What are the units for effective mass in the formula m* = (h/2pi)2(d2E/dk2)-1?

In summary, The effective mass, represented by m*, has units of kg and is calculated using the formula m* = (h/2pi)2(d2E/dk2)-1. This is determined by canceling out the units of h and E, which are in J-s and J respectively, and taking into account the units of k, which has units of inverse length. Therefore, the units of m* are kg.
  • #1
magnifik
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0
Are the units for effective mass in kg? I have been trying to wrap my head around the concept then realized I wasn't even sure about the units.

The formula is: m* = (h/2pi)2(d2E/dk2)-1

the units of h are in J-s, and the units of E are in J so...
(J-s)2/J = J-s2
J = kg m2/s2
kg m2 s2/s2 = kg m2

why am i left with a m2 unit??
 
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  • #2
k has units of inverse length. You have a k^2 in the numerator, which has units of m^-2, which will cancel the m^2, and leave you with m* having units of kg, which is correct.
 

1. What is effective mass and why is it important in science?

Effective mass is a concept used in physics to describe the behavior of particles in a material. It is the mass that a particle appears to have when it is moving in a solid, and it is important because it affects how particles interact with each other and how they respond to external forces.

2. How is effective mass measured and calculated?

Effective mass is measured experimentally using techniques such as Hall effect or cyclotron resonance. It is also calculated theoretically using band structure calculations and quantum mechanical models.

3. What are the units for effective mass?

The units for effective mass depend on the type of particle being considered. For electrons in a semiconductor, the unit is typically the mass of an electron (me). In other cases, it could be expressed in terms of the mass of a proton (mp) or the mass of a neutron (mn).

4. How does effective mass differ from rest mass?

Rest mass is the mass of a particle when it is at rest, while effective mass is the mass that a particle appears to have in a material. Effective mass can be larger or smaller than the rest mass, depending on the properties of the material and the type of particle being considered.

5. What are some practical applications of effective mass?

Effective mass is important in understanding the behavior of electrons and holes in semiconductors, which is crucial for the development of electronic devices. It is also used in the study of superconductivity and other quantum effects in materials. Additionally, effective mass plays a role in the design of materials for applications such as solar cells and lasers.

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