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Calculate the KE of an electron emitted from the beta decay of a neutron

  1. May 29, 2012 #1
    1. The problem statement, all variables and given/known data

    What is the maximum kinetic energy (in keV to 3 significant figures) of an electron emitted in the beta decay of a free neutron? Write down the decay equation using accepted notation.

    Mass of a Neutron: 1.008665 u
    Mass of a Proton: 1.007276 u
    Mass of an Electron: 0.00054858 u
    the energy mass equivalence for this question is 931.5 MeV/amu

    2. Relevant equations

    e=mc^2

    beta decay equation:
    A / Z X -> A / (Z+1) Y + e- + v

    3. The attempt at a solution

    beta decay equation:
    A / Z X -> A / (Z+1) Y + e- + v

    by A / Z i mean A over Z, not divided by.

    i really have no idea how to do this. But:

    for the neutron:
    e= mc^2
    e= (1.008665 u)(2.9979x10^8 m/s)^2
    e= 9.065x10^16 amu m^2 s^2

    for the proton:
    e= (1.007276 amu)(2.9979x10^8 m/s)^2
    e= 9.052x10^16 amu m^2 s^2

    for the electron:
    e=mc^2
    e= (0.00054858amu)(2.9979x10^8 m/s)^2
    e= 4.93x10^13 amu m^2 s^2

    if i subtract the energy of the proton from the neutron you get the energy of the electron and its KE:
    9.052x10^16 - 9.065x10^16
    = -1.2x10^14 amu m^2 s^2

    then to get the ke of the electron:

    -1.2x10^14 - 4.93x10^13
    = -1.693x10^14 amu m^2 s^2


    I know the answer is wrong because i havent converted amu into energy. I dont get fully what they mean by "if the energy mass equivalence is 931.5 MeV/amu". I could probably convert amu -> kg, then kg -> J, then J -> MeV, then MeV -> keV BUT, i'm dont think thats what they're asking given they've stated "the energy mass equivalence is 931.5 MeV/amu" does that just mean that for 1 unit of amu = 931.5 OR to divide 931.5 BY the value i've obtained in amu.

    Insight appriciated :( i am quite stuck.
     
  2. jcsd
  3. May 30, 2012 #2
    Yes, it means that there are 931.5 MeV for every amu. Think about it from an algebraic point of view:

    k = 931.5 MeV/amu

    2 amu * k → 2 amu * 931.5 MeV / amu

    The 'amu's cancel out to leave MeV

    2 * 931.5 MeV → 1863 MeV

    NR
     
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