# Homework Help: Calculate the KE of an electron emitted from the beta decay of a neutron

1. May 29, 2012

### chirumu

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. May 30, 2012

### NemoReally

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