# beta particles

by Physicsissuef
Tags: beta, particles
P: 909
 Quote by 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.
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?
 Sci Advisor HW Helper P: 4,739 Physicsissuef: you can find the forumulas (and how to derive them) for the beta-probablity distribution in Kranes nuclear textbook - Introductory Nuclear Physics.
 P: 12 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
 P: 909 So there are only 2 kinetic energies for every nuclei?
HW Helper
P: 4,739
 Quote by Physicsissuef So there are only 2 kinetic energies for every nuclei?

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.
 P: 909 Why there are 2 points M_1 and M_2 is my question??
HW Helper
P: 4,739
 Quote by Physicsissuef Why there are 2 points M_1 and M_2 is my question??
And as I said, if you want to find out why this probability distribution arises check the reference I gave you..

P: 21,417
 Quote by Physicsissuef Why there are 2 points M_1 and M_2 is my question??
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 Emax), and Emax is an upper limit.
 P: 909 I mean, how is possible for one value of beta particles, to have 2 values for the kinetic energy of the electrons?
 Sci Advisor HW Helper P: 4,739 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.
 P: 909 On the x-axis I have number of beta particles, and on the y-axis I have the kinetic energy of electrons...
P: 21,417
 Quote by Physicsissuef On the x-axis I have number of beta particles, and on the y-axis I have the kinetic energy of electrons...
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.
 Sci Advisor HW Helper P: 4,739 No. please look at your images again. y axis goes up, x axis goes to the right. It is the most used convention.
 P: 909 Yes, sorry it was typo. So how is possible that for one value of beta particles, to have 2 kinetic energies for the electrons?
 P: 12 It's statistic!!! A single electron can't have 2 different energy at the same time, but on a population of milion of electrons emitted by that radionuclide you will know how many ( % ) got a E1 energy and how many got E2 energy and so on from 0 to Emax. I.E. if you use a distribution of human population weight, you can have that 20% of them that weight "A" Kg and another 20% that weight "B" kg , but that dosen't mean that you have a man that weight both "A" kg and "B" kg at the same time.
HW Helper
P: 4,739
 Quote by 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?
What is 'value of beta particles'??

beta particle = electron, same thing, different names..

And it is a PROBABILITY DISTRIBUTION. The figures you have is a distrubtion cure where one has plotted the number of electrons with repsect to their energy. To obtain this figure, one has recorded several milions of beta-particles.

So each electron has ONE value of kinetic energy, and several electrons can have the same kinetic energy.
 P: 12 Ah yes i'm sorry, statistic is another thing...sorry again for my italian interpretaion of english words.

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