Millikan measured the charge of the electron in electrostatic units, esu. The data that he collected included the following series of charges found on oil drops: \(9.60 \times 10^{-10} \mathrm{esu}, 1.92 \times 10^{-9} \mathrm{esu}\), \(2.40 \times 10^{-9} \mathrm{esu}, 2.88 \times 10^{-9} \mathrm{esu}\), and \(4.80 \times 10^{-9}\) esu. (a) From this series find the likely charge on the electron in electrostatic units. (b) Predict the number of electrons on an oil drop with the charge \(6.72 \times 10^{-9}\) esu.

The electron charge quantization concept is fundamental to the understanding of atomic structure and electrical phenomena. It states that the charge on an electron is a discrete quantity, meaning it cannot be divided into smaller parts. This was a groundbreaking discovery because it suggested that electric charge is not continuous, but instead comes in 'packets' or 'quanta'.

In the context of Millikan's oil drop experiment, quantization is observed through the analysis of charges on oil drops. All observed charges were found to be whole-number multiples of a fundamental value, the charge of a single electron. This phenomenon supports the idea that charge is quantized and that the electron carries a specific, unvaryable amount of negative charge. Understanding this concept is critical for students not only in physics, but also in chemistry and all fields that deal with atomic and electronic interactions.

Electrostatic units (esu), also known as statcoulombs, are a part of the centimeter-gram-second (CGS) system of units. They are used to measure charge and describe how strong an electric field is generated by a quantity of charge. In the Millikan oil drop experiment, the charges on the oil drops are measured in esu, which is essential for the calculations involved.

The CGS system is less common now, being largely replaced by the International System of Units (SI), where the unit of charge is the coulomb. However, understanding esu is significant when studying historical experiments like Millikan's or when dealing with electrostatic phenomena in the context of the CGS system. The relationship between esu and coulombs can help bridge the gap between these two systems for students.

The charge to mass ratio of an electron is a crucial physical constant and is represented by the symbol e/m. It describes how much charge an electron carries relative to its mass. This ratio was famously used by J.J. Thomson to first identify the electron as a particle and measure its properties.

Understanding this ratio helps students grasp why electrons behave the way they do under the influence of electric and magnetic fields. It is also instrumental in the operation of instruments like cathode-ray tubes and accelerators. In analyzing the Millikan experiment, this concept isn't directly measured, but understanding the distinct and separate determination of charge and mass deconstructs the electron's identity into understandable parts, enhancing our comprehension of atomic-scale physics.

In the scope of the Millikan oil drop experiment, the fundamental charge calculation is critical as it helps determine the elementary charge of an electron. By dividing the measure of various oil drop charges by the smallest common factor, Millikan inferred the likely charge of an electron in electrostatic units.

Understanding how to calculate this fundamental charge involves data analysis skills and number theory basics, requiring students to find the greatest common divisor among observed charges. This reinforces not only their grasp of the electron's properties but also bolsters mathematical and analytical skills. Recognizing that the fundamental charge is a constant value that quantizes other charges deepens our understanding of the microscopic world and supports the quantum theory's assertions.