beta particles

Astronuc

Ah, my apologies, I was thinking of mass, rather than one's OP.

The population distribution is continuous, more or less. It is based on the measurement of a large population in which each decay is a discrete event with a unique beta energy. Taken together, with some large N, e.g. 10²⁰ (arbitrary example), one observes that population distribution when one plots the number of particles of energy between E and some ∆E. When ∆E gets very small the distribution looks like a continuum.

Each radionulide has a unique distribution, with a unique mean and max value, but the shapes are much the same, because although the energies are different, the same weak process applies.

Physicsissuef

Thank you very much. I suppose you made excellent posts, but, (maybe it is because of the translation or the difficulty, more of the things I can't understand. Can you explain with simpler words, and maybe give me some simple analogy to understand what you mean?

Physicsissuef

Why then there are only two dots (M_1 and M_2). If there is unique distribution for every radionuclide, then there will be infinite numbers of distributions, or not?

Physicsissuef

Astronuc, please answer me, my last question...

malawi_glenn

Physicsissuef: you can find the forumulas (and how to derive them) for the beta-probablity distribution in Kranes nuclear textbook - Introductory Nuclear Physics.

PhilippH

Beta- emission, may vary from a radionuclide to another but in general the energy distribution graph looks like the same for every radionuclide, apart for the maximum energy.
The spectrum of the Beta emission is continuos due to the random ripartition of momentum and energy betwen neutrino.

Energy distribution for B-emission of P32

Physicsissuef

So there are only 2 kinetic energies for every nuclei?

malawi_glenn

NO! There exists an energy distribution, which is quite similar for each nucleus. You nay want to look for the derivation of this distribution shape, see for instance the reference i gave you.

Physicsissuef

Why there are 2 points M_1 and M_2 is my question??

malawi_glenn

And as I said, if you want to find out why this probability distribution arises check the reference I gave you..

Perhaps you should google 'probability distribution' to learn more about this concept.

Astronuc

Because the function is always positive and it increases from zero to some maximum and then decreases to zero again, so that for each ordinate value, there are two corresponding values on of the abscissa. Note that there is one maximum value.

Draw an inverted parabola, and one would see that for each y there are two values of x, except for the maximum value of which there is one.

There is a continuum of energies (between 0 and E_max), and E_max is an upper limit.

Physicsissuef

I mean, how is possible for one value of beta particles, to have 2 values for the kinetic energy of the electrons?

malawi_glenn

now you are just writng things I cant understand.. check your english.

on your y-axis you have the NUMBER of electrons emitted. On the x-axis you have their energy. Please check 'probability distribution function' on google, I think you need this.

Every beta particle has just ONE value of Energy, but what energy - and the fraction of the beta particles who has a perticular energy- is given by the distribution function.

Physicsissuef

On the x-axis I have number of beta particles, and on the y-axis I have the kinetic energy of electrons...

Astronuc

On the very first image posted, the vertical (y) axis (ordinate, dependent variable) is number of particles and the horizontal (x) axis (abscissa, or independent variable) is the energy.

By convention, in Cartesian coordinates y-axis is vertical and x-axis is horizontal when looking.

malawi_glenn

No. please look at your images again.

y axis goes up, x axis goes to the right. It is the most used convention.

Physicsissuef

Yes, sorry it was typo. So how is possible that for one value of beta particles, to have 2 kinetic energies for the electrons?