Exploring the Mystery of Neutrinos: Mass, Production, and Purpose

[D4rthV4D3r]

I posted this question on Yahoo Answers and got no responses than I found this site and figured it would be more reliable...



I am no physicist but I have been reading up on particle physics for fun lately and have come across something i do not understand. We know that the mass of a neutrino is extremely small but non-zero. I couldn't find the exact measurement anywhere but then I thought that you should be able to solve it algebraically knowing that in Electron Capture: 1Proton + 1Electron = 1Neutron + 1ElectronNeutrino


Knowing the following:
Proton = 1.672621637 X 10^-27
Neutron = 1.67492729 X 10^-27
Electron = 9.10938215 X 10^-31
Electron Neutrino = variable x

After simple addition we can say that (1.67353258 X 10^-27) = (1.67492729 X 10^-27) + x
This would conclude that the mass of an electron neutrino (x) is approx. -1.39471 X 10^-30 which makes no sense.


I am clearly missing something here... I'm assuming that it has to do with the loss/gain of energy but I do not know. If its obvious what I did wrong please don't be a jerk about it, I'm only in High School and am just trying to learn some of this stuff via the internet.

Please enlighten me

 

[Parlyne]

The piece you're missing is that mass is not conserved in interactions that change particle types. I'm sure you're familiar with Einstein's equation $E=mc^2$. What this equation means, in practice, is that mass is a type of energy and should be included in energy conservation equations, rather that having its own conservation. In this context, what the calculation you've done actually shows is that an electron and a proton each at rest do not have enough energy to produce a neutron and a neutrino. And, in fact, if you read about electron capture, you'll find that it does require either the electron or the proton (or both) to have some kinetic energy.

As for the neutrinos, there are no direct mass measurements as yet that give results inconsistent with 0. What we really know is that the three neutrino masses have to be different from each other, which means that no more than one of them can be 0. We know this from the observation that neutrinos oscillate. This means that neutrinos created as one species (say, electron neutrinos) can sometimes be detected as one of the other species (under well understood conditions and with predictable probability).

As it turns out, this can only happen under two conditions. First, it must be the case that the neutrino states that we detect (those corresponding to the charged leptons - the electron, the muon, and the tau) must each actually be mixtures of the states with well-defined masses. And, second, the masses of the neutrinos in those states of well-defined mass must be different from each other. (In fact, the first condition can only be true when the second is true; but, the second could be true when the first isn't.)

 

[D4rthV4D3r]

The piece you're missing is that mass is not conserved in interactions that change particle types. I'm sure you're familiar with Einstein's equation $E=mc^2$. What this equation means, in practice, is that mass is a type of energy and should be included in energy conservation equations, rather that having its own conservation. In this context, what the calculation you've done actually shows is that an electron and a proton each at rest do not have enough energy to produce a neutron and a neutrino. And, in fact, if you read about electron capture, you'll find that it does require either the electron or the proton (or both) to have some kinetic energy.

As for the neutrinos, there are no direct mass measurements as yet that give results inconsistent with 0. What we really know is that the three neutrino masses have to be different from each other, which means that no more than one of them can be 0. We know this from the observation that neutrinos oscillate. This means that neutrinos created as one species (say, electron neutrinos) can sometimes be detected as one of the other species (under well understood conditions and with predictable probability).

As it turns out, this can only happen under two conditions. First, it must be the case that the neutrino states that we detect (those corresponding to the charged leptons - the electron, the muon, and the tau) must each actually be mixtures of the states with well-defined masses. And, second, the masses of the neutrinos in those states of well-defined mass must be different from each other. (In fact, the first condition can only be true when the second is true; but, the second could be true when the first isn't.)

ok, thank you that helps alot.

so if I take my result of -1.39471 X 10^-30 and make it positive (the mass needed to make the P+E=N) then plug it into E=mc^2...

