How to calculate relative effective mass?

In summary, relative effective mass is a measure of the effective mass of a particle in a given material compared to its mass in a vacuum. It is calculated by taking the ratio of the particle's mass in the material to its mass in a vacuum and is important in materials science for understanding particle behavior and material properties. Factors such as interaction with the crystal lattice, energy level, and material type can influence the relative effective mass, which in turn can affect properties such as electrical and thermal conductivity, optical properties, and particle mobility within the material.
  • #1
bl965
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Homework Statement


A simplified E versus k curve for an electron in the conduction band is given. the value of a is 10 Å. Determine the relative effective mass m* / m0.
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Homework Equations


[/B]
m* = ħ2 / (d2E /dk2)

m0 = 9.11 E-31kg

3. The Attempt at a Solution


The second derivative must be constant.
 
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  • #2
d2E /dk2 = (2E(a) - E(0)) / (3a2)m* / m0 = ħ2 / [(2E(a) - E(0)) / (3a2)] m* / m0 = (1.054 E-34)(3a2) / (2E(a) - E(0)) m* / m0 = (3.162 E-34)(100) / (2E(10) - E(0)) m* / m0 = 3.162 E-32 / (2E(10) - E(0))
 

Related to How to calculate relative effective mass?

1. What is relative effective mass?

Relative effective mass is a measure of the effective mass of a particle, such as an electron, in a given material. It compares the mass of the particle in the material to its mass in a vacuum.

2. How is relative effective mass calculated?

Relative effective mass is calculated by taking the ratio of the particle's mass in the material to its mass in a vacuum. This can be determined experimentally or by using theoretical calculations.

3. Why is relative effective mass important in materials science?

Relative effective mass is important in materials science because it helps to understand the behavior of particles in different materials. It can also provide insights into the electrical and thermal properties of materials.

4. What factors influence the relative effective mass?

The relative effective mass of a particle can be influenced by several factors, including its interaction with the crystal lattice, its energy level, and the type of material it is in.

5. How does relative effective mass affect the properties of a material?

The relative effective mass can affect the electrical and thermal conductivity, as well as the optical properties, of a material. It can also impact the mobility of particles and their ability to move through the material.

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