yes, it is changing due to the Bhor can be found from the ratio of the relative dielectric constant for undoped and the effective mass of the charged particles. when doped, the dopant atoms can be considered as independent sources of charged carriers
The Bohr radius is a constant for measuring distances (0.53 angstroms) . It is the same value in vacuum and in solid state physics. It doesn't depend of the electric permittivity at all because the Bohr atomic model is not employed in solid state (excitons take a some characteristics only) or other parts of the Physics.
Thank you Behnam,
Exactly! The Bohr radius is 0.53 angstroms as I have said. They cialculate an "effective Bohr radius" using a hydrogen model which is not serious and this is not a good publication. Do you read this kind of literature? Please, nobody use the Bohr atomic model even in atomic physics, would you tell me that in solid state physics this is serious? Also do you are going to change the Rydberg energy? These are constants of physics that you can find in any text.
https://physics.nist.gov/cgi-bin/cuu/Value?bohrrada0
Dear Behnam,
I have been working in the Max Planck of Stuttgart a little later that von Klipzing received the nobel prize and I can tell you that I have used the Prague many times. That is one book which nowadays is a little old due to the evolution of such subject, but I haven't found anything serious on the effective Bohr radius. Forget it please!
The other two references that I don't know I'm sure that they are not going to use the Bohr radius in a different form that I unit of distance.
Dear Priyadharsini,
If your question reduce to:
Bohr radius value of nanomaterials changes with dopant?
The answer is no.
Bohr radius is the value of orbital of the electron for the Bohr model of the hydrogen atom which provides nowadays a unit of ditance. This is the same as the angstrom, nanometer, light-year, parsec, Planck length, Compton radius, classical electron radius, etc...
Nevertheless, the Bohr radius (only for hydrogen atom) extends to give one idea of the distance between charges and it appears as the effective Bohr radius in:
1. Excitons (mainly applied in the confinement of quantum dots)
rB=ħ2Ɛ/e2 (me-1 + mh-1)
2. Electronic gas in 2D between insulator-semiconductor materials based in the existence of central potential as in the hydrogen.
3. Impurities in semiconductors. I attach you how this "effective" radius is defined in this context.
If I may attempt to bring more light (and less heat) to the conversation, it is important to draw the distinction between the Bohr radius of a system, and the Bohr as a unit of length.
The Bohr radius is the most likely distance to find an electron (measured from the nucleus) in a spherical orbit around a massive positive point charge. The radius depends principally on the mass of the electron, the charge of the nucleus and the dielectric permittivity. It can of course be applied as a model more generally, e.g. positrons bound to a negative charge.
The Bohr unit of length is the Bohr radius of a hydrogen atom in vacuum, assuming the proton is infinitely massive. This unit of length is sometimes referred to as the "Bohr radius", which I think is where the confusion is arising in this discussion, but it is only the Bohr radius for a very specific case, and in condensed matter the unit is usually referred to simply as a "Bohr".
The two uses may be combined. We sometimes ask our 1st year students to calculate the Bohr radius of a proton-muon system, expressed in Bohrs, since this gives a natural length for comparison with the proton-electron system (hydrogen). (This calculation also illustrates why the "true" Bohr model needs the reduced mass, though for hydrogen the difference is very small.)
Dear Philip,
My advice is that you ask to your teacher of quantum mechanics. The Bohr radius is a constant used as unit of length, the same as the Bohr magneton is one unit of magnetic moment without being related with an actual atomic system.
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