The radius of an atom of tungsten (W) is about 2.10 Å. (b) How many tungsten atoms would have to be lined up to create a wire of 2.0 mm?

Name: Chemistry: The Central Science
Author: Brown
ISBN: 9780134414232

Verified step by step guidance

Convert the wire length from millimeters to angstroms. Since 1 mm = 10^7 Å, multiply 2.0 mm by 10^7 to get the length in angstroms.

Understand that the diameter of a tungsten atom is twice its radius. Therefore, calculate the diameter of a tungsten atom by multiplying the given radius (2.10 Å) by 2.

To find out how many tungsten atoms are needed to line up to the length of the wire, divide the total length of the wire in angstroms by the diameter of one tungsten atom.

Set up the division: (length of wire in Å) / (diameter of one tungsten atom in Å).

Perform the division to find the number of tungsten atoms needed to line up to the length of the wire.

Key Concepts

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

Atomic Radius

The atomic radius is a measure of the size of an atom, typically defined as the distance from the nucleus to the outermost electron shell. For tungsten (W), the atomic radius is approximately 2.10 angstroms (A), which is equivalent to 2.10 x 10^-10 meters. Understanding atomic radius is crucial for calculating how many atoms can fit into a given length.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one unit to another unit. In this problem, we need to convert the length of the wire from millimeters (mm) to angstroms (A) to match the units of the atomic radius. This involves using conversion factors, where 1 mm equals 10^10 A, allowing for accurate calculations of the number of atoms in the wire.

Avogadro's Number

Avogadro's number (approximately 6.022 x 10^23) is the number of atoms, ions, or molecules in one mole of a substance. While not directly needed for this specific calculation, understanding Avogadro's number is essential in chemistry for relating macroscopic measurements to atomic-scale quantities, especially when dealing with large numbers of atoms in calculations.

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