How many molecular orbitals are present in the valence band of a sodium crystal with a mass of 5.45 g?

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Determine the number of moles of sodium in the given mass using the formula: \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \). The molar mass of sodium (Na) is approximately 22.99 g/mol.

Calculate the number of sodium atoms using Avogadro's number (\(6.022 \times 10^{23}\) atoms/mol). Multiply the number of moles by Avogadro's number to find the total number of sodium atoms.

Understand that in a sodium crystal, each sodium atom contributes one valence electron to the formation of molecular orbitals in the valence band.

Recognize that the number of molecular orbitals in the valence band is equal to the number of valence electrons, which is the same as the number of sodium atoms in the crystal.

Conclude that the number of molecular orbitals in the valence band is equal to the number of sodium atoms calculated in step 2.

Key Concepts

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

Molecular Orbitals

Molecular orbitals are formed by the linear combination of atomic orbitals when atoms bond together. In a solid, such as a sodium crystal, these orbitals can be filled with electrons and are crucial for understanding the electronic properties of the material. The valence band consists of the highest energy molecular orbitals that are filled with electrons at absolute zero.

Valence Band

The valence band is the range of energy levels that electrons occupy in a solid before they can be excited to higher energy levels, such as the conduction band. In metals like sodium, the valence band is typically filled with electrons that contribute to electrical conductivity. Understanding the number of molecular orbitals in the valence band helps in analyzing the material's electronic structure and behavior.

Sodium Crystal Structure

Sodium crystals have a face-centered cubic (FCC) structure, where each sodium atom contributes to the formation of the crystal lattice. The mass of the sodium sample can be used to determine the number of atoms present, which directly influences the number of molecular orbitals in the valence band. This relationship is essential for calculating the total number of molecular orbitals based on the number of sodium atoms in the crystal.

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