Measurement of e/m Value of Electron and Mass of Electron

Measurement of e/m Value of Electron and Mass of Electron

In 1897, J.J Thomson devised an instrument to measure the e/m value of electron. The device includes a discharge tube. The cathode rays are permitted to go through electric and magnetic fields. When both the fields are off then a beam of cathode rays, included electrons, produces a luminous area at P1 on the fluorescent screen.

The north and south poles of the magnetic field are perpendicular to the plane of the paper in the diagram. The electrical field is in the plane of the paper. When the only magnetic field is used, the cathode rays are deflected in a circular path and fall at the point P3.

When only the electrical field is used, the cathode rays produce an area at P2. Both electrical and magnetic fields are then used at the same time and their strengths changed in such a way that cathode rays once again struck the point P1. In this way, by comparing the strengths of the two fields one can identify the e/m value of electrons. It comes out to be 1.7588 x 1011 coulombs kg-1. This indicates that 1 kg of electrons has 1.7588 x 1011 coulombs of charge.

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Measurement of Charge on Electron – Millikan’s Oil Drop Experiment

The oil drop experiment was carried out by Robert A. Millikan and Harvey Fletcher in 1909 to determine the elementary electrical charge. The experiment happened in the Ryerson Physical Laboratory at the University of Chicago. Millikan received the Nobel Reward in Physics in 1923.

In 1909, Millikan identified the charge on an electron by a basic arrangement. The apparatus includes a metallic chamber. It has two parts. The chamber is filled with air, the pressure of which can be changed by a vacuum pump. There are two electrodes A and A’. These electrodes are used to create an electrical field in the area in between the electrodes. The upper electrode has a hole in it.

A fine spray of oil droplets is created by an atomizer. A couple of droplets travels through the hole in the top plate and into the area between the charged plates, where one of them is observed through a microscope. This droplet, when brightened perpendicularly to the direction of view, appears in the microscope as a bright speck against a dark background. The droplet falls under the force of gravity without applying the electric field. The speed of the droplet is figured out. The velocity of the droplet (V1) depends upon its weight, mg.

v1α mg (Eq 1)

where ‘m’ is the mass of the droplet and ‘g’ is the velocity due to gravity. After that, the air in between the electrodes is ionized by X-rays. The droplet under observation uses up an electron and gets charged. Now, connect A and A’ to a battery that produces an electric field having a strength, E. The droplet moves upwards against the action of gravity with a speed (v2).

v α Ee − mg (Eq 2)

where ‘e’ is the charge on the electron and Ee is the upward driving force on the droplet due to the applied electric field of strength E.

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Dividing formula (1) by (2)

v1/v2 = mg/Ee -mg (Eq 3)

The values of v1 and v2 are recorded with the help of a microscopic lens. The elements like g and E are also understood. Mass of the droplet can be identified by differing the electrical field in such a way that the droplet is suspended in the chamber.

For this reason, ‘e’ can be computed. By changing the strength of the electrical field, Millikan discovered that the charge on each droplet was different. The tiniest charge which he found was 1.59 x 10-19 coulombs, which is very close to the recent value of 1.6022 x 10-19 coulombs.

This smallest charge on any droplet is the charge of one electron. The other drops having more than one electron on them, have double or triple the quantity of this charge. The charge present on an electron is the tiniest charge of electrical energy that has been measured so far.