Quick question about positive beta decay and mass defect?

In summary, in nuclear physics, we have a proton becoming a neutron and kicking out a positron and an electron neutrino. The extra electron mass-energy comes from the fact that the original atom was electrically neutral, but after this decay we are one proton short.
  • #1
jeebs
325
4
Hi,
I was wondering about something in my notes that I don't quite understand. In positive beta decay in nuclear physics, we have a proton becoming a neutron and kicking out a positron and an electron neutrino (which is assumed massless here).

In the expression for the energy released, Q = [M(A,Z) - M(A,Z-1) - 2me]c2, we have the kinetic energy of the products is equal to the mass-energy of the original nucleus minus the mass energy of the new nucleus minus TWO electron masses.
This factor of two is what confuses me.

All my notes really say is that this is due to an excess of electrons. Now I assume what this means is that originally the atom is electrically neutral, with equal numbers of protons and electrons. After this decay, we are one proton short, so there is on excessive electron in an atomic electron shell.

I still do not see where this extra electron mass-energy comes from though, because the excess electron in question is not being created, it was always there. All that has been created is one positron, and we are assuming the neutrino to be massless.

Can anyone explain this?

Thanks.
 
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  • #2
If we were to use nuclear masses in the calculation, there would be no factor of 2:

[tex]Q = M_{nuc}(A,Z) - M_{nuc}(A,Z-1) - m_e[/tex]

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

[tex]Q = [M(A,Z) - Zm_e] - [M(A,Z-1) - (Z-1)m_e] - m_e[/tex]

Remove the brackets and parentheses, collect terms, and you end up with your equation with the "extra" factor of 2.
 
  • #3
ah cheers for that jtbell.

can I ask what the justification is for using the atomic mass? its just that the title of my module is "nuclear physics" after all.
 
  • #4
Probably because what we measure in mass spectrometers etc. is the atomic mass, or something close to it, e.g. a singly-charged ion. It's kind of hard to strip all the electrons off, say, an iron or a uranium atom.
 
  • #5
I am as confused as the thread starter =)

I get that the M(A,Z) - M(A,Z-1) - 2Me is from the atomic mass..

I just don't know how to relate these graphically..
 

Related to Quick question about positive beta decay and mass defect?

1. What is positive beta decay?

Positive beta decay, also known as beta-plus decay or positron emission, is a type of nuclear decay where a proton in the nucleus of an atom is converted into a neutron, resulting in the emission of a positron (a positively charged particle) and a neutrino.

2. How does positive beta decay differ from negative beta decay?

Positive beta decay is the opposite of negative beta decay, which is also known as beta-minus decay or electron emission. In negative beta decay, a neutron in the nucleus of an atom is converted into a proton, resulting in the emission of an electron and an antineutrino. This process results in a decrease in atomic number, while positive beta decay results in an increase in atomic number.

3. What is the role of the weak nuclear force in positive beta decay?

The weak nuclear force is responsible for mediating positive beta decay. This force is one of the four fundamental forces of nature and is responsible for the radioactive decay of subatomic particles. In positive beta decay, the weak nuclear force allows a proton to be converted into a neutron, emitting a positron and a neutrino in the process.

4. Why is mass defect observed in positive beta decay?

Mass defect is observed in positive beta decay because the total mass of the products (neutron, positron, and neutrino) is slightly less than the mass of the initial proton. This difference in mass is known as the mass defect and is converted into energy according to Einstein's famous equation, E=mc^2. This energy is carried away by the emitted particles.

5. How is positive beta decay used in medical imaging?

Positive beta decay is used in medical imaging techniques such as positron emission tomography (PET). In PET scans, a radioactive isotope that undergoes positive beta decay is injected into the body. As the positrons emitted by the isotope interact with electrons in the body, they produce gamma rays that can be detected by the PET scanner. This allows for the creation of detailed images of the body's internal structures and functions.

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