The Nucleus and Radioactivity

Size: px

Start display at page:

Download "The Nucleus and Radioactivity"

Christina Allen
5 years ago
Views:

1 Chapter 0 The Nucleus and Radioactivity Practice Problem Solutions Student Textbook page 904. Conceptualize the Problem - The mass defect is the difference of the mass of the nucleus and the sum of the masses of the individual particles. - The mass defect, m, for beryllium-8 Known Implied Unknown m nucleus u m p u N A 8 m n u m Z 4 Calculate the number of neutrons. N A Z N 8 4 N 4 Determine the total mass of the m ptotal u separate nucleons by finding the m ptotal u masses of the protons and neutrons and adding them together. m ntotal u m ntotal u m total u u m total u Find the mass defect by subtracting the mass of the nucleus from the total nucleon mass. The mass defect is u. m u u m u Mass defects are expected to be a fraction of an atomic mass unit for light nuclei, and this is the case. Note that mass defects that are not a fraction of an atomic mass unit could indicate an error in the number of protons or neutrons used. Also, mass defects that are negative could indicate that an atomic mass which includes the mass of the electrons in the atom, instead of a nuclear mass, was used. In this text, most problems are given with nuclear masses. Chapter 0 The Nucleus and Radioactivity MHR 498

2 . Conceptualize the Problem - The mass defect is the difference of the mass of the nucleus and the sum of the masses of the individual particles. - The energy equivalent of the mass defect is the binding energy for the nucleus. The binding energy, E, for helium-3 Known Implied Unknown m nucleus u m p u N A 3 m n u m Z c m/s E Calculate the number of neutrons. N A Z N 3 N Determine the total mass of the m ptotal u separate nucleons by finding the m ptotal.0455 u masses of the protons and neutrons and adding them together. m ntotal u m ntotal u m total.0455 u u m total u Find the mass defect by subtracting the mass of the nucleus from the total nucleon mass. Convert the mass into kilograms. m u u m u m u kg/u m kg Find the energy equivalent of E mc the mass defect. E kg m/s E J E.37 0 J The binding energy is.37 0 J. The binding energy per nucleon is expected to be a few MeV per nucleon see Figure 0.4 in the text: E A.37 0 J J/MeV MeV, so the answer is reasonable. 3. Conceptualize the Problem - The mass defect is the difference of the mass of the nucleus and the sum of the masses of the individual particles. - The energy equivalent of the mass defect is the binding energy for the nucleus. The binding energy, E, for uranium-35 Chapter 0 The Nucleus and Radioactivity MHR 499

3 Known Implied Unknown m nucleus u m p u N A 35 m n u m Z 9 c m/s E Calculate the number of neutrons. N A Z N 35 9 N 43 Determine the total mass of the m ptotal u separate nucleons by finding the m ptotal u masses of the protons and neutrons and adding them together. m ntotal u m ntotal u m total u u m total u Find the mass defect by subtracting the mass of the nucleus from the total nucleon mass. Convert the mass into kilograms. m u u m u m u kg/u m kg Find the energy equivalent of the E mc mass defect. E kg m/s E J E J The binding energy is J. The binding energy per nucleon is expected to be several MeV per nucleon see Figure 0.4 in the text: E A J J/MeV 35 Practice Problem Solutions Student Textbook page MeV, so the answer is reasonable. 4. Conceptualize the Problem - The half-life of a radioactive isotope determines the amount of a sample at any given time. The time interval,, since the lava solidified Known m mg m 8.3 mg N T a Unknown Chapter 0 The Nucleus and Radioactivity MHR 500

4 Write the mass decay relationship. N T N 0 Note, in this case, both and N T are measured in mg. Solve for the time interval. About years had passed since the lava solidified. N log N T T log log N log a log 8.3 mg 7.4 mg log a a The mass of the original sample has decreased by less than a factor of two, which indicates that less than one half-life has passed. The solution is less than one half-life, so it is reasonable. 5. Conceptualize the Problem - The half-life of a radioactive isotope determines the amount of a sample at any given time. The age,, of the ashes Known 0.3 Bq N 0.5 Bq T 5730 a Unknown Write the mass decay relationship. N T N 0 Note, in this case, both and N T are measured in Bq. Solve for the time interval. The ashes are about years old. N log N T log log N T log 5730 a log 0.5 Bq 0.3 Bq log 3533 a a Chapter 0 The Nucleus and Radioactivity MHR 50

