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

In summary: G = 1863 MeVIn summary, the maximum kinetic energy of an electron emitted in the beta decay of a free neutron can be calculated using the equation e=mc^2, where e represents energy, m represents mass, and c represents the speed of light. The beta decay equation, A / Z X -> A / (Z+1) Y + e- + v, can be used to represent the decay process. The energy mass equivalence for this question is 931.5 MeV/amu, meaning that there are 931.5 MeV for every amu. By converting the masses of the neutron, proton, and electron into energy using the equation e=mc^2, the maximum kinetic energy of the
  • #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.
 
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  • #2
chirumu said:

Homework Statement

...
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.

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
 

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

1. What is the formula for calculating the kinetic energy of an electron emitted from beta decay?

The formula for calculating the kinetic energy (KE) of an electron emitted from beta decay is KE = (Q - mn) - me, where Q is the total energy released in the beta decay, mn is the mass of the neutron, and me is the mass of the electron.

2. How do I find the values for Q, mn, and me in the KE formula?

The value for Q can be obtained from the energy level diagram of the specific beta decay reaction. The values for mn and me can be found in a reference table or calculated using the atomic mass and atomic number of the particles involved in the decay.

3. Why is the mass of the electron subtracted in the KE formula?

The mass of the electron is subtracted in the KE formula because it is the mass that is converted into kinetic energy during the beta decay process. This conversion is due to the release of a neutrino, which has a very small mass compared to the electron.

4. Is the KE of the emitted electron always the same in beta decay?

No, the KE of the emitted electron can vary in beta decay reactions. This is because the energy released in the decay can be distributed differently between the electron and the neutrino, resulting in a range of possible KE values for the electron.

5. How is the KE of an electron from beta decay related to the energy of the emitted photon?

The energy of the emitted photon in beta decay is equal to the difference between the total energy released (Q value) and the KE of the emitted electron. This is because the energy released is shared between the electron and the neutrino, and the remaining energy is carried away by the photon.

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