How many molecular orbitals are present in the conduction band of a lithium crystal with a mass of 11.2 g?

Verified step by step guidance

1. Determine the number of moles of lithium in the given mass using the formula: \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \). The molar mass of lithium is approximately 6.94 g/mol.
2. Calculate the number of lithium atoms using Avogadro's number \( 6.022 \times 10^{23} \text{ atoms/mol} \). Multiply the number of moles by Avogadro's number to find the total number of atoms.
3. Recognize that in a lithium crystal, each lithium atom contributes one electron to the conduction band. Therefore, the number of molecular orbitals in the conduction band is equal to the number of lithium atoms.
4. Understand that in a solid, the molecular orbitals form bands. The conduction band is formed by the overlap of atomic orbitals from all the lithium atoms in the crystal.
5. Conclude that the number of molecular orbitals in the conduction band is equal to the number of lithium atoms calculated in step 2.

Key Concepts

Molecular Orbitals

Molecular orbitals are formed by the linear combination of atomic orbitals when atoms bond together. In a solid, these orbitals can extend over many atoms, leading to the formation of bands, such as the conduction band, which allows for the movement of electrons. Understanding how these orbitals combine is crucial for analyzing the electronic properties of materials.

Conduction Band

The conduction band is a range of energy levels in a solid where electrons can move freely, contributing to electrical conductivity. Electrons in this band are not bound to any particular atom, allowing them to conduct electricity. The number of molecular orbitals in the conduction band is related to the number of atoms in the crystal and their respective atomic orbitals.

Lithium Crystal Structure

Lithium, being a metal, has a body-centered cubic (BCC) crystal structure, which influences its electronic properties. The arrangement of lithium atoms in this structure determines how many atomic orbitals combine to form molecular orbitals in the conduction band. The mass of the lithium crystal can help determine the number of atoms present, which is essential for calculating the total number of molecular orbitals.