take for the activityof this material to decrease to 1.00 10 3 of theoriginal activity?22. After a plant or animal dies, its 14 C content decreaseswith a half-life of 5 730 yr. If an archaeologistfinds an ancient firepit containing partiallyconsumed firewood, and the 14 C content of thewood is only 12.5% that of an equal carbon samplefrom a present-day tree, what is the age of theancient site?23. A freshly prepared sample of a certain radioactiveisotope has an activity of 10.0 mCi. After 4.00 h, theactivity is 8.00 mCi. (a) Find the decay constant andhalf-life of the isotope. (b) How many atoms of theisotope were contained in the freshly preparedsample? (c) What is the sample’s activity 30 h after itis prepared?