How can beta decay have energy of 3-4 MeV

[Moazin Khatri]

First of all let me tell that I am a high school student and I have no background in particle physics.
If we apply the Heisenberg's uncertainty principle to an electron confined in the nucleus it tells us that the energy of the electron must be something like 3.8X10^8eV .. but in a beta decay the energy of the electron is 3-4 MeV.
The moment a neutron decays into a proton and an electron and a neutrino particle the electron will be in the region of nucleus for some small time at least. While in that region, according to Heisenberg's principle it must have such a large energy. But experimentally we find that beta particles have an energy of 3-4 MeV. Why?
Please clarify me as much as possible and correct me wherever i am wrong.
I read about this from this link: http://elearning.vtu.ac.in/e-con/Phys/html/0018.htm

 

[Vanadium 50]

Why do you think the electron is localized to the nucleus in beta decay? Isn't it outside the nucleus when you detect it?

 

[Moazin Khatri]

If it comes from the decay of a down quark it has to come from the nucleus. And for some small time it will be in that region. And yes that's true that we detect it when it is outside the nucleus but still, the question remains, does it loose energy as it comes out of the nucleus because for some time it would be in the region of nucleus and must have high energy.

 

[Orodruin]

No, it will not. Your view of how the decay occurs is too classical.

 

[Moazin Khatri]

Yes sir. I understand that. But if any simpler basic level explanation can be provided I will be very grateful.
I do understand some of the basic ideas of quantum mechanics. So if a simple explanation based on few basic ideas of quantum mechanics can be given I will welcome it.

 

[Vanadium 50]

some time it would be in the region of nucleus and must have high energy.

That's simply not true. Just being "in the region" doesn't do anything. Forget radioactive decay for a second and just consider atoms. Electrons are sometimes in the region of the nucleus, but there energy doesn't skyrocket when this happens.

 

[Orodruin]

Forget radioactive decay for a second and just consider atoms. Electrons are sometimes in the region of the nucleus, but there energy doesn't skyrocket when this happens.

This depends on what you mean by "sometimes in the region of the nucleus". If you would actually locate the electron to the nucleus this would add a large amount of energy to the electron. It is not the same thing as the wave function having a non-zero value within the nucleus, which is a large part of the reason we have electron capture in some elements.

 

[Vanadium 50]

If you would actually locate the electron to the nucleus this would add a large amount of energy to the electron.

That's true, but it doesn't happen in either case.