# How is the mass of an electron/proton measured?

1. Jun 16, 2012

### Michio Cuckoo

title.

2. Jun 16, 2012

Staff Emeritus

3. Jun 16, 2012

### Karimspencer

I researched but nobody told me the way i wanted, people told me : Check atomic mass on the periodic table. However , i want to know what experiment they used to find the mass in the first place.

4. Jun 16, 2012

### Reptillian

I think it has to do with how they move in magnetic fields. You know the charge on them, can calculate the magnetic force, then measure the radius of curverature in their path through the magnetic field to calculate the mass. Lorentz force law combined with good ol' F=ma.

5. Jun 16, 2012

### Karimspencer

I got lost when you talked about the radius, what does this have to do with the mass, shouldn't you consider acceleration?

6. Jun 16, 2012

When particle with charge q and mass m passes through magnetic field B it experiences force
$\vec{F} = q\vec{v}\times \vec{B}$
so it's acceleration is given by
$\vec{a} = \frac{q}{m}\vec{v}\times \vec{B}$
This acceleration is always perpendicular to the velocity so it curves the trajectory of particle. By measuring the curvature you can calculate the acceleration from which you can calculate mass.

7. Jun 16, 2012

### Karimspencer

Oh ok , that makes perfect sense...

8. Jun 16, 2012

### Staff: Mentor

Keep in mind that it requires to measure the electron or proton charge first. This can be done with the oil drop experiment or electrolysis.

That is the historical approach, as the experiments can be done with basic equipment (and as experiment for students). Today, there are more options to measure masses. Some examples:

If you know the charge:
- Accelerate the particles with a known energy in electric fields and measure their velocity afterwards.
- Instead of the radius at a given velocity, measure the oscillation frequency of the particles in a magnetic field. That allows to measure the mass of nuclei with a relative error of something like 1-10 parts in a billion if I remember that correctly.

If you do not know the charge:
- Measure the density of atoms in a solid object and its macroscopic size. Weight it, divide by the number of atoms, and you get the mass per atom (all particles together).

And here a fancy one, which requires quantum field theory and spectroscopy, but nothing else:
- Do precision spectroscopy of the hydrogen atom [and other atoms to see that the electron is light compared to a proton]. It is possible to calculate the fine-structure constant from the relative differences between the electron energy levels. Using this constant and the binding energy of the individual levels, it is possible to calculate the rest energy of electrons. The relation E=mc^2 for particles at rest then gives the mass.
- To extend this, do precision spectroscopy of several isotopes. The mass of the nucleus influences the energy levels, therefore it is possible to measure the proton and neutron mass, too.

9. Jun 16, 2012

### Michio Cuckoo

woah seems like a lot of prerequisites are required. How do you measure such a high frequency for instance?

10. Jun 17, 2012

I thought the method was still used in particle detectors (like CMS) to identify particles.

11. Jun 17, 2012

### ZapperZ

Staff Emeritus
This thread is a bit vague on what it actually wants (which is a good reason to NOT be lazy in typing out some details on what one wants).

Do you want just a method to determine these masses, or do you want to know how the standard values that is being used were determined? There appears to be a lack of information for the latter.

Determining any physics quantities isn't straight forward, because it requires that you know OTHER quantities, especially the fundamental constants. So the uncertainty in any physical values depends on the uncertainty of the other fundamental constants involved, not just the uncertainty in the experiment being done. Knowing the mass of an electron may, for example, require the knowledge of the Rydberg constant.

I would strongly suggest going through the CODATA report on the fundamental constants.

http://arxiv.org/abs/1203.5425

Zz.

12. Jun 17, 2012

### Bob S

One standard way of measuring the electron mass, once the charge is known, is to use the e/m method of measuring the radius of curvature of a known energy electron in a known magnetic field, as mentioned above.

This can be done in an undergraduate physics lab using a Helmholz coil and the special vacuum tube, as described in http://www.clemson.edu/ces/phoenix/labs/cupol/eoverm/index.html

Be sure to click on Fig. 1 to enlarge it (beautiful photograph). It is very obvious during the experiment that the force on the electron is orthogonal to both the electron velocity and the magnetic field.

13. Jun 17, 2012

### nucl34rgg

This was a very fun lab to do indeed.

14. Jun 18, 2012

### Staff: Mentor

~100MHz for protons in a field of 1 Tesla (quite strong) and less for smaller fields. This corresponds to radio frequencies, which can be observed easily.
In a similar way, ~1GHz for electrons in a field of 5mT.

Curvature in magnetic fields? This just gives a momentum measurement. To measure the mass, you need an additional velocity measurement (energy would work in theory, but gives large uncertainties). This can be done, and LHCb and ALICE have several methods to measure the velocity of particles.