Problem 45 - Chemistry A Molecular Approach

Question

On a dry day, your body can accumulate static charge from walking across a carpet or from brushing your hair. If your body develops a charge of \(-15 \mu\) C (microcoulombs), how many excess electrons has it acquired? What is their collective mass?

Step-by-Step Solution

Answer

The body has acquired approximately \(9.36 \times 10^{13}\) excess electrons, with a collective mass of about \(8.52 \times 10^{-17} kg\).

Step 1: Convert microcoulombs to coulombs

First, convert the charge from microcoulombs to coulombs by using the conversion factor that 1 microcoulomb (\textmu C) is equal to 1 x 10^-6 coulombs (C). So, \(-15 \textmu C = -15 \times 10^{-6} C\).

Step 2: Calculate the number of excess electrons

To find the number of excess electrons, use the elementary charge, which is the charge of one electron and is approximately \(-1.602 \times 10^{-19} C\). Divide the total charge of the body by the charge of one electron: Number of electrons = \(-15 \times 10^{-6} C \/ (-1.602 \times 10^{-19} C/electron)\).

Step 3: Calculate the collective mass

Once you have the number of excess electrons, use the mass of one electron, which is approximately \(9.109 \times 10^{-31} kg\), to calculate the collective mass by multiplying the number of electrons by the mass of one electron.

Key Concepts

Electric Charge

Electric charge is a fundamental property of matter that causes it to experience a force when placed in an electromagnetic field. There are two types of electric charge: positive and negative. Opposite charges attract each other, while like charges repel. This concept is a cornerstone of electrostatics, the study of stationary electric charges or static electricity.

In the given exercise, your body accumulates static charge, specifically negative charge, due to friction - a process known as triboelectric charging. When you walk on a carpet or brush your hair, electrons are transferred to your body, giving it a net negative charge. Measuring this charge in coulombs helps us to quantify the extent of this accumulation and enables calculations such as determining the number of excess electrons.

Elementary Charge

Understanding the Basic Unit of Charge

The elementary charge is the smallest unit of electric charge that is observed in nature and is denoted by the symbol 'e'. One elementary charge is approximately equal to -1.602 × 10^-19 coulombs (C). This is the charge of a single electron (or the opposite charge of a single proton).

When solving the exercise, the elementary charge plays a crucial role. By understanding that the net electric charge on an object can be quantified as a multiple of the elementary charge, we can calculate the number of excess electrons on your charged body. This is done by dividing the total observed charge by the elementary charge, revealing how many individual electron units of charge are present.

Electron Mass

Mass of an Electron

The mass of an electron is another fundamental constant in physics. While the charge of an electron influence's an object's electrical properties, the electron's mass is significant for its dynamics and quantum properties. The mass of an electron is approximately 9.109 × 10^-31 kilograms (kg).

To find the collective mass of the excess electrons in the exercise, we multiply the number of electrons by the electron mass. Despite the seemingly large number of excess electrons, their collective mass is extremely small due to the incredibly low mass of an individual electron. This demonstrates how, even with a significant static charge, the mass contribution of electrons is almost negligible in everyday scenarios.