Ch.2 - Atoms & Elements

Problem 43

Chapter 2, Problem 43

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

Verified step by step guidance

Step 1: Understand that the Millikan oil drop experiment was designed to measure the charge of an electron. In this experiment, the charge on each oil drop is a multiple of the elementary charge (the charge of one electron).

Step 2: Look at the charges given for each drop. Notice that they are all negative, which is consistent with the negative charge of an electron.

Step 3: Find the greatest common factor (GCF) of the charges. This is because the charge of each drop is a multiple of the elementary charge, so the GCF should give the charge of a single electron.

Step 4: Convert the charges into the same units if they are not already. In this case, all charges are given in coulombs (C), so no conversion is necessary.

Step 5: Calculate the GCF of the charges. This can be done by listing the factors of each charge and finding the largest factor that they all share. This will give the charge of the electron in this imaginary universe.

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Key Concepts

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

Millikan Oil Drop Experiment

The Millikan oil drop experiment is a pivotal experiment in physics and chemistry that measured the charge of the electron. By balancing the gravitational and electric forces on tiny oil droplets, Millikan was able to determine the charge of individual electrons. This experiment is foundational for understanding atomic structure and the quantization of electric charge.

Quantization of Charge

Quantization of charge refers to the principle that electric charge exists in discrete units, specifically as integer multiples of the elementary charge. In the context of the Millikan experiment, the charges measured on the oil drops should be multiples of the fundamental charge of the electron. This concept is crucial for interpreting the results of the experiment and understanding how charges interact.

Charge in Different Universes

The idea of charge in different universes suggests that fundamental constants, such as the charge of the electron, can vary in hypothetical scenarios. In this question, the electron has a different charge than in our universe, which requires recalculating the charge based on the provided measurements. Understanding how to adapt known principles to new contexts is essential for solving problems in theoretical chemistry.

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Textbook Question

Which statements are consistent with Rutherford's nuclear theory as it was originally stated? Why? a. The volume of an atom is mostly empty space. b. The nucleus of an atom is small compared to the size of the atom. c. Neutral lithium atoms contain more neutrons than protons. d. Neutral lithium atoms contain more protons than electrons.

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Textbook Question

Which statements are inconsistent with Rutherford's nuclear theory as it was originally stated? Why? a. Since electrons are smaller than protons, and since a hydrogen atom contains only one proton and one electron, it must follow that the volume of a hydrogen atom is mostly due to the proton. b. A nitrogen atom has 7 protons in its nucleus and 7 electrons outside of its nucleus. c. A phosphorus atom has 15 protons in its nucleus and 150 electrons outside of its nucleus. d. The majority of the mass of a fluorine atom is due to its 9 electrons.

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 -15 µC (microcoulombs), how many excess electrons has it acquired?

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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 -15 µC (microcoulombs), what is their collective mass?

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