Homework 12


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        Enter numbers without commas. 23,546 should be 23546
        Always enter a * for multiplication. g(H+h) should be g*(H+h).


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        Submitted Answers will be graded M 12/8, T 12/9, W 12/10, and Th 12/11 at 12:00 noon.


        Problem 12.1
          What you should learn: The first three questions are again reading questions.
        Problem: Did you read Chapter 44 Sections 1-5? Type Y or N in the box.  
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        Problem 12.2
          What you should learn: Reading...
        Problem: Did you read Chapter 46 Sections 1-6? Type Y or N in the box.  
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        Problem 12.3
          What you should learn: Reading...
        Problem: Did you read Chapter 46 Sections 7-10? Type Y or N in the box.  
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        Problem 12.4
          What you should learn: An estimate of a nuclear radius is given by r = r0A1/3 where r0 = 1.2 fm.
        Problem: What is the approximate radius of a 168O nucleus?  
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        Answer range: r = 2.00 to 4.00 fm
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        Problem 12.5
          What you should learn: The binding energy of a nucleus is given by adding the rest energy of all the protons and neutrons and subtracting the rest energy of the nucleus.
        Problem: Find the binding energy per nucleon for 19779Au  
        Constants and fixed variables:
          Mass of electron: me = 0.000549 u
          Mass of neutron: mn = 1.008665 u
          Mass of 1H: mH = 1.007825 u
          Mass of 197Au: mAu = 196.966552 u
          1 u = 931.494 MeV
        Hints:
           Note that the masses given are atomic masses, and hence include electrons.
           Since you're subtracting numbers, be sure to keep as many significant digits as you can until the final answer.
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        Answer range:  6.00 to 9.00 MeV
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        Problem 12.6
          What you should learn: The semiempirical binding energy formula (Eq. 44.3 in the 7th edition) comes from the liquid drop model.
        Problem: Use the semiempirical binding energy formula to estimate the binding energy per nucleon of 19779Au.  
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        Answer range: 6.00 to 9.00 MeV
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        Problem 12.7
          What you should learn: The basic relationship for radioactive decay is N(t) = N0e–λt
        Problem: An organism has m = 1.00 ng of 14C in it at the time of its death. How many disintegrations  per second (R) occur after a time t given below:  

        Constants and fixed variables:
          Half-life of 14C: T  = 5730 yr
          Molecular weight of 14C: W = 14.00  g/mol
          Avagadro's number: NA = 6.022 × 1023 atoms/mol
          Number of days in a year: 365.25

        Variables that must be changed with each submission:
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        Hints:
           How does decay rate relate to N(t)?
           The decay constant and half-life are related by the equation λ T1/2 = ln 2
           λ will probably be in units of yr–1, so your answer will be in counts per year until you do the conversion to counts per second.
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        Answer range: 135 to 150 counts/second
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        Problem 12.8
          What you should learn: The Q value of a nuclear reaction is the rest energy of the initial particles minus the rest energy of the final particles.
        Problem: 55Fe decays by electron capture. What is the Q value of the reaction?
         

        Constants and fixed variables:
          Mass of 5526Fe: mFe  = 54.938298 u
          Mass of 5525Mn: mMn  = 54.938050 u
          Mass of 5527Co: mCo  = 56.936296 u
          Mass of 5626Fe: mFe56  = 55.934942 u
          Mass of 5426Fe: mFe54  = 53.939615 u
          Mass of electron: me  = 0.000549 u

        Hints:
           In calculating Q values, always be careful to consider electron masses.
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        Answer range: Q = 0.100 to 0.400 MeV
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        Problem 12.9
          What you should learn: One more Q value problem...
        Problem: If 55Fe decayed by β+ emission, what would its Q value be? Note that negative Q values mean that the process will not occur unless external energy is supplied.
         
        Hints:
           This is another bookkeeping process, but remember to be careful with electron masses.
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        Answer range: Q = –1.00 to –0.400 MeV
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        Problem 12.10
          What you should learn: The uncertainty principle relation ΔEΔt ≥ ħ/2 can be used to estimate the range of forces if we know the mass of the particle that mediates the force.
        Problem: Using the same method as Yukawa in predicting the mass of the π meson, estimate the range of a force if the mediating particle has a mass m.  
        Constants and fixed variables:
          Planck's constant: h = 4.136 x 10–21 MeV s
          Speed of light: c = 2.998 × 1023 fm/s
        Variables that must be changed with each submission:
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        Hints:
           Look at equations 46.2 and 46.3 in the text.
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        Answer range: R = 0.0800 to 0.125 fm
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        Problem 12.11
          What you should learn: The force between quarks is called the "color force." The strong force are the close range forces between colorless objects.
        Problem: Quarks can be thought of as continuously emitting and reabsorbing colored gluons, causing the color of the quark itself to constantly change. This is responsible for:
          A. camouflage
          B. trifurcation
          C. confinement
          D. renormalization
          E. gluon alignment

        Note that you will only be allowed two submissions on this problem and the following multiple choice problems.

         
        Hints:
           Refer to the Power Point slides for this one.
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        Problem 12.12
          What you should learn: By considering the quark composition of a meson, you can easily determine its antiparticle.
        Problem: What is the antiparticle of a π+ meson?
          A. γ
          B. πo
          C. π–
          D. ωo
          E. ω+
          F. ω–
         
        Hints:
           Look at Table 46.4.
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        Problem 12.13
          What you should learn: This problem relates to the quark composition of baryons and mesons. When particles are created in the strong interaction, the quark composition remains the same before and after the interaction, if we consider combinations such as dđ (d d-bar) to cancel each other out.
        Problem:  In the reaction π+ + n → K0 + X, X must be:
          A. p
          B. Δ+
          C. Σ+
          D. Ξ+
         
        Hints:
           Look at Tables 46.4 and 46.5.
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        Problem 12.14
          What you should learn: The last two equations relate to conservation laws.
        Problem: Which conservation laws does the the reaction Ξ0 → p + π–  violate?
          A. Conservation of baryon number
          B. Conservation of lepton number
          C. Conservation of muon number
          D. Conservation of electron number
          E. Conservation of strangeness
          F. Conservation of charge
        Express your answer as as A+B if A and B are both violated.
         
        Hints:
           Particle properties can be found in Table 46.2.
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        Problem 12.15
          What you should learn: The last problem is also one on conservation laws.
        Problem: Which conservation laws does the the reaction n → π+ + μ–  violate?
          A. Conservation of baryon number
          B. Conservation of lepton number
          C. Conservation of muon number
          D. Conservation of electron number
          E. Conservation of strangeness
          F. Conservation of charge
        Express your answer as as A+B if A and B are both violated.
         
        Hints:
           Particle properties can be found in Table 46.2.
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