Quick question on the mass condition for beta decay

In summary, the equations for β- and β+ decay involve the removal or emission of an electron from an atom. However, the equations differ in that for β+ decay, the charge on the right side of the equation must be corrected to reflect the emission of a positron, resulting in an overall increase in the number of electrons and the addition of two electron masses to the equation. This is due to the fact that the emitted positron and the neutral atom both require an additional electron to achieve an overall neutral charge.
  • #1
rwooduk
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For β- we have:

##M(A,Z)>M(A,Z+1) + m_{e} - m_{e}##

An electron is removed from the atom and therefore we need to take that away from the M(A,Z+1) term

But for β+ we have been given:

##M(A,Z)>M(A,Z+1) + m_{e} + m_{e}##

What is this saying? A positron is emitted, therefore shouldn't we minus the mass of the positron from the atomic mass? which would give the same expression as for β-? I'm confused as to why it is plus, it's probably something really simple but I can't figure it for some reason.

Thanks for any help/ideas

edit also a quick side question, is β+ decay the same as electron capture? As they give the same daughter nucleus.
 
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  • #2
rwooduk said:
But for β+ we have been given:

##M(A,Z)>M(A,Z+1) + m_{e} + m_{e}##

What is this saying? A positron is emitted, therefore shouldn't we minus the mass of the positron from the atomic mass? which would give the same expression as for β-? I'm confused as to why it is plus, it's probably something really simple but I can't figure it for some reason.

Thanks for any help/ideas

edit also a quick side question, is β+ decay the same as electron capture? As they give the same daughter nucleus.

Probably those who have given the equation are confused in explaining what the equation is for.
Positron decay and electron capture are not the same - daughter nucleus is the same, but other ingredients are not. They therefore have different mass conditions.
 
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  • #3
snorkack said:
Probably those who have given the equation are confused in explaining what the equation is for.

So is the mass condition that we have been given for β+ decay incorrect?
snorkack said:
Positron decay and electron capture are not the same - daughter nucleus is the same, but other ingredients are not. They therefore have different mass conditions.

Thanks! also i realized the spectrum is different, beta decay being broad and Auger giving discrete emission lines.

thanks for the reply
 
  • #4
The beta+ equation is wrong in some way - if the left side is supposed to be the initial state (the ">" suggests this) then the charge at the right side is wrong. Fix that and the equation makes sense. Note that the number of electrons for the final atom (which is included in those mass values) is different for the two processes.
 
  • #5
mfb said:
The beta+ equation is wrong in some way - if the left side is supposed to be the initial state (the ">" suggests this) then the charge at the right side is wrong. Fix that and the equation makes sense. Note that the number of electrons for the final atom (which is included in those mass values) is different for the two processes.

Thanks. Would you mind writing out the correct equation? I'm unsure what you mean by "the charge at the right side" when they are masses. thanks again for your help.
 
  • #6
Z+1 in the brackets is the charge of the nucleus. If you emit a positive particle (a positron) the proton number has to decrease.
$$M(A,Z)>M(A,Z-1) + m_{e} + m_{e}$$The two more electron masses compared to beta- decay come from the additional positron and the fact that you suddenly have an additional electron that does not "belong to" the atom - so you have the new neutral atom plus one electron plus one positron, and the original atom has to have enough energy to produce all of them.
 
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  • #7
mfb said:
Z+1 in the brackets is the charge of the nucleus. If you emit a positive particle (a positron) the proton number has to decrease.
$$M(A,Z)>M(A,Z-1) + m_{e} + m_{e}$$The two more electron masses compared to beta- decay come from the additional positron and the fact that you suddenly have an additional electron that does not "belong to" the atom - so you have the new neutral atom plus one electron plus one positron, and the original atom has to have enough energy to produce all of them.

That's great thanks. Although I think I'm getting confused; Z is the number of protons, after decay it turns to a new element with Z-1 with an emitted positron, so then why are we adding the mass of an electron?
 
  • #8
Let's consider an example:
$${}^{40}_{19}Ka \to {}^{40}_{18}Ar + e^+ + \nu_e$$
Potassium on the left side normally has 19 electrons, so we still have 19 electrons on the right side - but Argon just has 18 protons, so one electron is surplus. We can write the reaction as
$${}^{40}_{19}Ka \to {}^{40}_{18}Ar + e^- + e^+ + \nu_e$$
to get neutral atoms, because the mass numbers refer to those neutral atoms.
 
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  • #9
mfb said:
Let's consider an example:
$${}^{40}_{19}Ka \to {}^{40}_{18}Ar + e^+ + \nu_e$$
Potassium on the left side normally has 19 electrons, so we still have 19 electrons on the right side - but Argon just has 18 protons, so one electron is surplus. We can write the reaction as
$${}^{40}_{19}Ka \to {}^{40}_{18}Ar + e^- + e^+ + \nu_e$$
to get neutral atoms, because the mass numbers refer to those neutral atoms.

Of course, number of protons = number of electrons, so 1 electron is surplus. Sorry it's been 20 years since my GCSE chemistry, but still should know this lol

Many thanks!
 

1. What is the mass condition for beta decay?

The mass condition for beta decay is a principle in nuclear physics that states that the mass of the parent nucleus must be greater than the combined masses of the daughter nucleus and the emitted beta particle for the decay to occur.

2. Why is the mass condition important in beta decay?

The mass condition is important because it determines whether a particular nucleus will undergo beta decay or not. If the mass of the parent nucleus is not greater than the combined masses of the daughter nucleus and beta particle, then beta decay cannot occur.

3. How is the mass condition related to the conservation of energy in beta decay?

The mass condition is directly related to the conservation of energy in beta decay. The total mass of the parent nucleus, daughter nucleus, and beta particle must remain the same before and after the decay. If the mass condition is not satisfied, then energy is not conserved and the decay cannot occur.

4. Is the mass condition the same for all types of beta decay?

No, the mass condition can differ slightly for different types of beta decay. For example, in beta-minus decay, the mass of the parent nucleus must be greater than the combined masses of the daughter nucleus and emitted electron, while in beta-plus decay, the mass of the parent nucleus must be greater than the combined masses of the daughter nucleus and emitted positron.

5. How is the mass condition affected by the presence of neutrinos in beta decay?

The mass condition is not affected by the presence of neutrinos in beta decay. Neutrinos have very small masses and are not included in the calculation of the total mass of the particles involved in the decay. Therefore, the mass condition still applies even in the presence of neutrinos.

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