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Measuring the electron

There is a classic experiment that is studied in physics to measure the relationship between the charge and the mass of an electron, is the Thomson experiment and uses a cathode ray tube. I found a fantastic book by David Prutchi and Shanni R. Prutchi (Exploring Quantum Physics through Hans-on Projects) that described a variant of the Thomson experiment easier to perform with small cathode tubes. In fact the book suggests using the Philips 2AP1 model, a small 2" tube and green phosphor screen and I found exactly this model on eBay for about $30.

The idea of ​​the experiment is to introduce the CRT (cathode ray tube) into a coil that covers it completely. The electron beam accelerated between the cathode and the anode deflects with an alternating current between two plates of the tube and a line is generated on the screen. But when we apply voltage to the coil, the electron beam is subjected to a magnetic field through which it makes a helical path. If the appropriate voltage is applied to the coil as a function of the acceleration of the beam (which depends on the potential difference between the cathode and the anode), the electron beam is hit on the screen of the tube in a complete circle.

Known the acceleration voltage V, the length L from the deflector to the screen of the tube (section covered by the coil) and the magnetic field B applied to get the path of the beam to be exactly one revolution, we have the following formula for calculate the relationship between e and m:

The data we need to calculate is the magnetic field B generated by the coil. For this we use the following formula that allows us to calculate it from the length of the coil, the number of turns and the intensity applied:

The way to perform the experiment is to establish an acceleration power, and increase the intensity applied to the coil until the line that forms the beam is turning and ends up disappearing at a point. When this happens, the electron beam will have traveled a complete turn and the equality of the equation that relates e / m to V, B and L will be met. Specifically, I made two measurements, one with an acceleration voltage of 800V and another with 900V with the following results:

  • For 800V the intensity that is applied to the coil to complete the turn of the beam is 0.82A

  • For 900V the intendiad to be applied is 0.88A


From these measurements of the experiment and keeping in mind that the number of turns is 1162, the length of the coil 0.155m and the length from the deflector of the tube to the screen is 0.075m, a ratio for e / m obtained is:

  • For the experiment with 800V, the result is 1.88175E11 coulomb / Kg

  • And for 900V, the result is 1.83813E11 coulomb / Kg


Both data are very similar to the real value of 1.76E11 coulomb / Kb, representing an average error of the order of 5%.

To carry out the experiment, a bit of DIY has been required:

  • Manufacture of high voltage DC power supply to generate acceleration voltage of up to 1000V. The recommendations and circuit of the book mentioned above have been followed.

  • Realization of a circuit (also according to the recommendations of the book) to generate the alternate beam deflection voltage, the supply voltage to release the electrons that will then accelerate, as well as the adjustment of the beam intensity and focus.

  • Make the coil, on a PVC tube in which the tube fits, keeping in mind that the best way to know the number of turns of the coil is to count them as they are winding. A mechanical lap counter was used.

  • For the coil supply, a standard 12 or 24VDC variable source can be used.

  • Mount the set on a stand





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