How Many Conduction Electrons Are There in a 2.50 MM Diameter Gold Wire That Is 50.0 CM Long?

Conduction electrons refer to the electrons that are free to move within a material and are responsible for electrical conductivity. To determine the number of conduction electrons in a gold wire, we need to consider its dimensions and the properties of gold.

Gold is a metal with a face-centered cubic (FCC) crystal structure, which means it has a specific arrangement of atoms that allows for the movement of conduction electrons. It is known that in an FCC lattice, each atom contributes one conduction electron.

First, let’s calculate the volume of the gold wire. The volume of a cylinder can be determined using the formula V = πr^2h, where r is the radius and h is the height (or length in this case). Given that the diameter of the wire is 2.50 mm, the radius is 1.25 mm (or 0.0125 cm). The length of the wire is 50.0 cm.

Using the formula, V = π(0.0125 cm)^2(50.0 cm), we find that the volume of the wire is approximately 0.0247 cm^3.

Next, we need to determine the number of gold atoms present in this volume. The density of gold is 19.3 g/cm^3, and its molar mass is 196.97 g/mol.

To convert the volume of the wire to grams, we multiply it by the density: 0.0247 cm^3 x 19.3 g/cm^3 = 0.477 g.

To convert grams to moles, we divide the mass by the molar mass: 0.477 g / 196.97 g/mol = 0.00242 mol.

Lastly, we multiply the number of moles by Avogadro’s number (6.022 x 10^23 electrons/mol) to find the number of conduction electrons: 0.00242 mol x 6.022 x 10^23 electrons/mol = 1.46 x 10^21 conduction electrons.

Therefore, there are approximately 1.46 x 10^21 conduction electrons in a 2.50 mm diameter gold wire that is 50.0 cm long.

Common Questions and Answers:

1. What are conduction electrons?

Conduction electrons are the electrons that are free to move within a material and are responsible for electrical conductivity.

2. Why are gold wires commonly used in electrical applications?

Gold wires are highly conductive due to the presence of a large number of conduction electrons, making them ideal for transmitting electrical signals.

3. Are all metals good conductors of electricity?

Most metals are good conductors of electricity because they have a high number of conduction electrons. However, some metals may have lower conductivity due to impurities or crystal defects.

4. How do the dimensions of a wire affect the number of conduction electrons?

The volume of the wire determines the number of atoms and, consequently, the number of conduction electrons. A larger volume of material will have more conduction electrons.

5. Does the temperature affect the number of conduction electrons?

Temperature can affect the number of conduction electrons indirectly by altering the mobility of the electrons. As temperature increases, the resistance of the material may also increase, reducing the number of effective conduction electrons.

6. Can non-metallic materials have conduction electrons?

Non-metallic materials generally do not have conduction electrons. However, some materials, such as graphite, can exhibit some conductivity due to the presence of delocalized electrons.

7. How do conduction electrons differ from valence electrons?

Valence electrons are the outermost electrons of an atom and are involved in chemical bonding. Conduction electrons, on the other hand, are free to move within a material and are responsible for electrical conductivity.

8. How are conduction electrons related to electrical current?

Conduction electrons are responsible for the flow of electrical current. When a voltage is applied, these electrons move in a particular direction, creating a flow of charge.

9. Are all the conduction electrons in motion?

Not all conduction electrons are in motion at a given time. The motion of electrons depends on the presence of an electric field or voltage potential.

10. Do conduction electrons have a specific location within the material?

Conduction electrons are not localized to a specific location within the material. They move freely throughout the lattice structure of a material.

11. Can the number of conduction electrons be changed in a material?

The number of conduction electrons in a material is determined by its atomic structure and cannot be easily changed. However, doping or introducing impurities can alter the number of conduction electrons.

12. Do all metals have the same number of conduction electrons?

No, the number of conduction electrons can vary among different metals. It depends on the atomic structure and arrangement of atoms within the material.