In Terms of The Avogadro Constant and Faraday Constant
If the Avogadro constant NA and the Faraday constant F are independently known, the value of the elementary charge can be deduced, using the formula
(In other words, the charge of one mole of electrons, divided by the number of electrons in a mole, equals the charge of a single electron.)
In practice, this method is not how the most accurate values are measured today: Nevertheless, it is a legitimate and still quite accurate method, and experimental methodologies are described below:
The value of the Avogadro constant NA was first approximated by Johann Josef Loschmidt who, in 1865, estimated the average diameter of the molecules in air by a method that is equivalent to calculating the number of particles in a given volume of gas. Today the value of NA can be measured at very high accuracy by taking an extremely pure crystal (in practice, often silicon), measuring how far apart the atoms are spaced using X-ray diffraction or another method, and accurately measuring the density of the crystal. From this information, one can deduce the mass (m) of a single atom; and since the molar mass (M) is known, the number of atoms in a mole can be calculated: NA = M/m.
The value of F can be measured directly using Faraday's laws of electrolysis. Faraday's laws of electrolysis are quantitative relationships based on the electrochemical researches published by Michael Faraday in 1834. In an electrolysis experiment, there is a one-to-one correspondence between the electrons passing through the anode-to-cathode wire and the ions that plate onto or off of the anode or cathode. Measuring the mass change of the anode or cathode, and the total charge passing through the wire (which can be measured as the time-integral of electric current), and also taking into account the molar mass of the ions, one can deduce F.
The limit to the precision of the method is the measurement of F: the best experimental value has a relative uncertainty of 1.6 ppm, about thirty times higher than other modern methods of measuring or calculating the elementary charge.
Read more about this topic: Elementary Charge, Experimental Measurements of The Elementary Charge
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