Beta Negative Decay: Is Mass Defect Calculated Correctly?

[coreluccio]

During beta negative decay, in an unstable isotope, a neutron is converted into a proton, electron, and antineutrino. The electron and antineutrino are ejected from the atom and the proton remains in the nucleus to become the new daughter element.

For a beta negative decay reaction for some element, I decide to calculate the mass defect of the reaction by subtracting the masses of the reactants from the masses of the products. I use a chart of common atomic isotopes, each isotope's mass given in its neutral state.

Now, the daughter element has one more proton than the parent element did, but they both have the same number of electrons. The daughter element, then, has a positive charge of +1, right? So the mass of the daughter element, given on the chart, will give its neutral mass, assuming it has one more electron than it really does, and thus falsifying my calculations.


Is this the case or am I wrong on something?

 

[jtbell]

If we were to use nuclear masses in the calculation, we would have to include the mass of the outgoing electron:

$$Q = M_{nuc}(A,Z) - M_{nuc}(A,Z+1) - m_e$$

However, the masses that we actually find in the standard tables are atomic masses of neutral atoms, which include the mass of Z electrons: $M(A,Z) = M_{nuc}(A,Z) + Zm_e$. Substituting for the nuclear masses in the first equation:

$$Q = [M(A,Z) - Zm_e] - [M(A,Z+1) - (Z+1)m_e] - m_e$$

Remove the brackets and parentheses, collect terms, and $m_e$ drops out.

See the following thread for a discussion of positive beta decay, in which case the result is different:

https://www.physicsforums.com/showthread.php?t=375065

 

[masch]

jtbell, I am also interested to know where can we find the extra electron.. can you redescribe using layman's terms?

Specifically, 4He beta(-) decays to 3He (neutron changes to Proton and emitting a beta particle). So the nucleus now has 3 protons and one neutron, whereas the orbitting electrons there are only two.. where will the extra electron come from to make the atom neutral?

(p/s - I'm not sure of 4He can beta decay at all - just an example, pls feel free to correct me)

Basically, I understand from your reply how to calculate the mass (and Q energy) conservation, but I can't figure out charge conservation.

To me it looks like the daughter product has an extra +ve charge.. so will it get an extra electron from somewhere?

 

[minerva]

jtbell, I am also interested to know where can we find the extra electron.. can you redescribe using layman's terms?

Specifically, 4He beta(-) decays to 3He (neutron changes to Proton and emitting a beta particle). So the nucleus now has 3 protons and one neutron, whereas the orbitting electrons there are only two.. where will the extra electron come from to make the atom neutral?

(p/s - I'm not sure of 4He can beta decay at all - just an example, pls feel free to correct me)

Basically, I understand from your reply how to calculate the mass (and Q energy) conservation, but I can't figure out charge conservation.

To me it looks like the daughter product has an extra +ve charge.. so will it get an extra electron from somewhere?

Um, no, He-4 certainly cannot beta decay. Even if it could beta decay, it would decay to Li-4, not He-3.

H-3, for a more realistic example, will beta decay, becoming He-3.

 

[masch]

OK that makes sense..

Lets say Tritium, 1 proton + 2 neutrons then beta-decays to 3He (2 protons + 1 neutron)

Beta- decay = 1 neutron changes into a proton and releases a beta particle.

Now the atom, originally having 1 electron in orbit (Hydrogen) and 1 proton in nucleus.. having a neutral charge. But now, it has 2 protons in nucleus and only 1 electron (still) in orbit.. as the beta- particle is ejected out of the atom.. So is He-3 a +1 charged atom then?

 

[jtbell]

Temporarily, you have a singly-charged He-3 ion. It soon picks up an electron from a neighboring atom, which in turn becomes an ion and picks up an electron from a neighboring atom, etc., until finally some ion in the chain picks up the electron that was ejected in the original beta decay.

 

[masch]

Temporarily, you have a singly-charged He-3 ion. It soon picks up an electron from a neighboring atom, which in turn becomes an ion and picks up an electron from a neighboring atom, etc., until finally some ion in the chain picks up the electron that was ejected in the original beta decay.

Hi JtBell, thanks for your answer..

But isn't that a bit far fetched? Why can't the other atoms around the He-3 ion hold on to their own electrons? Also, if this is true, then there will be lots and lots of electrons jumping around from atom to atom - and this means there are a lot of electricity being passed around us - wireless electricity..

 

[fatra2]

Hi there,

But isn't that a bit far fetched? Why can't the other atoms around the He-3 ion hold on to their own electrons?

Because of the energy carried by the decay electron. It can carry up to ~15keV of kinetic energy. This means that it needs to slow down, before it can be captured by an atom.

Also, if this is true, then there will be lots and lots of electrons jumping around from atom to atom - and this means there are a lot of electricity being passed around us - wireless electricity..

Lots and lots of electrons are jumping around in matter, no matter what. It does not mean anything more than moving electron. To have "electricity" in the sense that we understand it, the electrons must be moving "all" in the same direction. In this case, the movement is completely random, since a electrons can move left, right, up, or down, giving no measurable current.

Cheers

 

[DrDu]

Hi JtBell, thanks for your answer..

But isn't that a bit far fetched? Why can't the other atoms around the He-3 ion hold on to their own electrons? Also, if this is true, then there will be lots and lots of electrons jumping around from atom to atom - and this means there are a lot of electricity being passed around us - wireless electricity..

Yes, that's the principle of a SNAP (system for nuclear auxiliary power) as used for generating energy e.g. in satellites.