5 The original activity has decreased by less than a factor of two, which indicates that less than one half-life has passed. The solution is less than one half-life, so it is reasonable. 6. Conceptualize the Problem - The half-life of a radioactive isotope determines the amount of a sample at any given time. The amount of I-8, N, remaining after.0 h Known.0 h 40.0 mg 4.99 min h T Unknown N Write the mass decay relationship. N T N 0.0 h Substitute values and solve. N h 40.0 mg After.0 h, mg of the sample remain. N mg The time interval,.0 h, is more than 4 half-lives, so it is expected that most of the original amount of I-8 will have decayed. The answer seems reasonable. Chapter 0 Review Answers to Problems for Understanding Student Textbook page 99. a Calcium: 0 p, 8 e, 0 n c Chlorine: 7 p, 8 e, 8 n b Iron: 6 p, 6 e, 30 n 3. a Carbon 6C has six protons and six neutrons in the nucleus. m Zm p + Nm n m C Zm e m u u [ u u] m u E mc E u kg u m s E J or ev b Cesium 33 55CS has 55 protons and 78 neutrons. m Zm p + Nm n m Cs 33 Zm e m u u [3.905 u u] m.0 45 u Chapter 0 The Nucleus and Radioactivity MHR 50

6 E mc E.0 45 u kg u m s E Jor ev Th 4 6 He + 88 Ra 5. a 4 b 4 6 c a Mass defect is mass of radium nucleus mass of radon nucleus mass of alpha particle. m u u u m u E mc E u kg u E Jor3.85 MeV m s b You have to conserve momentum. m radon v radon m helium v helium u kg v u radon u v helium 55.46v radon You have to conserve energy kg u v helium m radonvradon + m heliumvhelium J u kg v u radon u kg v u helium J vradon vhelium J Substitute for v helium vradon v radon J v radon m s v helium 55.46v radon v helium m s v helium m s c m alphav alpha E total u kg u J 98.% m s N N o N 0.5 g T N g days day Chapter 0 The Nucleus and Radioactivity MHR 503

7 8. N N o T g g 3.6 min g g 3.6 min log log min 9. N N o T 3.6 min Bq 0.3 Bq log log a a a a 0. a Ten minutes is two half-lives, so one quarter of the original sample would remain. 800 atoms 00 atoms 4 b After 0 min, atoms of daughter nuclei that must have been produced. c There must be 5 5 half-lives. 3 of the parent nuclei left, because 5 min is 800 atoms 3 5 atoms d After 5 min, atoms of daughter nuclei that must have been produced. e N N o T N 800 atoms. 0 4 a 5 min Chapter 0 The Nucleus and Radioactivity MHR 504

8 . a N N o T N Pb N U0 N U N Pb N U0 N U N Pb N U N Pb N U0 T N U0 T N U0 T T b For a ratio of.08: T N U0 N U N Pb T T a a a a a 0.59 log a log a a Similarly, for a ratio of.:, a and for a ratio of.75:, a. c Since the ratios and therefore the ages differ, the rocks must not have solidified at the same time. d If the ratio is less than one, more than half of the uranium has decayed. Therefore, more than a half-life or more than years has passed since the rock solidified. Chapter 0 The Nucleus and Radioactivity MHR 505

Nuclear Physics Questions. 1. What particles make up the nucleus? What is the general term for them? What are those particles composed of?

Nuclear Physics Questions. 1. What particles make up the nucleus? What is the general term for them? What are those particles composed of? Nuclear Physics Questions 1. What particles make up the nucleus? What is the general term for them? What are those particles composed of? 2. What is the definition of the atomic number? What is its symbol?