In order to find the mass of an electron experimentally, we find the value of e/m and we find the value of e. From these two values, we find the value of m. Has any experiment been done, which measures the mass of an electron without finding its charge?
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2 Answers
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Yes, the mass of the electron can be measured by the energy of the gamma rays involved in electron-positron annihilation. The mass of an electron is equal to the energy (divided by the speed of light squared) of one of those gamma rays, as measured in the center of momentum frame.
The measurement of gamma ray energies is known as Gamma-ray spectroscopy. The general idea is that the gamma ray is absorbed by some material, and the resulting ionization is detected in some way (cheaper detectors tend to use a scintillating material, while more expensive detectors use semiconductor technologies). The detector response is calibrated with a source of known gamma energies, and then the energy of another gamma ray can be measured.
The detector has a finite resolution, but the measurement can be enhanced by looking at extra features at the spectrum. For instance, there's a "Compton edge" that appears from gamma rays that Compton scatter rather than being absorbed, and an extra peak at twice the electron mass (when both gamma rays from the annihilation are absorbed).
That said, the relative uncertainty on the electron mass is only around $10^{-8}$, which is much better than you can get with standard gamma ray spectroscopy.
Some physics programs (Rutger's, for instance) have their students actually run this experiment in a lab course.
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$\begingroup$ Thanks. Do both methods give the same value for mass of electron? $\endgroup$– AvinashCommented Feb 7, 2018 at 3:13
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$\begingroup$ Yep, the measurements are consistent. $\endgroup$– Chris ♦Commented Feb 7, 2018 at 3:16
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$\begingroup$ Can this method be used in practice? Has it actually been used? How does one measure the energy of a single photon? Consider adding a reference to back up your claims. Cheers! $\endgroup$ Commented Feb 7, 2018 at 3:51
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1$\begingroup$ its not immediately obvious to me that an ionizing detector does not depend on the value of e indirectly somewhere $\endgroup$– jk.Commented Feb 7, 2018 at 13:04
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1$\begingroup$ @jk. if you calibrate with a known source then there's no need to know the actual charge of a single charge carrier in your detector. $\endgroup$ Commented Feb 7, 2018 at 13:40
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One can measure the mass of the electron using diffraction of electrons.
EDIT (2/6/2018): The de Broglie wavelength only depends on the mass and velocity, so if electrons diffract, say, on a crystal or on two slits, one can determine the distance between the maxima of the diffraction pattern and calculate the mass, if the velocity of electrons is known. One does not need to know the charge of electrons to prepare a bunch of electrons with known velocity (using, for example, a thermal emission source and the time of flight method).
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$\begingroup$ A Wien filter also suffices for producing electrons of known velocity. The electrons have to be charged, but the actual value is irrelevant. $\endgroup$– Chris ♦Commented Feb 7, 2018 at 4:41
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$\begingroup$ @Chris: With a Wien filter, you need to measure the electric and magnetic field to determine the velocity (and you need to know the velocity to measure the electron mass), as far as I can see. My feeling is this defeats the purpose:-), but this may be a matter of taste. $\endgroup$ Commented Feb 7, 2018 at 6:28
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$\begingroup$ I had to think about that for a second. The definition of the ampere (and thus the coulomb) makes reference only to the force between two wires, and the definition of electric and magnetic fields follow from there, with no reference to the charge of an electron. So you can measure $E$ and $B$ fields without needing to know the electron charge ;) $\endgroup$– Chris ♦Commented Feb 7, 2018 at 8:00
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2$\begingroup$ @akhmeteli That seems entirely implausible as a realistic experiment to me, but I guess it does make for an acceptable gedankenexperiment. $\endgroup$ Commented Feb 7, 2018 at 15:01
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2$\begingroup$ @EmilioPisanty: I agree that this is not the simplest way to measure the velocity of electrons :-), but your words "entirely implausible" may be too strong: remember that the rotating wheel method was used to measure the speed of light (scienceworld.wolfram.com/physics/FizeauWheel.html), and I just consider the same approach but applied to electrons. $\endgroup$ Commented Feb 7, 2018 at 15:11