Understanding Beta Particles and Their Role in Radioactivity | Diagram Included

[Physicsissuef]

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.

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]

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?

 

[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.

http://r8vogq.blu.livefilestore.com/y1pldgTfHaQFOXoZlF3yYP64dp8coOvIfGhHHg-bWwW5sw7XoC5HzygOSM9EIyG8b_nHVvyr6bx63YEWt9uqwoCuA/Nuovo%20Immagine%20bitmap.JPG"

 

[Physicsissuef]

So there are only 2 kinetic energies for every nuclei?

 

[malawi_glenn]

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.

 

[Physicsissuef]

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

 

[malawi_glenn]

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..

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

 

[Astronuc]

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 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 can't 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 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.

 

[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?

 

[PhilippH]

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.

 

[malawi_glenn]

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.

 

[PhilippH]

Ah yes I'm sorry, statistic is another thing...sorry again for my italian interpretaion of english words.

 

[Physicsissuef]

Hm... I still can't understand why two points...

 

[malawi_glenn]

Hm... I still can't understand why two points...

Ok, let's take this thing to the very beginning..

Do you know how a histogram works?

You measure a lots of object of same kind, and record their property. Then you keep track on how many of those objects who has a certain property.

Lets take cars or instance.

You stand at the road, and look at the colors of the cars passing by. For each color you have a column, and when a car with color green passes by you increase the number of green cars by 1, and when a red car passes by you increase the number of red cars with 1, etc.

Then when you don't want to recornd anymore; you plot the result - you will get a histogram (http://en.wikipedia.org/wiki/Histogram ), the number of cars with respect to their color.

Do the same thing with a huge amount of radioactive nuclei, and record the number of electrons (cars) of a certain energy (color), here energy is a CONTINOUS variabe, wheras color is a discrete, so you will obtain a probability distribution (a continuous historgraf if you like) - with the number of recorded electrons with respect to energy.

The reason why you have two ponits is just that you record the same number of electrons with energy M_1 as electrons having energy M_2; nothing strange - it is the same thing you would get if you recorded 20 red cars and 20 black cars, nothing strange at all!

 

[Physicsissuef]

So you want to say that for different radioactive nuclei I will have different kinetic energies of the electrons?

 

[Astronuc]

So you want to say that for different radioactive nuclei I will have different kinetic energies of the electrons?

For two different radionuclei, which decay by beta-emission, the range of beta particle energies may overlap.

The two points (same number) on the energy distribution curve (number of particles as a function of energy) simply means that the probability of measuring two particles with those two energies is the same. It's a bit like rolling a pair of dice, and having two faces with the same value occur. Most of the time, the dice will have different values.

 

[malawi_glenn]

So you want to say that for different radioactive nuclei I will have different kinetic energies of the electrons?

yes.

and for each kind of isotopes you will get different SHAPES of this distribution. i.e C-17's shape (histogram) will not look 100% as the distribution from Cl-41. But they will be similar due to theory of beta-decay (see the reference I gave you for instance).

You can compare this with the color of the cars at the road which I told you of before. changing isotopic kind means in this analogy that you change the place (rood) where you study the color of the cars. Maybe in the city of New York you will get a larger number of yellow cars (Taxi cars) than you would do in a small city in greece..

 

[Physicsissuef]

yes.

and for each kind of isotopes you will get different SHAPES of this distribution. i.e C-17's shape (histogram) will not look 100% as the distribution from Cl-41. But they will be similar due to theory of beta-decay (see the reference I gave you for instance).

You can compare this with the color of the cars at the road which I told you of before. changing isotopic kind means in this analogy that you change the place (rood) where you study the color of the cars. Maybe in the city of New York you will get a larger number of yellow cars (Taxi cars) than you would do in a small city in greece..

so for one beta particle there may have infinite number of M points, right?

For two different radionuclei, which decay by beta-emission, the range of beta particle energies may overlap.

The two points (same number) on the energy distribution curve (number of particles as a function of energy) simply means that the probability of measuring two particles with those two energies is the same. It's a bit like rolling a pair of dice, and having two faces with the same value occur. Most of the time, the dice will have different values.

The two points are for same number of paricles... So it means that the probability of measuring two particles, the particles are same, right?

 

[malawi_glenn]

so for one beta particle there may have infinite number of M points, right?

No!

a Beta particle = an electron; same thing but different name!

Each electron will only have ONE value of energy (M).

you must learn what a beta particle is.

The two points are for same number of paricles... So it means that the probability of measuring two particles, the particles are same, right?

No!

It just means that there is an equal probabilty that you get energy M1 as energy M2, but there are many many more values for possible energy of the electron.

 

[Physicsissuef]

No!

a Beta particle = an electron; same thing but different name!

Each electron will only have ONE value of energy (M).

you must learn what a beta particle is.



No!

It just means that there is an equal probabilty that you get energy M1 as energy M2, but there are many many more values for possible energy of the electron.

I mean there are infinite possible kinetic energies for the electron, so there are infinite M points... Its the same, as you said...

 

[malawi_glenn]

I mean there are infinite possible kinetic energies for the electron, so there are infinite M points... Its the same, as you said...

Yes, but that was not what you wrote however.

 

[Physicsissuef]

Yes, but that was not what you wrote however.

And why did I said then? However, malawi_glenn, Astronuc and all others thank you very much for the help. Thanks again...

 

[malawi_glenn]

And why did I said then?

I don't understand you now.. please have a look at your spelling again.

My intention is not to mock you because of your bad english, I just want to know what you mean, it is very hard to understand some of the things that you write.

 

[Physicsissuef]

My real point was that there are infinite possible kinetic energies for the electron, so there are infinite M points, and probably the graphic is not correct... Sorry for any mistranslation...

 

[Physicsissuef]

the conclusion is that the graphic is partly correct, there are infinite M points.

 

[malawi_glenn]

the conclusion is that the graphic is partly correct, there are infinite M points.

the point that the graph wanted to make, was that each y-value is obtained by two x values. Execpt for the y_max which only one x value can give.

Compare with this function:

y(x) = -x^2+4.5*x on the interval: x from 0 to 4.5

on this interval, each y value can be obtained by two different x-values. y = 2.5 is given by x = 0,69 and 3,88. Only y_max = 5,06 which is given by x= 2.25

It is the same thing for the distribution functions for beta decay.

 

[Physicsissuef]

But didn't we said that there should be infinite M points, not only 2? MAybe the graphic want to say that the kinetic energy of the electrons is not constant?

 

[malawi_glenn]

Yes there are infinite many values for the energy!

But it was your counlcusion made in post #67 i reacted on.

The ultimate thing the graph wants to point out is that all the electrons are not emitted with the same energy, but the energy spans over a range. This is typical for a 3body decay - there are infinite number of combinate conservation of momentum and energy when you have more than 2 bodies in the final state.

You first question was about these M1 and M2, and that question has been answered severel times in this thread, each y-value have two corresponding x values, except y_max.

The Graphic is totaly correct.