Among the experiments that have marked the history of physics, few have been as important and enlightening as Millikan’s experiment . At the basis of this famous experiment, which took place in the early 20th century, there is the precise determination of one of the fundamental constants of nature: the charge of the electron . But, even more significantly, the results of this experiment revealed a fundamental truth about the very nature of matter, laying the foundation for understanding the concept of quantization .
At a time when physics was experiencing a profound revolution, with theories and ideas that challenged traditional understanding of the world, Robert Millikan set out to probe one of the deepest mysteries of the atom : the nature and value of electronic charge. How could a particle as infinitely small as the electron have a definite charge? And how can we measure it precisely?
Millikan’s experiment, also known as the ” oil drop experiment “, not only answered these questions, but also revealed a surprising principle: the charge is not a continuum, but is “quantized”, that is, it can only take on certain discrete values . This discovery had revolutionary implications, suggesting that the microscopic world obeys laws and principles radically different from those of the macroscopic world that we directly perceive.
Millikan’s experimental apparatus consisted of:
- a nebulizer that sprayed droplets of oil into a compartmentTO; some of these, by rubbing on the torch, could acquire an electric charge of any sign
- at the base and in the middle of the container there were two plates connected to a circuit that acted as armatures of a capacitor: on the upper plate there was a hole that allowed the passage of small droplets of oil from the upper compartmentTOto the lower compartment�between the capacitor plates
- A uniform intensity electric field is created between the platesAND=Δ��Where,Δ�is the potential difference to which the plates are subjected e�is the distance between them
- in the sector�, between the plates of the capacitor, we have a microscope that is used to observe the droplets that move in the electric field created in the compartment
The droplets coming out of the nebulizer fell into the compartmentTOand, through the hole in the upper armature, they entered the electric field directed upwards generated by the capacitor in the compartment�. As long as the capacitor is discharged, it is observed under the microscope positioned in the compartment�that the droplets move downward at a constant speed due to the weight force and viscous friction of the air.
When charging the capacitor it can happen that:
- if the droplet is neutral , its motion will remain unchanged
- if the droplet is positively charged , its motion will tend to slow down and reverse its direction under the effect of the electric force generated by the electric field of the opposite direction to the weight force
- if the droplet is negatively charged , its motion will tend to accelerate because it is subjected to an electric force directed in the same direction as the weight force
The cases in which the droplets are charged (the second and third) are treated in the same way; we, for convenience, will examine only the second, with a positively charged droplet in the electric field.
The analysis of Millikan’s experiment and the birth of quantization
Millikan determined the radii of the droplets thanks to observations under the microscope and, knowing the density of the oil, calculated their masses .
He then dedicated himself to analyzing the motion of a positively charged droplet in the electric field of the compartment directed upwards.
The droplet in question is subjected to:
- to the weight force
- to the force of viscous friction�to=6 � � � �
- to the electric force�And=�⋅AND=�Δ��
It was observed experimentally that the droplet moved with uniform rectilinear motion which, translated according to the first law of dynamics, meant that the vector sum of the forces applied to it had to be zero.
To calculate the charge of the droplet, Millikan first had to know its speed, which is why he equipped the microscope with a grating that allowed him to calculate the space it traveled in a given time.�, from which to derive its own�.
The procedure is similar to the case in which the charge is negative, having made the appropriate change in direction of the electric force vector.
Millikan’s conclusions on quantization
After many measurements and repetitions of the experiment made over the course of about 4 years, Millikan came to a fundamental conclusion: the electric charge is quantized, that is, it takes on only integer and discrete values, multiples of a fundamental value, and , in accordance with the atomic models proposed at the beginning of the twentieth century, could only be the charge of an electron. In fact, in an atom, only electrons can move from one body to another, allowing the charge to be determined based on their excess or defect.