Charge to Mass Ratio of Electron

The charge to mass ratio of an electron, often denoted as (e/me), is a fundamental physical constant that has significant implications for theories of an atom.

In 1897, the British physicist Joseph John Thomson measured the electrical charge (e) to electron’s mass (me) ratio of the electron by using a cathode ray tube under the influence of electric and magnetic fields for the first time.

He applied electric and magnetic fields perpendicular to each other as well as the path of electron’s beam. The deflection of moving negatively charged particles, called electrons by magnetic and electric fields, depends upon

  • Magnitude of accelerating voltage.
  • Masses of the particles.
  • Charges on the particles
  • Strengths of the applied electric and magnetic fields.

To perform this, Thomson used the apparatus sketched in the below figure.

Set up for determining the charge to mass ratio of an electron.

Experimental Setup for Determining Charge to Mass Ratio of Electron

J. J. Thomson’s experiment to determine the charge to mass ratio of the electron involves the use of a cathode ray tube (CRT) in combination with electric and magnetic fields. The apparatus typically consists of the following components:

Cathode Ray Tube (CRT):

  • This is a sealed glass tube from which air has been evacuated to create a vacuum.
  • Inside the tube, there is a cathode (negative electrode) and an anode (positive electrode). When a high voltage is applied, electrons are emitted from the cathode and accelerate toward the anode, forming a beam known as a cathode ray.

Electric Field:

  • To create an electric field, two electric charged parallel plates are placed on either side of the electron beam within the tube. These plates are connected to a voltage source.
  • The electric field is perpendicular to the direction of the electron beam and exerts a force on the electrons, causing them to deflect.

Magnetic Field:

  • In the setup to determine the charge to mass ratio of an electron, a magnet is placed around the tube to create a magnetic field. This field is oriented from the north pole to the south pole of the magnet and is perpendicular to the plane of the diagram.
  • This arrangement makes the magnetic field perpendicular to both the electric field and the direction of motion of the cathode rays (electron beam).
  • The magnetic field deflects the cathode rays upwards in the vertical plane, as the field is directed from back to front.
  • The electric and magnetic fields are so arranged that they deflect the cathode rays in opposite directions in the vertical plane.

Fluorescent Screen:

  • At the end of the CRT, there is a fluorescent screen that glows when electrons strike on them, allowing visualization of the beam’s path and deflection.

In the experiment carried out by Thomson, the accelerating voltage was fixed so that only the charge to mass ratio (e/m) of an electron could be determined.

Observations Recorded by J. J. Thomson

During the experiment conducted to determine the charge to mass ratio, J. J. Thomson recorded the following observations.

(1) Without any fields applied, the electrons travel in a straight line from the cathode to the anode, and hits the fluorescent screen at the point B.

(2) The electron diverts from their actual path and strike at point A on the fluorescent screen of the cathode ray tube when only electric field is applied.

(3) When only the magnetic field is applied, the electron hits at the point C at the fluorescent screen of the cathode ray tube.

(4) When both electric and magnetic fields are applied equally, the electrons return to the original path because their effects are equal and opposite, the forces cancel each other out. In this case, they hit the screen at point B again.

Factors Affecting the Deflection of Particles in Electric and Magnetic Fields

While performing the discharge tube experiment, J. J. Thomson observed that the amount of deflection of the particles from their path depends on various factors. They are as:

(1) Magnitude of negative charge on the particle:

When the magnitude of negative charge on the particle is more, its interaction with the electric or magnetic field is more, showing greater deflection.

(2) Mass of the particle:

Lesser the mass of the particle, more is the deflection. Thus, the amount of deflection is inversely proportional to the mass of the particle.

(3) Strength of electric and magnetic fields:

The deflection of cathode ray particles from their original path is directly proportional to the strength of the electrical and the magnetic field applied. Thus, when the strength of the magnetic field increases or there is an increase in the voltage, the deflection of electrons from their original path also increases.

By measuring the deflection of cathode ray particles (electrons) in the presence of magnetic field or electric field strength, Thomson determined the numerical value of e/me (charge to mass ratio) that was of the order of 1011 C kg-1. But a later more precise determination gave 1.7 * 1011 C kg-1. The currently accepted charge to mass ratio (e/me ) value of an electron is approximately 1.758803 * 1011 C kg-1.

Calculation:

Charge of an electron e = 1.6 * 10-19 C

Mass of an electron me = 9.1 * 10-31 kg

Therefore, charge to mass ratio of an electron (e/me) = (1.6 * 10-19 C) / (9.1 * 10-31 kg) = 1.758 * 1011 C kg.

In the above (e/me) ratio, me represents the mass of an electron in kg, and e represents the magnitude of electron’s charge expressed in coulomb (C).

This experiment proves that the negatively charged particles present in the cathode ray tube are the fundamental particles which are present in all the matters. Thomson named these particles electrons which are expressed as e because they are negatively charged particles.

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