The Electron I

The Electron I is the tenth lecture in the Properties of Matter section of PH1011. It covers electrolysis, the unit Faraday, cathode rays and the effects of magnetic and electric fields.

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Electrolysis
Electrolysis involves passing charge through a solution via electrodes (anode -> cathode) in order to cause the ions to become atoms and amass at the relative electrode. The mass produced is proportional to the amount of electrons transferred at that electrode. The charge (in Faradays) required to discharge one mole of a substance at an electrode is equal to the number of excess charges per ion.

In example -


 * 0.5A passed in one hour produces 2g silver metal on the cathode. This gives a total charge of (0.5Ax3600s) = 1800C . As the mass is 0.002kg, the charge per kg is (1800/0.002) ~ 106C/kg . Per mole (MAg = 108g/mol) this gives 97,500 C. Running the same calculation with hydrogen finds 100,000C required - and a more exact measurement finds a constant 96,500C/mol.

1 Faraday = 96,500C/mol

As the mole corresponds to a known number of atoms, 6.022x1023, the charge required per atom is (96500/6.022x1023)  1.6x10-19C . This proves charge to be quantised; overall charges required for materials are integer multiples of 96,500C.

Cathode rays
Cathode ray tubes are evacuated tubes through which a high energy stream of electrons are passed, travelling from a cathode to an anode. These are observed to travel in straight lines, bend in a magnetic field and a high electrostatic field, and pass through thin foils. Cathode rays were concluded to be tiny negative charges and dubbed electrons.

Magnetic and Electric Fields
The right hand rule states that F = qvB. Using this in conjunction with F=ma (as F is perpendicular to velocity here, perpendicular motion occurs) and magnetic force = mass x centripetal acc. (evB = mv2/r => e/m = v/(rB)) allows measurement of B and r, but v is still unknown.

Balancing the perpendicular electric field to the magnetic field with F=eE gives eE = Bev; therefore v = E/B. Experimental values give E/B = ~c/10; the electron is not an electromagnetic wave. Using v=E/B and e/m = v/(rB), e/m = v/(rB) = E/(rB2).

Summary
Electrolysis involves the passing of charge through solution to produce pure elements at the electrodes; the mass of these products depends on the quantity of charge input. The charge required to produce one mole of any substance is 96,500C, and the charge on an individual electron is 1.6x10-19C. A variety of equations can relate fields to electron speed; setting electric field strength equal to magnetic field strength allows calculation of the size and therefore velocity of the electron.