Electron mass/energy do not conform to e=mc^2

[timallard]

Using E=mc^2, if you use the standard Coloumb charge for an electron and the typical value in textbooks for its mass, the difference is 10^5 off, it's way too heavy, 9.11x10^-31 vs 1.78x10-36 kg.

What does this difference represent, shouldn't the mass conform to the equation for that energy value?

 

[mgb_phys]

How are you relating it's charge to it's energy?
And why does that energy have anything to do with it's mass?

 

[timallard]

How are you relating it's charge to it's energy?
And why does that energy have anything to do with it's mass?

Most renditions I've seen equate energy and charge so that's what I've been doing.

As far as I've studied, energy and mass are directly related and under certain circumstances can transform from one to the other.

Since I'm concerned about these things at relativistic velocities I use the extra term for the energy equation most of the time and don't often leave it out.

I was just "checking" the mass value and found the standard value given for rest mass does not work when you set velocity to zero for the energy of an electron volt.

I didn't expect that and don't know the answer to why the measured rest mass is so far from satisfying the equation, a factor of 10^5, that's a huge difference, my guess is along the lines of experimental procedures and so on, any clues appreciated.

 

[ZapperZ]

Most renditions I've seen equate energy and charge so that's what I've been doing.

As far as I've studied, energy and mass are directly related and under certain circumstances can transform from one to the other.

Since I'm concerned about these things at relativistic velocities I use the extra term for the energy equation most of the time and don't often leave it out.

I was just "checking" the mass value and found the standard value given for rest mass does not work when you set velocity to zero for the energy of an electron volt.

I didn't expect that and don't know the answer to why the measured rest mass is so far from satisfying the equation, a factor of 10^5, that's a huge difference, my guess is along the lines of experimental procedures and so on, any clues appreciated.

You really have not answered mgb's question. How did you get the "number" for the energy using the charge? Did it come to you in a dream, or did you use a particular "formula"? We know what it is using its mass.

Zz.

 

[Dale]

The mass of an electron is 511 keV/c², so when an electron and a positron anhillate you get two photons of 511 keV each. The m of the electron and positron are converted to the E of the photons.

If you didn't get something similar then you did a calculation wrong or used a formula incorrectly.

 

[timallard]

You really have not answered mgb's question. How did you get the "number" for the energy using the charge? Did it come to you in a dream, or did you use a particular "formula"? We know what it is using its mass.

Zz.

As stated in the original post, using the standard charge for an electron, 1.6x10-19 Coloumb in most texts, for E being used in E=mc^2, is there another value or equation I should be using?

 

[timallard]

The mass of an electron is 511 keV, so when an electron and a positron anhillate you get two photons of 511 keV each. The m of the electron and positron are converted to the E of the photons.

If you didn't get something similar then you did a calculation wrong or used a formula incorrectly.

Cool, I wasn't using the right energy value, thanks.

 

[Dale]

You're welcome.

As stated in the original post, using the standard charge for an electron, 1.6x10-19 Coloumb in most texts, for E being used in E=mc^2, is there another value or equation I should be using?

FYI, in the equation E=mc² the c is the speed of light, not the charge.

 

[ZapperZ]

As stated in the original post, using the standard charge for an electron, 1.6x10-19 Coloumb in most texts, for E being used in E=mc^2, is there another value or equation I should be using?

You're welcome. FYI, in the equation E=mc² the c is the speed of light, not the charge.

Good grief. If this is what truly happened, then this whole thread is moot.

Zz.

 

[timallard]

Good grief. If this is what truly happened, then this whole thread is moot.

Zz.

Well, I still don't understand what the relationship of charge and energy at rest for an electron is, none of that has been explained.

After thinking about it more, without knowing that relationship, what I want to learn has not been answered.

 

[timallard]

You're welcome. FYI, in the equation E=mc² the c is the speed of light, not the charge.

FYI: I use upper case C, or q, for charge, lower case c for speed of light ... for this was using E = q ...

 

[ZapperZ]

Well, I still don't understand what the relationship of charge and energy at rest for an electron is, none of that has been explained.

After thinking about it more, without knowing that relationship, what I want to learn has not been answered.

Then how in the world were you able to compare the energy of the two? I mean, you were the one who came up with this whole thing. Why are you asking me when both I and mgb are the ones asking for how you came up with such comparison?

This is making very little sense.

Zz.

 

[Dale]

for this was using E = q ...

But E does not equal q, the units aren't even right.

 

[timallard]

But E does not equal q, the units aren't even right.

