13 pl a. If 100 mg of thorium-234 decays to 82.04 mg in 1 week.determine the decay rate r.b. Find an expression for the amount of thorium-234 present atany time t.c. Find the time required for the thorium-234 to decay to one-half its original amount.11. The half-life of a radioactive material is the time required for anamount of this material to decay to one-half its original value. Showthat for any radioactive material that decays according to the equationQ-rQ, the half-life 7 and the decay rate r satisfy the equationrt = ln 2.12. According to Newton's law of cooling (see Problem 19 ofSection 1.1), the temperature u(t) of an object satisfies the differentialequationdudt= -k(u-T),where T is the constant ambient temperature and k is a positiveconstant. Suppose that the initial temperature of the object isu(0) =<= 10-a. Find the temperature of the object at any time.b. Let 7 be the time at which the initial temperature differenceuo - T has been reduced by half. Find the relation between kand T.13. Consider an electric circuit containing a capacitor, resistor, andN 14. Aof a certainWater contaia rate of 300rate. Assumepond.1.35a. Lett. Writeb. Solin the pc. Atis remmixturinitiald. Soremainbegine. HG f.This equat3.7.ClassificationThe main purposes of this book are to diequations and to present some of the mor, in some cases, in approximatingwe describe here several useful waysvocabulary is essential to selecting appof solutions of differential equations a. If 100 mg of thorium-234 decays to 82.04 mg in 1 week.determine the decay rate r.b. Find an expression for the amount of thorium-234 present atany time t.c. Find the time required for the thorium-234 to decay to one-half its original amount.11. The half-life of a radioactive material is the time required for anamount of this material to decay to one-half its original value. Showthat for any radioactive material that decays according to the equationQ-rQ, the half-life 7 and the decay rate r satisfy the equationrt = ln 2.12. According to Newton's law of cooling (see Problem 19 ofSection 1.1), the temperature u(t) of an object satisfies the differentialequationdudt= -k(u-T),where T is the constant ambient temperature and k is a positiveconstant. Suppose that the initial temperature of the object isu(0) =<= 10-a. Find the temperature of the object at any time.b. Let 7 be the time at which the initial temperature differenceuo - T has been reduced by half. Find the relation between kand T.13. Consider an electric circuit containing a capacitor, resistor, andN 14. Aof a certainWater contaia rate of 300rate. Assumepond.1.35a. Lett. Writeb. Solin the pc. Atis remmixturinitiald. Soremainbegine. HG f.This equat3.7.ClassificationThe main purposes of this book are to diequations and to present some of the mor, in some cases, in approximatingwe describe here several useful waysvocabulary is essential to selecting appof solutions of differential equations

Answered: Consider an electric circuit containing…

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Physics

Consider an electric circuit containing a capacitor, resistor, and

Physics for Scientists and Engineers with Modern Physics

10th Edition

ISBN:9781337553292

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter43: Nuclear Physics

Section: Chapter Questions

Problem 18P

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Data from the appendices and the periodic table may be needed for these problems. Natural uranium is 0.7200% 235U and 99.27% 238U. What were the percentages of 235U and 238U in natural uranium when Earth formed 4.5109 years age?
A sample of radioactive material is obtained from a very old rock. A plot InA verses t yieldsa slope value of 109s1 (see Figure 10.10(b)). What is the half-life of this material?
(a) Calculate the number of grams of deuterium in an 80.000L swimming pool, given deuterium is 0.0150% of natural hydrogen. (b) Find the energy released in joules if this deuterium is fused via the reaction 2H+2H3He+n. (c) Could the neutrons be used to create more energy? (d) Discuss the amount of this type of energy in a swimming pool as compared to that in, say, a gallon of gasoline, also taking into consideration that water is far more abundant.
Data from the appendices and the periodic table may be needed for these problems. (a) Natural potassium contains 40K, which has a halflife of 1.277109y. What mass of 40K in a person would have a decay rate of 4140 Bq? (b) What is the fraction of 40K in natural potassium, given that the person has 140 g in his body? (These numbers are typical for a 70kg adult.)
A nuclear physicist finds 1.0of 236Uin a piece of uranium ore (T1/2=2.348107y) . (a) Use die decay law to determine how much 236Uwould had to have been on Earth when it formed 4.543109yago for 1.0gto be left today, (b) What is unreasonable about this result? (c) How is this unreasonable result resolved?
Construct Your Own Problem Consider the decay of radioactive substances in the Earth's interior. The energy emitted is converted to thermal energy that reaches the earth's surface and is radiated away into cold dark space. Construct a problem in which you estimate the activity in a cubic meter of earth rock? And then calculate the power generated. Calculate how much power must cross each square meter of the Earth’s surface if the power is dissipated at the same rate as it is generated. Among the things to consider are the activity per cubic meter, the energy per decay, and the size of the Earth.