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

Determine the charge of an electron

The charge of an electron is called an elementary charge. Its value is approximately \(-1.6 \times 10^{-19} \mathrm{C}\). Since we are only interested in the magnitude of the charge, we will consider the elementary charge to be \(1.6 \times 10^{-19} \mathrm{C}\).

Calculate the number of electrons in the oil drop

To find the number of electrons in the oil drop, we will divide the total charge of the oil drop by the charge of a single electron. By doing so, we can find out how many elementary charges fit into the total charge of the oil drop. Number of electrons = \(\frac{\text{Total Charge on Oil Drop}}{\text{Charge of a Single Electron}}\)

Plug in the values and find the number of electrons

Now that we have the formula, we can plug in the values and find the number of electrons in the oil drop. Number of electrons = \(\frac{5.93 \times 10^{-18} \mathrm{C}}{1.6 \times 10^{-19} \mathrm{C}}\)

Calculate and round up the result

Divide the values and round up the result to the nearest whole number since we cannot have a fraction of an electron. Number of electrons ≈ \(\frac{5.93 \times 10^{-18}}{1.6 \times 10^{-19}} = 37\) Therefore, the oil drop contains approximately 37 negative charges (electrons).