The question describes the beta positive decay for Nitrogen-13 into Carbon-13.
After reading the explanation for the answer, it says that carbon ion will lose an electron in the decay process; therefore the the mass of products is the carbon nucleus + electron + positron.
But I'm just confused because the equation does not include an electron, yet its mass is added to the mass of the products. Why is that? and why isn't it the same for beta negative decay?
Reaction provided in the question:
Nitrogen-13 -> Carbon-13 + Positron + neutrino
Atomic Masses:
Nitrogen-13: 13.005739 u
Carbon-13: 13.003355 u
Electron/Positron: 0.000549 u
What I did:
E=Δmc^2
Δm=m(parent)-m(products)
Δm=nitrogen-13-(Carbon-13 + positron mass)
Δm= (13.005739u)-(13.003355u+0.000549u)
Δm= 0.001835 (931.5MeV/u)
E= 1.709 MeV
Solution:
E=Δmc^2
Δm=m(parent)-m(products)
Δm=nitrogen-13-(Carbon-13 + electron mass + positron mass)
Δm= (13.005739u)-(13.003355u+ 2(0.000549u))
Δm= 0.001286 (931.5MeV/u)
E= 1.198 MeV
Best Answer
You are modeling the following reaction:
Nitrogen-13 -> Carbon-13 + Positron + neutrino
This reaction is in the nucleus, so you should use the mass of the nucleus in the mass balance, not the atomic mass. However, we generally don't have the nucleus mass available, so we use the atomic masses. The atomic masses include the mass of the electrons.
The equation you should be using:
Δm=nucleus(N13)-(nucleus(C13) + positron mass)
Add 7 electrons to each side to use atomic mass:
Δm=nucleus(N13)+ 7(electron mass) -(nucleus(C13) + 7(electron mass) + positron mass)
Combine the nucleus mass and electron mass to get atomic mass. Note that the carbon atom only has 6 electrons, so you are left with an extra electron.
Δm=atomic(N13) -(atomic(C13) + electron mass + positron mass)
This is where the extra electron mass comes from.