Beta-Plus Decay: Exploring Mass Conservation

In summary, beta-plus decay is a nuclear decay process where a proton decays into a neutron and emits a positron. This process occurs in nuclei where the proton to neutron ratio is too high. The difference in binding energy between the mass of the nucleus before and after the decay accounts for the extra mass of the neutron. This process is not a proton decay process, as positron emission is a nuclear decay phenomenon. The energy difference between the masses of the involved particles allows for the creation of the positron and neutron.
  • #1
repugno
78
0
Hello all,

In beta-plus decay, a proton decays into a neutron and emmits a positron. If the neutron weighs more than the proton where did the extra mass come from?
 
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  • #2
This process occurs in nuclei where the proton to neutron ratio is too high. Under these conditions mass of the nucleus before is greater than the mass of the nucleus after (difference in binding energy). As I am sure you are well aware, proton to neutron decay does NOT occur in isolation.
 
  • #3
Thanks for the reply Mathman,

Mass of neutron = 1.675 * 10^-27 kg
Mass of proton = 1.673 * 10^-27 kg
Mass of positron = 9.1 * 10^-31 kg

This is what I can't understand. In Beta-plus decay, a proton decays into a neutron where a positron is also emmited.

(1.675 * 10^-27) + (9.1 * 10^-31) = 1.67591 * 10^-27

(1.67591 * 10^-27) - (1.673 * 10^-27) = 2.91 * 10^-30

Somehow 2.91 * 10^-30 kg of mass appeared.
 
  • #4
I guess you don't fully appreciate the point that I was trying to make. Positron emmssion is a nuclear decay process, not a proton decay process. For example, PET devices may use F18, which decays into O18.

The following table should help:

nuclide mass (amu) binding energy (kev)

O18 17.9991604 139807.0
F18 18.0009377 137369.2

energy difference 2437.8

Since a positron hass a mass equivalent to 511 kev, there is plenty left over for momentum.
 
  • #5
Originally posted by repugno
Thanks for the reply Mathman,

Mass of neutron = 1.675 * 10^-27 kg
Mass of proton = 1.673 * 10^-27 kg
Mass of positron = 9.1 * 10^-31 kg

This is what I can't understand. In Beta-plus decay, a proton decays into a neutron where a positron is also emmited.

(1.675 * 10^-27) + (9.1 * 10^-31) = 1.67591 * 10^-27

(1.67591 * 10^-27) - (1.673 * 10^-27) = 2.91 * 10^-30

Somehow 2.91 * 10^-30 kg of mass appeared.

What you have done is look at the isolated case of a particle decay.
Mathman has already said that this isolated process does not occur for the exact reason you have shown, the proton does not have enough energy to produce a neutron and a positron. What is happening in the systems where this happens is that it is more energetically favorable to have a proton turn into a neutron and positron. The system, as mathman said, are nuclei where there is a large proton to neutron ratio. Because of the odd things that happen in nuclei, the lower energy state is obtained by this new configuration. So in the whole system there is enough energy to create the positron and the neutron.
Hope this helps.
Cheers,
Norm
 
  • #6
Positron Decay...



One of the lightest nuclei that produces positronium decay:

[tex]^7_5B \to ^7_4Be + e^+(1.4 Mev)[/tex]

proton/neutron ratio: 5/2

Fusion produced Deuprotium positronium decay:
[tex]^2_2He(+5.294 Mev) \to ^2_2D + e^+(.24 Mev)[/tex]

proton/neutron ratio: 2/0

 
Last edited:

1. What is beta-plus decay?

Beta-plus decay is a type of radioactive decay in which a proton in an atom's nucleus is converted into a neutron, resulting in the release of a positron (a positively charged particle) and a neutrino. This process occurs in atoms that have too many protons relative to neutrons, causing the nucleus to become unstable.

2. How does beta-plus decay relate to mass conservation?

Beta-plus decay is a manifestation of the law of mass conservation, which states that matter cannot be created or destroyed, only transformed. In beta-plus decay, the total mass of the nucleus before and after the decay remains the same, but the number of protons and neutrons changes.

3. What is the role of the positron in beta-plus decay?

The positron, or anti-electron, is emitted during beta-plus decay to conserve charge. Since a proton has a positive charge and a neutron has no charge, the conversion of a proton into a neutron results in a net loss of positive charge in the nucleus. The positron helps to balance this charge by being emitted with an equal but opposite charge.

4. Can beta-plus decay occur in all types of atoms?

Beta-plus decay can only occur in atoms that have too many protons relative to neutrons, as this creates an unstable nucleus. This is typically seen in larger atoms with atomic numbers greater than 20.

5. How is beta-plus decay different from other types of radioactive decay?

Beta-plus decay is different from other types of radioactive decay, such as alpha and beta-minus decay, because it results in the conversion of a proton into a neutron instead of the release of a particle. It also releases a positron instead of an electron or alpha particle. Additionally, beta-plus decay typically occurs in larger atoms, while alpha and beta-minus decay can occur in smaller atoms as well.

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