Ch.2 - Atoms & Elements

Problem 47b

Chapter 2, Problem 47b

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 -22 mC (microcoulombs), what is their collective mass?

Verified step by step guidance

Understand that the problem involves finding the mass of electrons corresponding to a given charge.

Recall that the charge of a single electron is approximately \(-1.602 \times 10^{-19}\) coulombs.

Calculate the number of electrons by dividing the total charge by the charge of a single electron: \(\text{Number of electrons} = \frac{-22 \times 10^{-6} \text{ C}}{-1.602 \times 10^{-19} \text{ C/electron}}\).

Use the mass of a single electron, which is approximately \(9.109 \times 10^{-31}\) kg, to find the total mass: \(\text{Mass} = \text{Number of electrons} \times 9.109 \times 10^{-31} \text{ kg/electron}\).

Perform the calculations to find the collective mass of the electrons.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Coulomb's Law

Coulomb's Law describes the electrostatic force between charged objects. It states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This principle is fundamental in understanding how static charges interact and can help explain the accumulation of charge on the body.

Charge and Mass Relationship

In physics, the relationship between charge and mass is often explored through the concept of charge-to-mass ratio. While charge itself does not have mass, the energy associated with charged particles can be related to mass through Einstein's equation, E=mc². This relationship is crucial for calculating the effective mass of a system based on its charge.

Microcoulombs to Mass Conversion

To find the mass associated with a given charge, one can use the concept of energy stored in an electric field. The energy (E) can be related to charge (Q) and voltage (V) through the equation E = QV. By knowing the voltage and using the relationship between energy and mass, one can convert the charge in microcoulombs to an equivalent mass, which is essential for solving the problem.

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Energy to Mass Conversion

Related Practice

Textbook Question

A chemist in an imaginary universe, where electrons have a different charge than they do in our universe, performs the Millikan oil drop experiment to measure the electron's charge. The charges of several drops are recorded here. What is the charge of the electron in this imaginary universe?

Drop # Charge

A –6.9×10^–19 C

B –9.2×10^–19 C

C –11.5×10^–19 C

D –4.6×10^–19 C

Imagine a unit of charge called the zorg. A chemist performs the oil drop experiment and measures the charge of each drop in zorgs. Based on the results shown here, what is the charge of the electron in zorgs (z)? How many electrons are in each drop?

Drop # Charge

A –4.8×10^–9 z

B –9.6×10^–9 z

C –6.4×10^–9 z

D –12.8×10^–9 z

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 -22 µC (microcoulombs), how many excess electrons has it acquired?

Textbook Question

How many electrons are necessary to produce a charge of -11.0 C? What is the mass of this many electrons?

Textbook Question

Which statements about subatomic particles are true? a. If an atom has an equal number of protons and electrons, it will be charge-neutral. b. Electrons are attracted to protons. c. Electrons are much lighter than neutrons. d. Protons have twice the mass of neutrons.

Which statements about subatomic particles are false? a. Protons and electrons have charges of the same magnitude but opposite sign. b. Protons have about the same mass as neutrons. c. Some atoms don't have any protons. d. Protons and neutrons have charges of the same magnitude but opposite signs.