Monday, January 18, 2016

CHEM 418 Nuclear Chemistry, Winter 2016: Lecture 5 Beta Decay

Beta decay is presented in this lecture. The neutrino hypothesis and its relationship with beta decay is discussed. A review of Q value calculations for beta decay is provided.  The importance of spin and parity, and how it can be used to assess beta decay, is discussed. Modeling beta decay through the weak force is provided. The impact of Coulomb interactions on positron and electron spectral shape is presented.  The use of Kurie plots in understanding beta decay is introduced.  Selection rules in beta decay and beta transitions are explained. Calculating logft and its relation to spin and parity are presented. Double beta decay is discussed.

29 comments:

  1. This comment has been removed by the author.

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  2. Calculating log(ft) values... I'm having some troubles.


    So for beta decay we may use the following formula.


    log(f) = 4*log(Qrxn) + 0.78 +(0.02)*Zdaughter- 0.005*(Zdaughter - 1)*log(Qrxn)

    Qrxn = delta(241-Pu) - delta(241-Am)
    Qrxn > 0
    Qrxn = 0.0208 MeV

    Let Zdaughter = 95
    and Zdaughter -1 = 94

    then falling from the calculation of log(ft)


    log(ft) = -10.9910... [MeV units?]

    This value must be wrong. Can someone point me in the right direction?

    Thanks!

    -Faruq

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    1. So if I push through on the calculation of log(ft)


      log(ft) = log(f) + log(t1/2)


      t1/2 = 14.290*(3.157*10^7) [seconds]
      log(f) = -10.9910 [? probably time]

      log(ft) = -10.9910 + + log(14.290*(3.157*10^7))

      log(ft) = 8.93629


      6 < log(ft) < 10

      and is therefor the first Forbidden Transition.


      How wrong is this answer?

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    2. A great way to check your answer for the log ft data is the table of the isotope. For 241Pu, go to A=241. The beta decay of 241Pu goes to 241Am. If you look at this level you see 241Pu goes to the 241Am ground state. The logft is 5.8. You number should be closer to this.

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    3. log f (B-) = 4logE+0.78+0.02Z-0.005(Z-1)logE
      E=0.020, Z=95 (the Z for Am), you have 94. I would try this again. The half life in seconds is 4.53E8, very close to yours.

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    4. Thanks Ken, I'll swing it again

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    5. excellent. let me know if you need any further assistance.

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    6. So I was able to get all the questions except for the log(ft) value for Ti's beta decay. I have trouble making calculations on this beta decay reaction because Q is quite negative...


      45-Ti --> 45-V + e + v + Q

      Q < 0

      45-Ti = -39.009121 MeV
      45-V = -31.880549 MeV

      Mass Difference: Q = (45-Ti) - (45-V)

      Q = -7.12857 MeV

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    7. Use the chart of the nuclides to determine the decay route of 45Ti. From the chart of the nuclides 45Ti decays by positron emission to 45Sc. Find the Q value for this reaction, use the Z of Sc, and use the log f equation for positron decay. You should get a logft around 5.

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    8. Use the chart of the nuclides to determine the decay route of 45Ti. From the chart of the nuclides 45Ti decays by positron emission to 45Sc. Find the Q value for this reaction, use the Z of Sc, and use the log f equation for positron decay. You should get a logft around 5.

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    9. emailed quiz 5, sorry im late

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  3. Submitted the quiz via email.
    I was a little confused on the 4 problems the neutrino fixed for beta decay. Antiparticle, energy conservation, and spin conservation are clear, but is the zero net charge supposed to be the 4th? That doesn't seem like it "fixes" a problem, it's more that the neutrino doesn't create any additional problems, if my logic makes sense. I listed it anyway, since I'm likely overthinking it.
    Thanks!
    -Taylor

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    1. thanks for the comment, definitely thoughtful.

      For the neutrino the lack of a charge is one of the reasons it is difficult to observe. Furthermore, a charge, or lack of one, needs to be assigned to the particle. The charge balance of the other particle means tne neutrino mush have no charge.

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  4. Lecture viewed and quiz submitted.

    I was confused when working on question 1, more specifically with the derivation of log ft. Why is it that we use the half life of the parent for log t, but the Z of the daughter for solving logf?

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    1. the f value can be thought of as half life corrected for differences in Z and W of the decay. W is the total kinetic energy, which is Q. Z is based on the perturbation from the Fermi function. This is the transition from the parent to the daughter,so the daughter Z is needed. For positron decay the Z is one less than the parent. For beta minus decay the daughter Z is greater than the parent. It is for this reason the Z of the daughter needs to be described.

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  5. I sent the lecture 5 pdf quiz as an attachment through email.
    I have a question about calculating the logft value. When I looked the Q value for the Ti45, I found out the Q value of Ti45 for EC is twice the Q value of poistron decay. In addition, when I looked the table isotope, I found the Q value of EC right below the nulcide. Why we find the log ft value of positron decay instead of EC?
    Thank you very much

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    Replies
    1. This is described on page 2 of the beta decay lecture. The positron decay needs to include 2 electron masses. This due to the positron and the extra electron in the daughter. Since the daughter is one less proton than the parent, it will have an extra electron that needs to be considered.

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    2. This is also explained in detail on page 6 of lecture 2.

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    3. So higher Q value does't mean it will be the primary decay mode? The primary decay has to be followed the chart of nulcide?

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    4. that is correct, especially comparing Q values for different decay modes.

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  6. Lecture watched. Quiz submitted through email. Thank you!

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  7. Quiz submitted through the Canvas email!

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  8. Quiz has been submitted via Canvas.

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  9. quiz was submitted via email

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  10. Lecture 5 viewed and pdf quiz emailed! (....late....)

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