chaoseverlasting said:Its given that the structure is a BCC type unit cell. The total number of atoms present in a BCC are 2. You are given the dimensions of this unit cell. Since its a cubic cell, you can find the volume enclosed by it.
Each cell contains two atoms, how many cells do you need to get Na (Avagardo Number) atoms?
Once you have that, you know the atomic weight of Na sodium atoms. This weight is equal to the weight of the protons+neutrons+electrons. You know the weight of one electron. You know how many free electrons are present in one sodium atom (valency). Hence you know how many electrons are present in Na sodium atoms.
You also know the total volume enclosed by Na atoms (which you calculated in the beginning). So now you have the total number of free electrons present in a given volume, and can now find the free electron density.
Free-electron density refers to the number of unbound or loosely bound electrons per unit volume of a material. It is a measure of the electron cloud present in a substance and is an important factor in determining its electrical and thermal properties.
The free-electron density can be calculated by dividing the total number of free electrons in a material by its volume. This can be determined using various techniques such as X-ray diffraction, electron microscopy, and spectroscopy.
The free-electron density in a material is influenced by several factors such as temperature, pressure, and the type of material. Metals tend to have a higher free-electron density compared to non-metals due to their structure and bonding properties.
The free-electron density plays a crucial role in determining the electrical and thermal conductivity of a material. It also affects other properties such as magnetism and optical properties. Understanding and controlling the free-electron density is essential in designing and developing new materials with desired properties.
The free-electron density is directly related to the band structure of a material. In metals, the electrons are delocalized and can move freely within the conduction band, resulting in a high free-electron density. In contrast, in insulators and semiconductors, the electrons are tightly bound to atoms and have limited movement, leading to a lower free-electron density.