1. How do you measure the mass of an electron in a synchotron?
Can you calculate the mass increase just knowing the KE it possesses? Is it just dividing it by the energy/mass of the electron i.e. 1.23 x 10 ^20 Hz?
If an electron has 1 TeV what is its mass and how do you calculate its speed?

Thanks.

2.

3. Originally Posted by monalisa
How do you measure the mass of an electron in a synchotron
To keep a charged particle confined to a circle of a given radius, a certain combination of E and B fields needs to be applied to it, and the combination of those fields is a function of the particle's mass. See also Lorentz force.

Can you calculate the mass increase just knowing the KE it possesses? Is it just dividing it by the energy/mass of the electron i.e. 1.23 x 10 ^20 Hz?
I am really not sure what you are asking here.

If an electron has 1 TeV what is its mass and how do you calculate its speed?
The eV is a unit of energy, in other words a measure of the total energy the electron possesses. Since total relativistic energy is a function of both rest mass and momentum, you need to know at least one of these to calculate the other. In other words - just knowing that a particle has 1 TeV of energy does not allow you to tell either rest mass or speed, unless more information is given.

4. [QUOTE=Markus Hanke;467421]
Originally Posted by monalisa
- just knowing that a particle has 1 TeV of energy does not allow you to tell either rest mass or speed, unless more information is given.
Why not, if an electron has (been given) 1 TeV KE, can't we divide 10^12/511,000 and get its relativistic mass : 1,957,000 masses?
Can't you calculate its speed with relativity formulas?

5. We already know the rest mass of an electron to 9.10^-31kg so all you got to do is input it and you will get the relativistic speed#

6. Originally Posted by monalisa
Why not, if an electron has (been given) 1 TeV KE, can't we divide 10^12/511,000 and get its relativistic mass : 1,957,000 masses?
Can't you calculate its speed with relativity formulas?
You can, but only so long as you know the rest mass ( which of course we do in the case of the electron ). What I was trying to say is that in cases where both the rest mass and the speed are unknown, then the energy does not give us enough information to make the calculation.

7. Originally Posted by Markus Hanke
You can, but only so long as you know the rest mass .
Is my calculation of masses correct? Is there a way in practice to verify the real mass increase?
and what is the speed? can you give me a link where I can find a real instance of speeds close to c?

8. Originally Posted by monalisa
Is there a way in practice to verify the real mass increase?
and what is the speed? can you give me a link where I can find a real instance of speeds close to c?
The RHIC ( Relativistic Heavy Ion Collider ) is a rather striking example : RHIC | Physics of the Relativistic Heavy Ion Collider

9. Originally Posted by monalisa
How do you measure the mass of an electron in a synchotron?
Can you calculate the mass increase just knowing the KE it possesses? Is it just dividing it by the energy/mass of the electron i.e. 1.23 x 10 ^20 Hz?
If an electron has 1 TeV what is its mass and how do you calculate its speed?

Thanks.
These are rather ill-formed questions. The starting point is that charged particles are deflected in the presence of a electro-magnetic field due to the Lorentz force. The equations of motion are:

Under particular conditions () , we can solve the above equations and we get the speed of the particle as a function of and the observed radius (since the particle moves in a circle):

i.e.

Solve the above equation for v.

From that, the "relativistic mass" is :

10. Originally Posted by monalisa
How do you measure the mass of an electron in a synchotron?
.
I just wanted to know if it is possible to measure in practice the mass increase of an electron and verify the accuracy of the formulas.
If it is, how is it done ?

Is it possible for an electron and a positron at relativistic speed to annihilate into a gamma ray?

11. Originally Posted by monalisa
Originally Posted by monalisa
How do you measure the mass of an electron in a synchotron?
.
I just wanted to know if it is possible to measure in practice the mass increase of an electron and verify the accuracy of the formulas.
If it is, how is it done ?

Is it possible for an electron and a positron at relativistic speed do annihilate into a gamma ray?
When they annihilate the produce a photon#

12. Originally Posted by merumario
When they annihilate the produce a photon#
A pair, actually, to conserve momentum.

Does the extra kinetic energy change the energy of the generated photons? I don't know. I assume it must because I can't see where else the energy can go.

Edit: here you go, the extra energy can produce all sorts of particles: Electron–positron annihilation

13. Originally Posted by monalisa
Originally Posted by monalisa
How do you measure the mass of an electron in a synchotron?
.
I just wanted to know if it is possible to measure in practice the mass increase of an electron and verify the accuracy of the formulas.

If it is, how is it done ?
...by measuring the radius of the trajectory.

Is it possible for an electron and a positron at relativistic speed to annihilate into a gamma ray?
Yes. Two photons.

14. Originally Posted by xyzt
If it is, how is it done ?
...by measuring the radius of the trajectory.
.
That is what I asked for, thanks a lot....
But the radius of a synchrotron is limited for billions of rest masses, isn't it?

15. Originally Posted by monalisa
But the radius of a synchrotron is limited for billions of rest masses, isn't it?
What do you mean?

16. I'd appreciate if someone could describe a concrete example in order to let me understand properly:

suppose an electron is circling in a synchrotron and has 1 TeV energy,
it has nearly 2 million rest masses, you get the precise figure considering the radius of the circle? what should it be?
its wavelength is about 2 x 10^-10 cm, right, what is the amplitude of the wave? is the formula to derive this the same that applies to orbitals Markus gave me?

