Question

In an experiment it was found that the total charge on an oil drop was \(5.93 \times 10^{-18} \mathrm{C}\) . How many negative charges does the drop contain?

Short answer

The oil drop contains approximately 37 negative charges (electrons).

Step-by-step solution

Identify the given information

We are provided with the total charge on the oil drop: \(Q = 5.93 \times 10^{-18} \mathrm{C}\). We also know the fundamental charge of an electron: \(e = -1.6 \times 10^{-19} \mathrm{C}\).

Determine the number of electrons needed for the net charge

To determine the number of electrons on the oil drop, we will take the total charge (Q) and divide it by the charge of one electron (e). The formula is: \[n = \frac{Q}{e}\]

Calculate the number of electrons on the oil drop

Plugging the given values into the formula, we get: \[n = \frac{5.93 \times 10^{-18} \mathrm{C}}{-1.6 \times 10^{-19} \mathrm{C}}\]

Simplify the equation and find the result

By dividing the values of the charges, we get the number of electrons: \[n \approx 37.06\] Since the number of electrons must be a whole number, we round to the nearest whole number: \[n \approx 37\] So, the oil drop contains approximately 37 negative charges (electrons).

Key concepts

Fundamental Charge of Electron

The fundamental charge of an electron is one of the most important constants in physics. It represents the smallest unit of electric charge that exists independently. The electron has a negative charge, quantified as approximately \(e = -1.6 \times 10^{-19}\) Coulombs (abbreviated as C). This value is integral in calculations involving charge. Each electron contributes this fixed amount of charge to any system, making it a building block for understanding electrical phenomena.
Understanding the fundamental charge helps clarify how charge quantization works. Quantization implies that charge occurs in discrete units, much like currency cannot be divided beyond its smallest denomination. Thus, when dealing with any charged object or system, its total charge is a multiple of the electron's charge. This discrete nature is crucial in comprehending more complex concepts like the structure of atoms and battery chemistry.
Knowing the electron's charge is also key in experimental setups like the oil drop experiment, which measure very small charges by comparing their values to this fundamental constant.

Number of Electrons Calculation

Calculating the number of electrons involved in a given charge can help understand the quantization of charge. To find out how many electrons contribute to a specific charge, the total charge is divided by the fundamental charge of an electron. Let's break this down with an easy-to-follow approach using the provided formula:

• Identify the total charge of the system, denoted as \(Q\). For instance, \(Q = 5.93 \times 10^{-18}\) Coulombs in our example.
• Use the formula \[n = \frac{Q}{e}\]where \(n\) indicates the number of electrons, \(Q\) is the total charge, and \(e\) is the charge of a single electron.
• Plug in the values: \[n = \frac{5.93 \times 10^{-18}}{-1.6 \times 10^{-19}}\]On solving, you should obtain \(n \approx 37.06\), which rounds to 37 electrons.

Each electron contributes its fundamental charge, and so the cumulative charge of 37 electrons amounts to the total \(Q\) given. This calculation underscores the precision required in charge measurement, highlighting the sophisticated nature of electric charge measurability.

Oil Drop Experiment

The oil drop experiment is a famous experiment conducted by Robert Millikan to measure the electric charge of a single electron. The process involves observing microscopic oil droplets between two metal plates. By balancing gravitational and electric forces, the charge on each droplet can be determined.
The experiment works as follows:

• Small oil droplets are sprayed in a chamber and allowed to fall due to gravity between two electrically charged plates.
• The gravitational force pulls the droplets downward, while electric forces can push them upwards when voltage is applied across the plates.
• By adjusting the voltage to keep a droplet suspended, the net force acting on it becomes zero, allowing precise calculation of the droplet's charge.

Millikan found that the charge on the droplets always measured as an integer multiple of \(1.6 \times 10^{-19}\) C. This vital finding confirmed the quantized nature of electric charge and provided a precise value for the electron's charge. The experiment, which is a cornerstone in physics, underscores the significance of the electron's fundamental charge, proving that charge is transferred in distinct and describable amounts.