Ch.2 - Atoms, Molecules & Ions

Problem 95

Chapter 2, Problem 95

A period at the end of sentence written with a graphite pen-cil has a diameter of 1 mm. How many carbon atoms would it take to line up across the period if a single carbon atom has a diameter of 150 pm?

Verified step by step guidance

First, we need to convert the diameter of the period from millimeters to picometers. There are 1,000,000,000 picometers in a millimeter, so we multiply the diameter of the period by this conversion factor.

Next, we divide the diameter of the period in picometers by the diameter of a single carbon atom to find out how many carbon atoms can fit across the period.

Remember that when we divide the diameter of the period by the diameter of a single carbon atom, we are assuming that the carbon atoms are perfectly lined up and that there are no gaps between them.

This calculation will give us the number of carbon atoms that can fit across the period. However, this is an approximation because in reality, atoms are not perfect spheres and there may be some space between them.

Finally, round your answer to the nearest whole number, because you can't have a fraction of an atom.

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Key Concepts

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

Atomic Diameter

The diameter of an atom is a measure of its size, typically expressed in picometers (pm). For carbon, the diameter is approximately 150 pm, which is essential for calculating how many carbon atoms can fit across a given distance. Understanding atomic size helps in visualizing the scale of atoms in relation to macroscopic objects.

Conversion of Units

To solve the problem, it's crucial to convert units appropriately. The diameter of the period is given in millimeters (mm), while the diameter of a carbon atom is in picometers (pm). Knowing that 1 mm equals 1,000,000 pm allows for a direct comparison and calculation of how many carbon atoms can fit across the period.

Molecular Arrangement

Molecular arrangement refers to how atoms are organized in space. In this context, it involves lining up carbon atoms in a straight line across the diameter of the period. Understanding this concept is vital for visualizing how individual atoms can be counted and arranged in relation to larger structures.

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Related Practice

Textbook Question

What discovery about atomic structure was made from the results of Rutherford's gold foil experiment?

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Textbook Question

Prior to Rutherford's gold foil experi-ment, the 'plum pudding' model of the atom represented atomic structure. In this model, the atom is composed of elec-trons interspersed within a positive cloud of charge. If this were the correct model of the atom, predict how the results of Rutherford's experiment would have been different. (a) The alpha particles would pass right through the gold foil with little to no deflection. (b) Most of the alpha particles would be deflected back toward the source. (c) Most of the alpha particles would be absorbed by the atom and neither pass through nor be deflected from the gold foil.

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Textbook Question

A period at the end of sentence written with a graphite pencil has a diameter of 1 mm. If the period represented the nucleus, approximately how large is the diameter of the entire atom in units of m?

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Textbook Question

What is the difference between an atom's atomic number and its mass number?

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Textbook Question

What is the difference between an element's atomic number and its atomic weight?

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Textbook Question

The subscript giving the atomic number of an atom is often left off when writing an isotope symbol. For example, 6 often written simply as 13C. Why is this allowed?

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