E = (1.39471 X 10^-30) X (299,792,458)^2
E = 4.18123539 X 10^-22 (what unit goes here? Newtons? joules?)

so the answer above is the energy needed to account for 1P+1E=1N but it doesn't account for the energy needed to create the electron neutrino... Am I able to conclude that the energy necessary to complete Electron Capture must be greater than (4.18123539 X 10^-22) ?

 

[Parlyne]

ok, thank you that helps alot.

so if I take my result of -1.39471 X 10^-30 and make it positive (the mass needed to make the P+E=N) then plug it into E=mc^2...

E = (1.39471 X 10^-30) X (299,792,458)^2
E = 4.18123539 X 10^-22 (what unit goes here? Newtons? joules?)

so the answer above is the energy needed to account for 1P+1E=1N but it doesn't account for the energy needed to create the electron neutrino... Am I able to conclude that the energy necessary to complete Electron Capture must be greater than (4.18123539 X 10^-22) ?

Don't forget to square c. Then you should get something like 1.25 x 10^-13 J.

Then, yes, this will be a lower limit on the amount of extra energy needed for electron capture to be possible. Given the present limits on neutrino masses, including neutrino mass here shouldn't increase this energy by more that about 1 x 10^-20 J (although, the particular bound that this comes from is somewhat model-dependent).

I'll also add that this minimum extra energy requires that the neutron and neutrino both be created at rest, meaning that the momenta of the proton and the electron must be equal and opposite. (The momenta of the neutron and neutrino are both 0, so conservation of momentum requires that the momenta of the electron and proton add to 0.)

 

[D4rthV4D3r]

thank you, that definitely helps me with my questions.

 

[jtbell]

In this context, what the calculation you've done actually shows is that an electron and a proton each at rest do not have enough energy to produce a neutron and a neutrino. And, in fact, if you read about electron capture, you'll find that it does require either the electron or the proton (or both) to have some kinetic energy.

Electron capture takes place naturally only in certain nuclei (isotopes), in which the resulting nucleus has a mass less than the the initial nucleus plus electron, with the extra energy becoming the energy of the outgoing neutrino. The differing nuclear masses come about because of differences in nuclear binding energy.

http://en.wikipedia.org/wiki/Electron_capture

In doing a mass/energy analysis you can't use the masses of a single proton and a single neutron in this case, but rather the masses of the initial and final nuclei. Actually, what you find in tables are the masses of the entire atoms including the orbital electrons, so it takes a bit of care to get things to balance correctly.

In principle, one could use measured initial and final atomic masses and decay energies to calculate the mass of the outgoing neutrino. The first major problem with this is that neutrinos with these energies are extremely difficult to detect to begin with, let alone measure their energies. Second, even if we could measure the neutrino energy with precision similar to what we can get with atomic masses, it still might not be enough. From neutrino oscillations, we expect the mass to be in the ballpark of a few eV, which is about 10^-36 kg.

 

[D4rthV4D3r]

Thank you jtbell

Another question on the topic of neutrinos... I have a feeling this a stupid question but I couldn't find it elsewhere so please don't jump all over me for asking...

Where exactly are neutrinos? Are they independent particles that travel through the universe? I can't imagine where they would fit within an atom. And if they are independent, what is their purpose? What do they make up?

 

[ASD16]

Thank you jtbell

Another question on the topic of neutrinos... I have a feeling this a stupid question but I couldn't find it elsewhere so please don't jump all over me for asking...

Where exactly are neutrinos? Are they independent particles that travel through the universe? I can't imagine where they would fit within an atom. And if they are independent, what is their purpose? What do they make up?

Well neutrinos are primarily produced in huge numbers in nuclear reactions...like it happens in the thermonuclear reactions at the center of the sun...each second about billions of neutrinos pass through ur body...most of which are produced in the thermonuclear reaction in the sun...they are independent particles...elementary particles indeed...and as far their purpose is concerned...very little is known about them...they are even the candidates of the so called dark matter...researches are going on around the world to study the properties of these particles...so to date not much reliable information is available...