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In the field of electrodynamics of charged particles, especially in electron optics and ion optics, the most widely used physical quantity is the mass-to-charge ratio (m/Q). This ratio is used In the scientific fields of electron microscopy, accelerator physics, cathode ray tubes, Auger electron spectroscopy, nuclear physics, cosmology, and mass spectrometry. In some cases, the charge-to-mass ratio (Q/m) is used instead, which is the multiplicative inverse of the mass-to-charge ratio.
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What is an Electron?
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The electron is a low mass subatomic negatively charged particle. These are generally considered elementary particles as they have no known components or substructure. It is also known to be the lightest and most stable subatomic particle.
According to Pauli Exclusion Principle and belonging to the fermions group, no two electrons can occupy the same quantum state. Electrons exhibit properties of both particles and waves similar to all elementary particles i.e. they can be diffracted like a light when they collide with other particles.
Electrons participate in gravitational, electromagnetic, and weak interactions as well as play an important role in numerous physical phenomena, such as electricity, magnetism, chemistry, and thermal conductivity.
The history of atomic structure and quantum mechanics can be dated back to ancient Greek times. It was first proposed by Democritus that matter is composed of atoms.
These theories could not be proved accurately due to the lack of technological advancements in those times. But gradually with the advent in the modern era, in the nineteenth and early twentieth century, experiments revealed that even an atom is not the ultimate particle and is made up of subatomic particles known as electron, proton, and neutron.
Protons and neutrons are found in the nucleus of the atom whereas electron is found in the shells or orbits around the nucleus. In the 19th century, J.J. Thomson first proposed the Thomson Atomic Model and conceived the idea of the electrons in it.
Mass of Electron
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The rest mass of an electron represented by me is an intrinsic mass of a stationary electron, also known as the invariant mass of the electron, and is considered one of the fundamental constants of physics. It has a value of about 9.109×10-31 kilograms or about 5.486×10-4 Daltons (5.486 10-4u or atomic mass units).
This mass corresponds to a rest energy of 0.511MeV or equivalent to about 8.187×10-14 joules, according to Einstein’s principle of mass-energy equivalence. Defining it in the relative terms of a proton, it can be found that the mass of an electron is 1/1836 of the mass of a proton. An electron is often considered nearly massless in comparison with a proton or a neutron, and hence the electron mass is not included in calculating the mass number of an atom. The mass of an electron is presented in the table below in different units –
| Constants | Values | Units |
|---|---|---|
| me | 9.1093837015(28)×10-31 | kg |
| me | 5.48579909065(16)×10-4 | Da |
| me | 8.1871057769(25)×10-14 | J/c2 |
| me | 0.51099895000(15) | Mev/c2 |
| Energy of me | 8.1871057769(25)×10-14 | J |
| Energy of me | 0.51099895000(15) | Mev |
The mass of the electron can be taken as approximately 0 amu because as we can see that it is very less, being almost of negligible value.
Charge on an Electron
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The electric charge of an electron is -1.602 10-19 C (or the experimental value -1.602176634 10-19 Coulombs). Coulomb is considered to be the basic unit of electric charge. It expresses the naturally occurring unit of electric charge and is considered to be a fundamental physical constant. The elementary charge as it is called is used as a standard unit of charge for subatomic particles. The symbol e denotes the elementary charge. it is to be noted that the electrical charge of an electron is equal to that of a proton, but with the opposite sign. Hence the electrical charge of an electron, an elementary particle, is denoted by e-. The minus sign denotes a negative charge. In the table below, the charge of an electron is presented in different units –
| Constants | Values | Units |
|---|---|---|
| e- | -1 | e |
| e- | -1.602 10-19 | C |
| e- | -4.803 10-10 | esu |
Charge to Mass Ratio of an Electron
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According to classical electrodynamics, the importance of the mass-to-charge ratio is that two particles with the same mass-to-charge ratio move in the same path in a vacuum, when subjected to the same electric and magnetic fields. Its SI units are kg/C but on some rare occasions, the Thomson has been used as its unit in the field of mass spectrometry. The mass and charge of an electron have already been discussed by us and hence, it can be provided that the charge to mass ratio of the electron is given by –
Magnitude of the Charge of an electron (e) in coulombs = 1.602 * 10-19 C
Mass of an electron (me) in kilograms = 9.109 * 10-31 kg
So, if the value is taken up to six digits after decimal, then it will be –
e/m = 1.758820 × 1011 C/kg-1
Apparatus for determining charge to mass ratio of an electron
Experimental setup for the determination of charge to mass ratio of the electron
It was observed by Thomson while carrying out the discharge tube experiment that the particles of the cathode deviate from their path and this amount of deviation that happened was deduced to be in the presence of an electrical or magnetic field depends on various related parameters. Some of them are –
- Greater interaction is experienced by particles with a greater magnitude with the electric or magnitic field. Thus, they exhibited greater deflection.
- Deflection is inversely proportional to the mass of the particle as it was seen that lighter particles experienced greater deflection.
- The strength of the electrical and the magnetic field present affects the deflection of the particle from their path in a directly proportional manner.
Things to Remember based on Charge to Mass Ratio of Electron
- The electron is a low mass subatomic negatively charged particle, where the electric charge is a negative elementary charge.
- The mass of an electron has a value of about 9.109×10-31 kilograms or about 5.486×10-4 Daltons.
- The electric charge of an electron is -1.602 10-19 C.
- Two particles with the same mass-to-charge ratio move in the same path in a vacuum, when subjected to the same electric and magnetic fields.
- Lighter particles experience greater deflection in the experiment for determining the charge to mass ratio.
Sample Questions based on Charge to Mass Ratio of Electron
Ques. What is an electron? (1 mark)
Ans. The electron is an elementary low mass subatomic negatively charged particle. It is also known to be the lightest and most stable subatomic particle.
Ques. Who invented the instruments needed to measure the e/m of the electron? (1 mark)
Ans. J.J. Thomson was a British physicist who pioneered the invention of the instruments and experimented to find the measurements of the mass as well as the charge of an electron.
Ques. State values for the mass and charge of electrons. (2 marks)
Ans. Mass of electron: 9.109×10-31 kilograms
Charge of an electron: -1.602 10-19 C
Ques. What is the mass of one proton? (1 mark)
Ans. Proton is the stable subatomic particle with a positive charge equal to that of an electron and a rest mass of 1.67262 1027 kg, or 1,836 times the mass of an electron.
Ques. What forces are responsible for the deflection of particles in the e/m ratio experiment? (2 marks)
Ans. The strength of the electrical and the magnetic field present affects the deflection of the particle from their path in a directly proportional manner.
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