The charge of an electron is \(1.6 \cdot 10 ^ {-19} C\). Here, we will learn about how the specific charge of an electron was determined, and the importance of determining the specific charge of an electron in physics.
How was the specific charge of an electron determined?
In 1897, JJ Thomson conducted experiments with cathode rays, or as they were known then, gas discharge tubes. Thomson discovered the existence of negatively charged particles, which he called 'corpuscles'. Even though this was the first observation of subatomic particles, they were not universally accepted at the time.
Even though JJ Thomson was able to measure the ratio between an electron's charge and its mass (qe / me), and calculate the mass of an electron approximately \(5.56 \cdot 10 ^{-4}\) times the mass of a hydrogen atom, he was not able to determine the exact charge of a single electron.
Similar results were found by George FitzGerald and Walter Kaufmann who experimented with electricity and magnetism, but were only able to explain that a charge is a continuous variable. These results were important, but lacking, in the same way that many properties of light could be explained with the wave theory of light back then; but physicists of the time still couldn't explain the photoelectric effect.
In 1909, 'the oil-drop experiment' was conducted by Robert Millikan and Harvey Fletcher for the purpose of determining a single electron's specific charge. The experiment is also known today as Millikan's experiment.
Millikan's oil drop experiment
Two horizontal metal plates were placed on top of each other with an insulating substance between them. The insulating material was pierced with four holes, three for light to enter from and one for examination using a microscope.
To create a uniform electric field between the two plates, a potential difference was applied across them. Because of the friction with the nozzle, some of the oil drops were electrically charged as they were sprayed. A source of ionising radiation, such as an X-ray tube, might potentially be used to charge the droplets as well.
A simplified diagram of Millikan's oil-drop experiment. Camacho - Vaia Originals
A chamber above the plates was sprayed with atomised oil drops. Oil was used instead of water because it does not evaporate fast and hence maintains a consistent mass. Later, one suitable drop (the last remaining one that hadn't dropped to the bottom plate) was selected to continue the experiment. By adjusting the potential difference between the plates, the net force (F) on the drop, which was the vectorial sum of the gravitational force (Fg), and the force applied to the drop by the electric field (FE) was adjusted to be zero.\[m_{drop} \cdot g = q_e \cdot E\]
Where:
m is the mass of the drop in grams
g is the gravitational constant, 9.8 m/s2 at Earth's surface
qe is the charge of the electron in Coulombs
E is the electric field in Newton/Coulomb
This also meant that the drop was allowed to fall at its terminal velocity (v) when the voltage source was turned off. The mass of the drop was determined by how rapidly it descended when the voltage was turned off. Since we know that the voltage (V) was adjusted to balance the forces on the drop, and the electric field (E) was a product of the voltage applied, we can show it with the equation below.
\[E = \frac{V}{d}\]
d is the distance between the plates in meters.
A diagram of the forces on the oil drop between the metal plates. Tezcan - Study Smart Originals
The charge of the electron may be estimated using the rearranged equation below after the mass of the drop is known.
\[q = \frac{m_{drop} \cdot g}{E} = \frac{m_{drop} \cdot g \cdot d}{V}\]
V is the voltage that holds the drop stationary.
Millikan had measured the charge of the electron qe to an accuracy of 1 percent and had raised it by a factor of 10 to a value of -1.60⋅10-19 C within a few years.
The importance of the specific charge of an electron
Determining the specific charge of an electron is one of the turning points in physics, which led to several new discoveries. Let's have a look at the role this discovery played.
- Since the charge of an electron is related to its mass, determining the specific charge of an electron also meant that the mass of an electron was determined.
- With the determination of the specific charge of an electron, the existence of subatomic particles was universally accepted. (Electrons being the first subatomic particles to be discovered.)
- Determining the specific charge of an electron also helped to understand the structure of an atom since the mass was discovered. Later on, the proton and the neutron were discovered and today we know that the proton-electron mass ratio is mp / me = 1836.15. This is also helpful in understanding the roles of the subatomic particles and how much of the mass of the atom they comprise.
Electron Specific Charge - Key takeaways
- The specific charge of an electron is 1.6⋅10-19.
- In 1909, the oil-drop experiment was conducted by Robert Millikan and Harvey Fletcher for the purpose of determining a single electron's specific charge. The experiment is also known today as Millikan's experiment.
- In Millikan's experiment, two horizontal metal plates were placed on top of each other with an insulating substance between them. The insulating material was pierced with four holes, three for light to enter from and one for examination with a microscope.
- Since the charge of an electron is related to its mass, determining the specific charge of an electron also meant that the mass of an electron was determined.
- Determining the specific charge of an electron also helped understand the structure of an atom since the mass was discovered. Later on, the proton and the neutron were discovered and today we know that the proton-electron mass ratio is mp/me = 1836.15. This is also helpful in understanding the roles of the subatomic particles and how much of the mass of the atom they cover.
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