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
360
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??
 
Physics news on Phys.org
  • #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.
 

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

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.

Similar threads

Finding slip-off angle for mass off of sphere?
    • Introductory Physics Homework Help
Replies
7
Views
245
What is the problem with the units in this state equation of a gas?
    • Introductory Physics Homework Help
Replies
12
Views
789
How do you derive the units for momentum for photons
    • Introductory Physics Homework Help
Replies
4
Views
803
Attempting to teach this: Momentum and Impulse
    • Introductory Physics Homework Help
Replies
10
Views
1K
How to find the equilibrium position of three masses (two of them fixed)?
    • Introductory Physics Homework Help
Replies
4
Views
917
What are the units for the slope in an Acceleration vs Mass Graph?
    • Introductory Physics Homework Help
Replies
3
Views
2K
Change in temperature of air in a closed system
    • Introductory Physics Homework Help
Replies
16
Views
1K
Confused about significant figures in official solutions
    • Introductory Physics Homework Help
Replies
6
Views
666
Understanding Units of Force (Newtons and Pascals)
    • Introductory Physics Homework Help
Replies
4
Views
965
A misconception I have about impulse formula interpretation
    • Introductory Physics Homework Help
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top