# The Naked Scientists Forum

### Author Topic: How do we measure the mass of an electron?  (Read 5529 times)

#### allan marsh

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##### How do we measure the mass of an electron?
« on: 13/07/2014 17:38:50 »
Electron accelerates and produces a magnetic field which resists the motion of the electron.
Is the resistance to change of motion of the electron.... Its mass
If true how do you find its rest mass?

Or is the mass you refer to, not inertial mass?
« Last Edit: 29/07/2014 08:02:22 by chris »

#### jccc

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##### Re: Electron mass
« Reply #1 on: 13/07/2014 20:20:06 »
This is a tough one. Puzzles me too.

#### Bored chemist

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##### Re: Electron mass
« Reply #2 on: 13/07/2014 21:07:57 »
Measure the mass at different velocities and extrapolate to zero velocity.

#### evan_au

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##### Re: Electron mass
« Reply #3 on: 14/07/2014 10:25:47 »
Some ideas:
In a magnetic field, charged particles like the electron and proton will follow a circular path.
They have the same charge, and the radius of the curve is related to the mass of the particles.

Or you could accelerate an electron through a known voltage, and then measure its velocity.

Provided the velocity is much less than the speed of light (eg < 1% of c), you don't need to do a relativistic correction.

#### allan marsh

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##### Re: Electron mass
« Reply #4 on: 14/07/2014 14:20:30 »
not understand!   i,m accelerating the electron in a vacuum in a straight line, i assume (but ignorance perhaps suggests) that a moving electron thru the ether!!?? creates a field ( surely must need energy to produce the field) which must??? relate to its energy hence Mass???
Can see you may work backwards to find rest mass, but cant understand your definition of rest mass.
« Last Edit: 14/07/2014 21:58:01 by evan_au »

#### UltimateTheory

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##### Re: Electron mass
« Reply #5 on: 14/07/2014 22:22:49 »
There is special device. Windmill that is moving after being struck by electrons.

Imagine you have electron gun in vacuum tube,
electron is accelerated by electric field,
stream of electrons is bend by magnets/electromagnets to hole,
passing through it and then are flying further to target
Target might be windmill made by some metal.

Windmill is starting rotating after collision with electrons.

At not relativistic velocities kinetic energy of electron is approximated to E.K.=1/2*me*v^2
You can reverse equation to calculate mass, knowing how much kinetic energy has object.
Mass of windmill is known.
You can calculate frequency at which it's rotating after hitting by electron.
You can calculate kinetic energy of electron from voltage, it's velocity.
You can calculate quantity of emitted electrons from ampere meter. Q=I*t (quantity = Q/e)
etc. etc.

There is other version of this device especially for photons. And most of physics have one of its version, as it's cheap toy:

Nobody here studied physics or have physics at high school??
« Last Edit: 15/07/2014 00:25:51 by UltimateTheory »

#### UltimateTheory

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##### Re: Electron mass
« Reply #6 on: 14/07/2014 22:33:27 »
Mass of electron can be also calculated from Compton frequency:

me = h*fc / c^2 = 6.62607*10^-34 * 1.23559*10^20 / 299,792,458 ^2 = 9.11*10^-31 kg

Compton frequency is frequency of photon created during annihilation of electron with positron.

Double Compton frequency (2*1.23559*10^20) is minimum photon energy needed to pair production (single photon and nucleus version of pair production).
Photon exceeding this frequency is emitted to nucleus and electron, positron pair is produced.

#### PmbPhy

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##### Re: Electron mass
« Reply #7 on: 15/07/2014 02:23:13 »
Quote from: Bored chemist
Measure the mass at different velocities and extrapolate to zero velocity.
There's no reason to do that. All someone has to to measure the proper mass, m_0, of a charged particle all you have to do is fire such a  particle into the uniform magnetic field of a cylotron in a plane which whose normal vector is parallel to the magnetic field. The particle will move in a circle, the radius of which can be measured. Then once you measure the radius of the circle, R, and since you know the magnetic field and the charge, you can calculate the mass since p = mv since p = qBR. Measuring the velocity is easy if you can measure the frequency of the orbiting particle.

http://home.comcast.net/~peter.m.brown/sr/cyclotron.htm

Since

m = m_0/sqrt[1 - v^2/c^2]

You can find the proper mass once you know its speed and momentum. There's no need to do any extrapolating or run more than one experiment. All you need to do is let the particle move in a cirlce and measure the radius of that cirlce. You can send in a particle whose speed is already known in fact, perhaps by using a velocity selector (i.e. a crossed magnetic and electric field).
« Last Edit: 15/07/2014 02:29:51 by PmbPhy »

#### Bored chemist

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##### Re: Electron mass
« Reply #8 on: 15/07/2014 20:37:55 »

There is other version of this device especially for photons. And most of physics have one of its version, as it's cheap toy:

Nobody here studied physics or have physics at high school??

I have studied enough physics to know that's not how a Crookes Radiometer works.

