# Charge to Mass Ratio

## What is Charge to Mass Ratio?

The history of quantum mechanics and the atomic structure is dated back to the times of Democritus, who is the man that first proposed the theory that matter consists of atoms. These theories did not, however, gain much importance since it lacked the technology needed. The experiments that were conducted during the nineteenth century and the early twentieth century had revealed that just an atom by itself is not the ultimate article. However, the continuous efforts of several scientists led to the discovery of different subatomic particles such as protons, neutrons, and electrons.

J. J. Thomson, in the nineteenth century, had proposed the Thomson Atomic Model which discovered the electron for marking the inception of subatomic particles. After the discovery of the electron, he continued with his experiments for calculating the mass and the charge of the electron. With the help of these calculations, he made a derived formula to calculate the charge to mass ratio of electrons. In this article, we will study the mass to charge ratio and the calculation of the charge by mass ratio.

### What is an Electron?

The electron is known as a negatively charged particle having relatively lower mass. As such, it is easily deflected by passing it closer to the other electrons or even the positively charged nucleus of the atom.

 Mass of Electron m = mass of electron in kg     = 9.10938356 × 10-31 kilograms. Charge of Electron e = magnitude of the charge of the electron in coulombs       = 1.602 × 10-19 coulombs.

### Charge to Mass Ratio of an Electron

The charge to mass ratio of an electron is denoted by the following formula :

$\frac {e} {m}$  = 1.758820 × 1011 C/kg

Where in,

m = mass of electron in kg

= 9.10938356 × 10-31 kilograms.

e  = magnitude of the charge of the electron in coulombs

= 1.602 10-19  coulombs.

### Experimental Setup to Determine the Charge to Mass Ratio of Electron

Thomson observed while carrying out the discharge tube experiment that the particles of cathode tend to deviate from their actual path. He noticed this deviation of the path in the presence of the magnetic or electric field being dependent on different related parameters. These parameters are as follows:

1. The particles having a greater magnitude of charge experienced much higher interaction with the magnetic or electric field. Hence, they possessed a higher deflection.

2. The lighter particles experienced a greater deflection when compared to the heavier ones. Hence, deflection is inversely proportional to the mass of that given particle.

3. The deviation of the particle from its actual path is directly proportional to the strength of the magnetic and the electric field that is present.

Let us understand these parameters by understanding the experimental observations.

1. The electrons underwent deviation from their path and hit the cathode-ray tube at a point x under the presence of the lone electric field.

2. The electrons, similarly, struck the point z of the discharge tube only when the magnetic field was present.

3. Hence, for making the electrons continue on their same path, balancing the magnetic as well as the electric field that is acting on them is important.

4. And finally, depending on the deflection of the electron, J. J. Thomson had calculated the charge to mass ratio value of the electron.

Just after the discovery of Electron J.J Thompson had done so many experiments in order to know and calculate the charge and mass of electrons. The article discusses the experimental setup to determine the charge-to-mass ratio of an electron.

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1. Why is the Charge to Mass Ratio important?

If we know the charge to mass ratio, it allows us to calculate the mass when we measure the charge effects. We use electrons in several different experiments since they are easily provided by the thermionic emission. The other charged particles are even difficult to get and capture.

Also, according to the second law of Newton’s theory, the acceleration of the particle is given by the force divided by mass. Since the force of the charged particle is directly proportional to the charge it contains, the deflection of the beam of the charged particles is the same for all the particles having the same charge by mass ratio. Hence, deflection is not dependent on just the charge and mass as long as we maintain the charge to mass ratio.

2. How did J. J. Thomson find the charge by the mass ratio of the electron?

J. J. Thomson had performed several experiments for determining that the atoms contain subatomic particles having both positive as well as negative charges. He had determined that the electrons, the negatively charged particles, weighed lighter than the protons, the positively charged particles. The charge to mass ratio of the electrons was measured when electrons were accelerated through a voltage, Vx towards the positively charged plate. Some of these electrons passed through a tiny hole present in the plate and formed an electric beam that travelled to a place wherein both the magnetic as well as electric fields were present.

3. What is the charge to mass ratio of an electron?

Only after the experiments of J.J. Thomson the formula of calculation of charge to mass ratio of the electron has been discovered which is as follows:

The charge to mass ratio of the electron is given by :

$\frac {e}{m}$ = 1.758820 × 1011 C/kg

Where,

m = mass of an electron in kg = 9.10938356 × 10-31 kilograms.

e = magnitude of the charge of an electron in coulombs = 1.602 x 10-19 coulombs.

In this experiment, J.J Thomson found that the cathode particles are not on the same path. He found out that there are different parameters on which the amount of deviation depends on the presence of electrical magnitude.

On one side the particles which had a greater magnitude of the charge had greater interaction with the electric or magnetic field which ultimately resulted in greater deflection.

On another end, lighter particles also had greater deflection which proved that deflection is inversely proportional to the mass of the particle.

4. What is the charge to mass ratio of a proton?

The alpha particle is a helium nucleus with two protons and two neutrons, with a charge twice that of a proton and a mass four times that of a proton.

5. Is the charge to mass ratio constant?

The charge to mass ratio is basically a physical quantity that is directly connected to the mass and electric charge of any given particle. It is measured in units of kilograms per coulomb (kg/C) commonly used in electrodynamics of electron and ion optics particles. The main importance of charge to mass ratio as per classical electrodynamics is when the two particles with the same charge to mass ratio go in the same direction in a vacuum with the same electric and magnetic field. On some occasions, the mass to charge ratio is also used which is said to be the inverse of the charge to mass ratio.

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