17. Originally Posted by monalisa
I'd appreciate if someone could describe a concrete example in order to let me understand properly:

suppose an electron is circling in a synchrotron and has 1 TeV energy,
it has nearly 2 million rest masses, you get the precise figure considering the radius of the circle? what should it be?
I have given you all the tools to figure this out by yourself, earlier, I showed you that:

From that , you get:

In a synchrotron B is given and so is the speed of electron injection, (constant).

18. No. You dont need synchotron to get mass of electron. Read for example this http://www.physics.mcgill.ca/~breton...xperiment4.pdf.
Also the waves are probability waves. Therefore the amplitudes will be 1 (depend on chosen normalization and Fourier transform prefactors) and square of these waves will give you probability distribution.

19. Originally Posted by Gere
No. You dont need synchotron to get mass of electron. Read for example this http://www.physics.mcgill.ca/~breton...xperiment4.pdf.
.
"monalisa" wanted the "relativistic" mass (the "mass increase") , hence the synchrotron.

21. Originally Posted by Gere
Interestingly, the answer is always , the only difference is how one interprets , in the classical case vs. in the relativistic case.

22. Originally Posted by Strange
Originally Posted by merumario
When they annihilate the produce a photon#
A pair, actually, to conserve momentum.

Does the extra kinetic energy change the energy of the generated photons? I don't know. I assume it must because I can't see where else the energy can go.

Edit: here you go, the extra energy can produce all sorts of particles: Electron–positron annihilation
Maybe# one can ask that how much energy will a photon poses so it can produce a particle and its anti? E.g (electron and positron)

One can easily calculate this by showing that E=hf is equivalent to E= 2mc^2........where the 2 is to indicate that the two particles are of same rest mass.(For our example 2* 9.10^-31kg*299792458^2=E(minimum energy the photon must poses)

For those new to this, its called pair production and the opposite is called pair annihilation.

Strange does it help?

23. Originally Posted by merumario
Originally Posted by Strange
Originally Posted by merumario
When they annihilate the produce a photon#
A pair, actually, to conserve momentum.

Does the extra kinetic energy change the energy of the generated photons? I don't know. I assume it must because I can't see where else the energy can go.

Edit: here you go, the extra energy can produce all sorts of particles: Electron–positron annihilation
Maybe# one can ask that how much energy will a photon poses so it can produce a particle and its anti? E.g (electron and positron)

One can easily calculate this by showing that E=hf is equivalent to E= 2mc^2........where the 2 is to indicate that the two particles are of same rest mass.(For our example 2* 9.10^-31kg*299792458^2=E(minimum energy the photon must poses)

For those new to this, its called pair production and the opposite is called pair annihilation.

Strange does it help?
The resulting positron-electron pair is not at rest, so using the rest energy is incorrect. The correct equation is (the speed of the resulting positron is not necesarily equal to the speed of the resulting electron). Anyway, you can't find a frame in which both speeds are 0, so you cannot write .

24. Originally Posted by xyzt
...by measuring the radius of the trajectory.
.

25. Originally Posted by monalisa
He has already answered that. There is a relation between the radius, and the applied E fields as well as speed. By knowing the radius and rest mass you can simply calculate the rest.

26. Originally Posted by Markus Hanke
Originally Posted by monalisa
He has already answered that. There is a relation between the radius, and the applied E fields as well as speed. By knowing the radius and rest mass you can simply calculate the rest.
The radius of the LHC or any other synchrotron is fixed, speed is practically always the same, c, how can the radius diminish billions of times, I asked?

27. Originally Posted by monalisa
The radius of the LHC or any other synchrotron is fixed, speed is practically always the same, c, how can the radius diminish billions of times, I asked?
I'm sorry, but I have no idea what you are asking. Of course the radius is fixed, it never varies - what does vary though are the electromagnetic fields which accelerate the particle and keep it on its trajectory.

28. Originally Posted by monalisa
Originally Posted by Markus Hanke
Originally Posted by monalisa
He has already answered that. There is a relation between the radius, and the applied E fields as well as speed. By knowing the radius and rest mass you can simply calculate the rest.
The radius of the LHC or any other synchrotron is fixed, speed is practically always the same, c, how can the radius diminish billions of times, I asked?
The radius does not "diminish", it is tied to the REST MASS, not to the relativistic mass, so your (repeated) question makes no sense, meaning that you aren't ready to understand the subject. Sorry.

29. Originally Posted by Markus Hanke
- what does vary though are the electromagnetic fields which accelerate the particle and keep it on its trajectory.
If I got it right, the radius of the trajectory becomes shorter when the mass increases, right? r = v/m B
so , if the electron has speed 0.9 c the radius is sa, the radius of the LHC. If you accellerate it to 0.999 999 999 999 999 ....9 c, its mass will be millions of times greater and its trajectory will have radius r = v/ 10^6/9m B, can it still fit the LHC? I hope I made myself clear

30. Originally Posted by monalisa
Originally Posted by Markus Hanke
- what does vary though are the electromagnetic fields which accelerate the particle and keep it on its trajectory.
If I got it right, the radius of the trajectory becomes shorter when the mass increases, right? r = v/m B
so , if the electron has speed 0.9 c the radius is sa, the radius of the LHC. If you accellerate it to 0.999 999 999 999 999 ....9 c, its mass will be millions of times greater and its trajectory will have radius r = v/ 10^6/9m B, can it still fit the LHC? I hope I made myself clear

As explained,
When , . All the physical entities in the right hand side are constant, unchanging and they are arranged such that the trajectory radius , is EQUAL to the radius of the synchrotron, otherwise things would not work. This is done by fixing the ratio .

31. Originally Posted by xyzt
In a synchrotron B is given and so is .
Thanks, I thought you meant B is fixed and anyway I thought it cannot vary that much

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