# Beta particles

1. Mar 29, 2008

### Physicsissuef

Hi! I read in my textbook, that when there is beta radioactivity, the beta particles are "carrying" the kinetic energy from the nuclei, and they are taking the most of the kinetic energy of the nuclei, so the electrons have less energy than them...
Here is diagram. I can't understand something about the diagram. If I put straight horizontal line among one point, there will be two points $$M_1$$ and $$M_2$$, for different energy levels of the electrons (W is the kinetic energy of the electrons). Why it is like that?

http://img151.imageshack.us/img151/7273/picture001copy1jg2.jpg [Broken]

http://img329.imageshack.us/img329/3677/picture001copyuc2.jpg [Broken]

Last edited by a moderator: Apr 23, 2017 at 11:52 AM
2. Mar 29, 2008

### Staff: Mentor

Those images are too small for me to read. I think you linked to thumbnail images, not to the full-size images.

3. Mar 29, 2008

### Staff: Mentor

Try

http://img151.imageshack.us/img151/7273/picture001copy1jg2.jpg [Broken]

http://img329.imageshack.us/img329/3677/picture001copyuc2.jpg [Broken]

They are energy distributions of beta particles. The peak is about Wmax/3.

The beta particle is very light compared to nuclei. M[nucleus] ~ A*1836*me.

If one looks at the momentum equation and energy equation, then one will see that the KE is apportioned by the momentum. If there are two particles MV = mv, and v = M/mV, for equal but opposite momentum vectors.

Last edited by a moderator: Apr 23, 2017 at 11:53 AM
4. Mar 29, 2008

### Physicsissuef

and why there is same energy level of the electrons for some number of beta particles, like on the picture 2? jtbell sorry for the pictures, I will correct now.

5. Mar 29, 2008

### Staff: Mentor

If one looks at a Poisson or Gaussian distribution, one will find two values of the population function f(x) with the same value but for two different x. All it means is that there is equal probability at those two different values of x, which in the case of the beta decay is the energy of the beta particle. Don't forget that there is a third, nearly massless particle, the neutrino (or anti-neutrino in the case of beta decay) which also takes some momentum and energy.

6. Mar 29, 2008

### Physicsissuef

The neutrino is the cause that there are two equal points for x, if the function is f(x)?

7. Mar 29, 2008

### neu

No.

The diagram you posted is a frequency distribution. f(x) = the number of particles with value x.

As Astronuc said, the fact that there are 2 values of x which give the same f(x) simply shows that the same number of particles are produced with x1 and x2.

8. Mar 29, 2008

### Physicsissuef

how is possible that with (lets say 100 beta particles), there will be 2 kinetic energy levels for the electrons. What is that cause? Why the energy of the electrons is not constant?

9. Mar 29, 2008

### Staff: Mentor

Because,

n -> p(in nucleus) + e- + $\overline{\nu_e}$, and the beta and antineutrino can each take any direction and share energy and momentum.

10. Mar 30, 2008

### Physicsissuef

Somebody told me that because of different kinetic energy distribution, the energy of electrons is not constant. Is this correct?
I have few questions more:

How the neutrino is "taking" the most of the kinetic energy of the nuclei, when it is electro neutral?

When there is $$\beta^-^1$$ decay (lets say of the C atom):

$$\stackrel{14}{6}C \rightarrow \stackrel{14}{7}N + \stackrel{0}{-1}e + \overline{\nu_e}$$

We decay C atom with 6 protons, and receive 7 protons. How come that?

Then, how is possible the period of half decay?

Last edited: Mar 30, 2008
11. Mar 30, 2008

### Staff: Mentor

This is not quite correct. If one were to measures a population of a specific nuclide, one would find a spectrum of energy of the beta particle and anti-neutrino. The energy distributions of the beta and anti-neutrino are complementary since there is a fixed energy available - i.e. the mass-energy difference between the radionuclide (parent) and the subsequent nuclide (product of decay).

The anti-neutrino has energy and momentum, just as photons (also neutral) have energy and momentum.

The neutron (n) decays into a proton, beta and anti-neutrino, so if 14C decays by beta emission, then 6p,8n becomes 7p,7n, because 1 n -> 1 p. The number of nucleons is preserved but Z increases by 1, and N (number of neutrons) decreases by 1.

What is meant by "period of half-decay"? Is one referring to half-life?

12. Mar 30, 2008

### Staff: Mentor

One of the neutrons in the C atom converts to a proton via the weak interaction:

$$n \rightarrow p + e^{-} + {\overline \nu}_e$$

More fundamentally, one of the d quarks in the proton converts to a u quark by emitting a virtual W boson:

$$d \rightarrow u + W^{-}$$

and then the W boson converts to an electron and antineutrino pair:

$$W^{-} \rightarrow e^{-} + {\overline \nu}_e$$

Both of these are fundamental weak-interaction processes. To anticipate your next "why?" question , they are this way because quarks have local SU(2) x U(1) gauge symmetry. We don't know why they have this particular symmetry. I suppose that's one of the things that string theory is trying to address.

13. Mar 30, 2008

### Physicsissuef

so because of the weak ineraction with the nucleus, they carry the kinetic energy of it, right?
By period of half-decay, I meant [itex]T_1_/_2[/tex]

14. Mar 30, 2008

### Staff: Mentor

With regard to beta decay and the weak process, please see - http://hyperphysics.phy-astr.gsu.edu/hbase/particles/proton.html#c3

It's not that the weak process causes kinetic energy, but that particles (electron and neutrino) have energy and momentum.

The half-life is derived from the 'statistical' treatment of radioactive decay. Basically, for each single nucleus of a given radionuclide, there is no way to determine when it will decay. It might decay in 1 second, or 10 years, or one century or a millenium from now.

However, if we have a collection (population) of the same radionuclide, one can measure the decays and one will find 'on average' that half of the radioactive nuclei will decay in some amount of time T. Then between T and 2T, half of the remaining nuclei (or 1/4 of the original) will decay. For each period of T, 'approximately' one-half of the remaining nuclei will decay, until eventually the last atom decays.

See - http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/halfli.html

15. Mar 30, 2008

### Physicsissuef

When some nuclei decays, are there alpha, beta and gamma particles at same time?? We are talking here about kinetic energy. Is W the kinetic energy, or it is the inner energy of the electrons?

16. Apr 1, 2008

### Physicsissuef

In my textbook, it says that the when the nuclei decays, it "pull" the electrons with it, so it gives them kinetic energy, but the neutrino is also there which is taking the most kinetic energy. How it is possible when it is electro neutral?

17. Apr 1, 2008

### Staff: Mentor

Alpha decay and beta decay are mutually exclusive, and while some radionuclides can experience both modes, any given nuclei will do one or the other, but not both simultaneously. Sometimes there is excess energy still remaining and a gamma ray is given off (as in Isomeric Transition).

Particles have energy and momentum, even electroneutral particles like photons (EM) and neutrinos. The neutron and neutral pion, which have mass as well as charge neutrality, have the properties of energy and momentum.

The charged particles, alpha and beta, will interact electrically with the atomic electrons surrounding the nucleus. As alpha and beta particles travel past/through other atoms, they will ionize or excite those atoms.

18. Apr 1, 2008

### Physicsissuef

I can't understand how the neutrinos are "carrying" the most of the kinetic energy when they don't have electro static forces, i.e they are electro neutral. How is this possible?

19. Apr 2, 2008