PmbPhy,
In the case you are talking about, you need to do a different extrapolation.
A charged particle moving in a circle is accelerating towards the centre and an accelerating charged particle emits radiation and loses energy.
So it doesn't actually move in a circle, it spirals inwards.
You have to extrapolate to the velocity it had before it lost some energy.
Of course, if the speed is small, the rate of loss is low.
On the other hand, if it's that low the relativistic effect is small enough to ignore so you can  get the mass from equating 1/2 mv^2 with QV
v = velocity
V = accelerator voltage
« Last Edit: 15/07/2014 20:44:57 by Bored chemist »

#### UltimateTheory

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##### Re: Electron mass
« Reply #9 on: 15/07/2014 21:48:10 »
I said "one of version".
There is other version of Crookes radiometer that has no air inside and relies completely on momentum/energy of photon.

#### PmbPhy

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##### Re: Electron mass
« Reply #10 on: 26/07/2014 15:31:03 »
Quote from: allan marsh
Electron accelerates and produces a magnetic field which resists the motion of the electron.
Is the resistance to change of motion of the electron.... Its mass
If true how do you find its rest mass?

Or is the mass you refer to, not inertial mass?
Hi Allan,

I neglected to fully answer your question. In addition to the creation of the magnetic field there is an increase in the electric field so energy comes from there too. This addition of mass from EM energy is called electromagnetic mass. There is an additional term which must be taken into account, i.e. stress. In order to hold a ball of charge together it requires a force to do so. That force creates stress and that stress contributes to the mass of the charged body. Since the electron is not a ball of charge there are problems associated with it being a point charge even in quantum field theory. Resolving this problem is called mass renormalization, a problem which does not yet have a satisfactory resolution to it.

To read more about this see the article on the subject in the American Journal of Physics by David J. Griffiths at http://booksc.org/dl/11386670/7d9b2d

#### Bored chemist

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##### Re: Electron mass
« Reply #11 on: 26/07/2014 16:54:56 »
I said "one of version".
There is other version of Crookes radiometer that has no air inside and relies completely on momentum/energy of photon.

This is just silly.
The Crookes radiometer is the one Sir William Crookes invented and it relies on there being some gas left in the bulb.

However, it doesn't matter because, since it's driven by light, it has nothing to do with the mass of the electron does it?

This, on the other hand might help (as long as you can calculate the number and speed of the electrons)

You can't just rely on energy transfer because you don't know how much is dissipated as heat and how much gets lost by electrons bouncing off the wheel.

#### allan marsh

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##### Re: How do we measure the mass of an electron?
« Reply #12 on: 04/08/2014 17:45:42 »
PmbPhy thanks I am getting there

#### alancalverd

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##### Re: How do we measure the mass of an electron?
« Reply #13 on: 04/08/2014 20:17:39 »
1. Measure the charge e on an electron: Millikan's classic "oil drop"experiment will do.

2. Measure the radius of an electron beam bending in a magnetic field. This depends on the mass/charge ratio m/e and the field strength H. Teltron Ltd make a very nice rig suitable for demonstrating this in schools.

3. Calculate m from e and m/e.

That said, I prefer the electron/positron annihilation experiment. You can increase the accelerating potential of an x-ray generator until the x-rays just have enough energy to create e-p pairs in air. At this point you can detect the characteristic secondary photons emitted when the pairs annihilate. This occurs only when the anode potential of your x-ray tube exceeds 1,022,000 volts so the mass of the electron must be 511 keV/c2 - assuming that the mass of a positron is the same.
« Last Edit: 04/08/2014 20:19:54 by alancalverd »

#### PmbPhy

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##### Re: Electron mass
« Reply #14 on: 04/08/2014 21:57:55 »
Quote from: Bored chemist
PmbPhy,
In the case you are talking about, you need to do a different extrapolation.
A charged particle moving in a circle is accelerating towards the centre and an accelerating charged particle emits radiation and loses energy.
So it doesn't actually move in a circle, it spirals inwards.
You have to extrapolate to the velocity it had before it lost some energy.
Of course, if the speed is small, the rate of loss is low.
On the other hand, if it's that low the relativistic effect is small enough to ignore so you can  get the mass from equating 1/2 mv^2 with QV
v = velocity
V = accelerator voltage
If I recall correctly (and I e-mailed a particle physicist I know to make sure) this is the method used in accelerator labs to measure the mass of charged particles. They don't measure the radius of the circle. They measure the curvature of the circle. When they do that they get the instantaneous momentum of the particle. Somehow they use a calorimeter to measure the kinetic energy and from that they can deduce the mass. Although there are a few things I'm not certain of but I'll get back to this when my particle physicist friend returns my e-mail.

For more on this please see
https://www.fnal.gov/pub/science/inquiring/questions/particlemassmsmt.html

#### The Naked Scientists Forum

##### Re: Electron mass
« Reply #14 on: 04/08/2014 21:57:55 »