Quantum Physics

Problems 97157. A by-product of some fission reactors is the isotope23994Pu, an alpha emitter having a half-life of24 120 yr. The reaction involved isPu : U 239Consider a sample of 1.00 kg of pure 94Pu at t 0.Calculate (a) the number of 94Pu nuclei present att 0 and (b) the initial activity in the sample.(c) How long does the sample have to be stored if a“safe” activity level is 0.100 Bq?58. (a) Find the radius of the C nucleus. (b) Find theforce of repulsion between a proton at the surfaceof a C nucleus and the remaining five protons.(c) How much work (in MeV) has to be done to overcomethis electrostatic repulsion in order to put thelast proton into the nucleus? (d) Repeat (a), (b),238and (c) for U.59.239941261262399223592In a piece of rock from the Moon, the 87 Rb contentis assayed to be 1.82 10 10 atoms per gram of materialand the 87 Sr content is found to be 1.07 10 9atoms per gram. (The relevant decay is 87 Rb :87 Sr e . The half-life of the decay is 4.8 10 10 yr.)(a) Determine the age of the rock. (b) Could the materialin the rock actually be much older? What assumptionis implicit in using the radioactive-datingmethod?60. Many radioisotopes have important industrial, medical,and research applications. One such radioisotopeis 60 Co, which has a half-life of 5.2 yr and decaysby the emission of a beta particle (energy0.31 MeV) and two gamma photons (energies1.17 MeV and 1.33 MeV). A scientist wishes to preparea 60 Co sealed source that will have an activity ofat least 10 Ci after 30 months of use. What is theminimum initial mass of 60 Co required?61. A medical laboratory stock solution is prepared withan initial activity due to 24 Na of 2.5 mCi/ml, and10.0 ml of the stock solution is diluted at t 0 0 to aworking solution whose total volume is 250 ml. After48 h, a 5.0-ml sample of the working solution ismonitored with a counter. What is the measured activity?(Note that 1 ml 1 milliliter.)62. A theory of nuclear astrophysics is that all theheavy elements such as uranium are formed in supernovaexplosions of massive stars, which immediatelyrelease the elements into space. If we assumethat at the time of an explosion there wereequal amounts of 235 U and 238 U, how long agowere the elements that formed our Earth released,given that the present 235 U/ 238 U ratio is 0.007?(The half-lives of 235 U and 238 U are 0.70 10 9 yrand 4.47 10 9 yr, respectively.)63. A fission reactor is hit by a nuclear weapon, causing5.0 10 6 Ci of 90 Sr (T 1/2 28.7 yr) to evaporateinto the air. The 90 Sr falls out over an area of 10 4km 2 . How long will it take the activity of the 90 Sr toreach the agriculturally “safe” level of 2.0 Ci/m 2 ?64. After the sudden release of radioactivity from theChernobyl nuclear reactor accident in 1986, theradioactivity of milk in Poland rose to 2 000 Bq/Ldue to iodine-131, with a half-life of 8.04 days. Radioactiveiodine is particularly hazardous, because the thyroidgland concentrates iodine. The Chernobyl accidentcaused a measurable increase in thyroidcancers among children in Belarus. (a) For comparison,find the activity of milk due to potassium. Assumethat 1 liter of milk contains 2.00 g of potassium,of which 0.011 7% is the isotope 40 K, whichhas a half-life of 1.28 10 9 yr. (b) After what lengthof time would the activity due to iodine fall belowthat due to potassium?65. During the manufacture of a steel engine component,radioactive iron ( 59 Fe) is included in the totalmass of 0.20 kg. The component is placed in a testengine when the activity due to the isotope is20.0 Ci. After a 1 000-h test period, oil is removedfrom the engine and is found to contain enough59 Fe to produce 800 disintegrations/min per liter ofoil. The total volume of oil in the engine is 6.5 L.Calculate the total mass worn from the engine componentper hour of operation. (The half-life of 59 Feis 45.1 days.)66. After determining that the Sun has existed for hundredsof millions of years, but before the discoveryof nuclear physics, scientists could not explain whythe Sun has continued to burn for such a long time.For example, if it were a coal fire, the Sun wouldhave burned up in about 3 000 yr. Assume that theSun, whose mass is 1.99 10 30 kg, originally consistedentirely of hydrogen and that its total poweroutput is 3.76 10 26 W. (a) If the energy-generatingmechanism of the Sun is the transforming of hydrogeninto helium via the net reaction11424H 2e : He 2 calculate the energy (in joules) given off by thisreaction. (b) Determine how many hydrogen atomsconstitute the Sun. Take the mass of one hydrogenatom to be 1.67 10 27 kg. (c) Assuming that thetotal power output remains constant, after whattime will all the hydrogen be converted into helium,making the Sun die? The actual projected lifetimeof the Sun is about 10 billion years, because only thehydrogen in a relatively small core is available as afuel. (Only in the Sun’s core are temperatures anddensities high enough for the fusion reaction to beself-sustaining).