Where Does the Extra Mass in Beta-Plus Decay Come From?

[repugno]

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?

 

[mathman]

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.

 

[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.

 

[mathman]

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.

 

[Norman]

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

 

[Orion1]

Positron Decay...



One of the lightest nuclei that produces positronium decay:

^7_5B \to ^7_4Be + e^+(1.4 Mev)

proton/neutron ratio: 5/2

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

proton/neutron ratio: 2/0