Ch.2 - Atoms & Elements

Problem 48

Chapter 2, Problem 48

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

Verified step by step guidance

Identify the charge of a single electron, which is approximately \(-1.602 \times 10^{-19}\) C.

Calculate the number of electrons needed to produce a charge of \(-11.0\) C by dividing the total charge by the charge of a single electron.

Use the formula: \( \text{Number of electrons} = \frac{-11.0 \text{ C}}{-1.602 \times 10^{-19} \text{ C/electron}} \).

Determine the mass of a single electron, which is approximately \(9.109 \times 10^{-31}\) kg.

Calculate the total mass by multiplying the number of electrons by the mass of a single electron.

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Key Concepts

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

Charge of an Electron

An electron carries a fundamental charge of approximately -1.602 x 10^-19 coulombs. This negative charge is essential for understanding how many electrons are needed to achieve a specific total charge, as the total charge can be calculated by multiplying the number of electrons by the charge of a single electron.

Calculating Number of Electrons

To find the number of electrons required to produce a certain charge, you can use the formula: number of electrons = total charge / charge of one electron. For a charge of -11.0 C, you would divide -11.0 C by the charge of a single electron, allowing you to determine how many electrons are necessary to achieve that charge.

Mass of an Electron

The mass of a single electron is approximately 9.11 x 10^-31 kilograms. To find the total mass of the electrons calculated earlier, you multiply the number of electrons by the mass of one electron. This step is crucial for understanding the physical implications of the charge in terms of mass.

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Related Practice

Textbook Question

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

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

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

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.

Textbook Question

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.

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Textbook Question

How many electrons does it take to equal the mass of a proton?