Hmmm, I thought they were both Nm²/s² ... the way this has been going I'd better check ...

 

[Dale]

In the SI system charge is in units of coulombs where 1 C = 1 A s

In the SI system energy is in units of joules where 1 J = 1 kg m²/s²

 

[timallard]

In the SI system charge is in units of coulombs where 1 C = 1 A s

In the SI system energy is in units of joules where 1 J = 1 kg m²/s²

If you balance an orbital with charge the C's cancel out from Coloumb's constant k, F=k(qq'/r²) is where I'm coming from.

I'm trying to take energy into account due to using the centrifugal force equation, mv²/r, with v = c - 1x10^-18.

So, since this is happening simultaneously, I thought the values used had to satisfy the energy equation E=mc²/(1-v²/c²)^1/2 at the same time satisfying k(qq'/r²) = mv²/r

 

[Hootenanny]

If you balance an orbital with charge the C's cancel out from Coloumb's constant k, F=k(qq'/r²) is where I'm coming from.

I'm not quite sure what you mean. Could you show us explicitly the calculations that you are doing?

 

[Dale]

If you balance an orbital with charge the C's cancel out from Coloumb's constant k, F=k(qq'/r²) is where I'm coming from.

But there is no energy in that equation, so I still don't see how you get that charge equals energy.

I agree with Hootenanny, please show us exactly what you are doing that makes you believe that charge is energy. I think you simply have a confusion about units, but if we can see exactly where it is coming from we can probably help you understand better.

 

[Hootenanny]

I'm trying to take energy into account due to using the centrifugal force equation, mv²/r

You still can't equate force with energy, they are not equivalent quantities.

v = c - 1x10^-18.

Where did you pull this relationship from? What are the units associated with the number 1x10^-18?

 

[Hootenanny]

So, since this is happening simultaneously, I thought the values used had to satisfy the energy equation E=mc²/(1-v²/c²)^1/2 at the same time satisfying k(qq'/r²) = mv²/r

Please stop editing your posts after we have responded to them. If you want to add more detail please use a new post.

I still have no idea what you're actually doing. I'll say again, can you show me explicitly from start to finish what your doing?

 

[timallard]

You still can't equate force with energy, they are not equivalent quantities.

Where did you pull this relationship from? What are the units associated with the number 1x10^-18?

Apology for editing without checking for replies.

I did make the mistake of trying to equate force with energy. Asking the question pretty says that one ... lol. And yes, using 5.11 keV works for rest mass no problem.

Units are meters/second ... speed of light minus 1x10^-18 m/s.

At this speed mass dilation is what I was looking at.

 

[timallard]

I still have no idea what you're actually doing. I'll say again, can you show me explicitly from start to finish what your doing?

Just trying to analyze k(qq'/r²) = mv²/r for an orbiting charged particle around a point source charge and at the same time because of the high velocity thinking E=mc²/(1-v²/c²)^1/2 must work for the same values.

 

[Hootenanny]

Just trying to analyze k(qq'/r²) = mv²/r for an orbiting charged particle around a point source charge and at the same time because of the high velocity thinking E=mc²/(1-v²/c²)^1/2 must work for the same values.

Note that in the Bohr model, the speed of the electron is approximately c/137 << c, so there is no need to invoke special relativity. The classical expression for energy will suffice. Furthermore, it would be worthwhile emphasising that that E in your equation above is the total energy of the electron, i.e. both the kinetic energy and the energy associated with it's rest mass.

 

[timallard]

Note that in the Bohr model, the speed of the electron is approximately c/137 << c, so there is no need to invoke special relativity. The classical expression for energy will suffice. Furthermore, it would be worthwhile emphasising that that E in your equation above is the total energy of the electron, i.e. both the kinetic energy and the energy associated with it's rest mass.

Nice, thanks, I've been trying to derive things from scratch so make mistakes and usually find why on my own but was staring at that one for a couple of days.

A follow up question then is about where for v does the relativistic effect kick in, if you don't mind me asking?

 

[russ_watters]

It depends on the purpose of the calculations and required precision, but at a quarter the speed of light, the mass increase via the lorenz factor is only 3%. The equation is pretty easy to use: http://en.wikipedia.org/wiki/Lorentz_factor

 

[timallard]

It depends on the purpose of the calculations and required precision, but at a quarter the speed of light, the mass increase via the lorenz factor is only 3%. The equation is pretty easy to use: http://en.wikipedia.org/wiki/Lorentz_factor

I'm gettin' this now, I wasn't onto how these pieces all fit together before, thanks a lot.