- #1
chirumu
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Homework Statement
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
Homework Equations
e=mc^2
beta decay equation:
A / Z X -> A / (Z+1) Y + e- + v
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 haven't converted amu into energy. I don't 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 don't think that's 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.