# Is the Beta Decay Mass Condition Dependent on Atomic Masses?

• Master J
In summary, the condition for beta decay, specifically positron emission, is that the atomic mass of the parent nucleus must be greater than the sum of the daughter nucleus and twice the mass of an electron. This is because one m_e accounts for the electron emitted by the nucleus, and the second m_e is the extra electron that must be added to the outer shell of electrons in the atom. Additionally, the most stable isobar on an atomic mass parabola is the most stable one, as it is a tautology. Finally, the electron that must be added to the shell during beta decay comes from outside the atomic system and does not affect the mass condition, as atomic masses are used in the calculation.
Master J
In beta decay, positron emission, how come the condition for decay is:

M_p > M_d + 2m_e

Thats: atomic mass of parent > "daughter + twice the mass of an electron.

I'm sure there is some simple way of showing it, but I can't seem to find it!

Also, is the most stable isobar on an atomic mass parabola the most stable one? It's a question my lecturer posed to us, and I have been thinking about it a while.

Thanks!

It is 2m_e because it is the atomic and not the nuclear mass.
One m_e is because of the electron emitted by the nucleus.
The second m_e is the extra electron that must be added to the outer shell of electrons in the atom.

that is since the daughter nucleus will have one electron less than the parent, and what is listed is ATOMIC masses. So if you calculate it with NUCLEAR masses it should of course be:

M_p > M_d + m_e

if now M is nuclear masses.

The other question is a homework - course work question, and should not be adressed in this forum but in the homework forum, with an attempt to solution.

"Also, is the most stable isobar on an atomic mass parabola the most stable one?"
As you write this question it is a tautology: Is the most stable the most stable?

For the parent p to decay to the daughter d by positron decay, the parent would have to create both a positron and electron (lepton number is conserved) before having sufficient energy to decay by positron emission. Example: could a proton decay to a neutron plus positron? What would the minimum proton mass be?

Bob S said:
For the parent p to decay to the daughter d by positron decay, the parent would have to create both a positron and electron (lepton number is conserved) before having sufficient energy to decay by positron emission. Example: could a proton decay to a neutron plus positron? What would the minimum proton mass be?

nope, the electron number is conserved by emitting a neutrino

beta+ decay on subnuclear level is:

p -> n + e(+) + neutrino

You are proposing:

p-> n + e(+) + e(-)

which violates electric charge conservation.

malawi_glenn said:
nope, the electron number is conserved by emitting a neutrino

beta+ decay on subnuclear level is:

p -> n + e(+) + neutrino

You are proposing:

p-> n + e(+) + e(-)

which violates electric charge conservation.
Mea Culpa. There are three types of beta decay exibited by nuclei: Here are 3 examples, all from Cu64
A) Positron emission (by proton), with an antineutrino
B) Electron emission (by neutron) , with a neutrino
C) K-shell electron capture (by proton) with only an antineutrino emission

(From Wiki):
64Cu has a half-life of 12.701 ± 0.002 hours and decays by 17.86 (± 0.14)% by positron emission, 39.0 (± 0.3)% by beta decay, 43.075 (± 0.500)% by electron capture

where does the electron that must be added to the shell then come from? if its from outside the atomic system in question, then surely it has no place in the mass condition?

Master J said:
where does the electron that must be added to the shell then come from? if its from outside the atomic system in question, then surely it has no place in the mass condition?

WHERE it comes from is not important, the issue is that you are using atomic masses.. as I explain to you.

## What is beta decay mass condition?

Beta decay mass condition is a physical law that states that the total mass before and after a beta decay reaction must be conserved. This means that the sum of the masses of the particles before the reaction must equal the sum of the masses of the particles after the reaction.

## What are the particles involved in beta decay?

The particles involved in beta decay are the beta particle (electron or positron), an antineutrino (for beta minus decay) or a neutrino (for beta plus decay), and the parent nucleus.

## How does beta decay affect the atomic number and mass number of an atom?

Beta decay can change the atomic number and mass number of an atom. In beta minus decay, an electron is emitted, which increases the atomic number by one but does not affect the mass number. In beta plus decay, a positron is emitted, which decreases the atomic number by one but also does not affect the mass number. In both cases, the resulting nucleus has a different element but the same mass number as the original nucleus.

## What is the difference between beta minus and beta plus decay?

Beta minus and beta plus decay are two types of beta decay that differ in the particles emitted. In beta minus decay, an electron is emitted from the nucleus, and in beta plus decay, a positron is emitted. Beta minus decay occurs in nuclei with excess neutrons, while beta plus decay occurs in nuclei with excess protons.

## What is the role of the weak nuclear force in beta decay mass condition?

The weak nuclear force is responsible for the beta decay process and ensures that the total mass before and after a beta decay reaction remains constant. This is because the weak nuclear force is the only force that can change the identity of a particle, allowing for the transformation of a neutron into a proton (beta minus decay) or vice versa (beta plus decay).

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