Calculating the Volume of an Electron

[sophiecentaur]

The problem here is that people are trying to be far too classical about this. For an item as small as an electron, you just can't say anything as definite as "how big is it?". For a start, depending on the context, you may have no idea where it actually is- for instance, when bound in an atom. How would you describe its sphere of influence when it has to be described in terms of a probability density function around a nucleus / solution to a wave equation? Heisenberg says that, if its momentum or energy state is known accurately then it could be just about anywhere so how does its "size" come into it?

 

[Antiphon]

How about saying it's at least the Planck length cubed? Isn't that the minimum meaningful volume of anything?

 

[sophiecentaur]

How about saying it's at least the Planck length cubed? Isn't that the minimum meaningful volume of anything?

How about saying that the size is not a meaningful question because the circumstances in which you try to measure it (which is what really counts) will totally dominate. And, remember, it's not 'really anything' - as with all modern Physics Concepts.

 

[dimension10]

correct me if i m wrong but mathematically having zero volume would mean that the electron occupies no space even though it has mass.
can anything has zero volume without being massless?

Well, a singularity can.

 

[sophiecentaur]

This thread is in danger of turning into a 'top trumps' game. The 'spec's of things like electrons don't really lend themselves to this sort of discussion.

 

[LoFish]

Another noob question: Imagine that you could grab two electrons and put them togheter, Can they get so close that they end up being in the same space?

 

[sankalpmittal]

This thread is in danger of turning into a 'top trumps' game. The 'spec's of things like electrons don't really lend themselves to this sort of discussion.

Energy on an electron ~ e²/r
so
mc² = e²/r

As e = 4.774 x 10^-10 esu
m=9.108 x 10^-28 g
c=3 x 10⁸ m/s

We solve for radius of electron and r= 2.780 x 10^-15 m

Now Volume of an electron = 4πr³/3 ~ 90 x 10^-45 m³
Volume of an electron approximately is 9 x 10^-44 m³

Woops ! This thread was 1 year old. I blindly posted here !
And now , I can't just delete it !

Another noob question: Imagine that you could grab two electrons and put them togheter, Can they get so close that they end up being in the same space?

Don't you hijack this thread lol ?

https://www.physicsforums.com/showthread.php?t=613639
https://www.physicsforums.com/showthread.php?t=261050
http://www.thenakedscientists.com/forum/index.php?topic=31820.0
http://www.jstor.org/discover/10.2307/95352?uid=3738256&uid=2129&uid=2&uid=70&uid=4&sid=47699125619907

 

[sophiecentaur]

Energy on an electron ~ e²/r

I'm not sure I'm happy with that; at least I don't recognise it. Shouldn't there be a 1/4πε₀ in there for your approximation? That would change the magnitude of things a bit. Or is it the units you're using? I tend to stick to SI for my EM understanding.
Perhaps you could give me a reference.

 

[sankalpmittal]

I'm not sure I'm happy with that; at least I don't recognise it. Shouldn't there be a 1/4πε₀ in there for your approximation? That would change the magnitude of things a bit. Or is it the units you're using? I tend to stick to SI for my EM understanding.
Perhaps you could give me a reference.

I know you are correct. And even I could not find this formula anywhere on the internet. Even a google search was not worth it.

Every sites say that we cannot precisely calculate volume of an electron but , we can say that Energy of an electron of any element at particular radius = -ze²/4πε₀r

where z is atomic number of that element and r is that particular radius.

But in my textbook it was written that Energy on an electron ~ e²/r.

Yet I cannot find any reference on internet. Then may be my textbook is wrong.

 

[sophiecentaur]

"Every sites say that we cannot precisely calculate volume of an electron but , we can say that Energy of an electron of any element at particular radius = -ze2/4πε0r"

that is the energy of the electron in its bound state in an atom - nothing to do with its own 'internal' potential energy. Why would they include z in the formula, otherwise?

 

[Drakkith]

Another noob question: Imagine that you could grab two electrons and put them togheter, Can they get so close that they end up being in the same space?

Yes and no. At the scale of individual electrons, called the quantum scale, effects that we label "quantum effects" become dominant. Such effects include quantum tunneling, uncertainty, etc. Two electrons cannot have the same "state", which basically means they can't occupy the same place at the same time with the same properties. Electrons belong to a class of particle called "Fermions" which all obey this rule, which is named the "Pauli Exclusion Principle". Changing the spin of one electron will allow it to occupy the same spot as another if their spins are opposite of each other. Electron atomic orbitals depend on this rule and this underpins all of chemistry. For more see the following links:
http://en.wikipedia.org/wiki/Fermion
http://en.wikipedia.org/wiki/Pauli_exclusion_principle

 

[sankalpmittal]

"Every sites say that we cannot precisely calculate volume of an electron but , we can say that Energy of an electron of any element at particular radius = -ze2/4πε0r"

that is the energy of the electron in its bound state in an atom - nothing to do with its own 'internal' potential energy. Why would they include z in the formula, otherwise?

Yeah you're right and this is what I am saying. I cannot find reference to formula : Energy on an electron ~ e²/r anywhere except my textbook. Logically , also this formula makes no sense. Also , the sites say that we can only find energy on an electron at certain radius in an atom of particular radius and there is nothing like electron's own energy which is independent of z and r of particular atom of element in formula E= -ze²/4πε0r.

Is my textbook wrong or not ? Please I am a student and its important for me to know.

 

[sophiecentaur]

I'd suggest that your textbook is wrong if you can find no reference to the same formula anywhere else. A textbook is not somewhere you'd expect to find 'brand new' knowledge. That paragraph may just have been garbled or a bit missed out and not been spotted during proof reading. I should just ignore it - you are hardly likely to be tested on it, after all.

 

[mikeph]

That is not the standard formula, I'd guess that either the tilde is supposed to represent "proportional to", or that they are working in non-SI units.

 

[sankalpmittal]

That is not the standard formula, I'd guess that either the tilde is supposed to represent "proportional to", or that they are working in non-SI units.

Energy on an electron ~ e²/r

Here , my textbook took e i.e. charge on an electron in esu : electrostatic units , r i.e radius of electron in centimetres. They are working in CGS system.

Now to check this equation by dimensional analysis :

We should get "ergs". Does (charge)²/distance yield energy ?

Lets see :
Standard formula is Energy = -ze²/4πε_or

Now since units of 1/4πε₀ in CGS are dyne cm²/esu²

Hence formula : Energy on an electron ~ e²/r seems to be dimensionally incorrect. Can you please recheck it ?

Moreover I think that equating mc² = e²/r is also not correct , which is given in my textbook.