Why the discrepancy in muonic H Bohr radius? 285 fm or 256 fm?

In summary, there is a discrepancy between the Bohr radius values reported for muonic hydrogen, with some sources stating it is 285 fm and others stating it is 256 fm. This is because the first value is a constant for an infinitely heavy nucleus, while the second value is a physical value that takes into account the reduced mass of the muon when forming an atom with a proton. This reduced mass varies depending on the type of nucleus, and can be seen in the range of values for different types of atoms. The concept of reduced mass is an important factor in understanding the differences in these reported values.
  • #1
seattle.truth
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Some places say (including this paper) claim the bohr radius of muonic hydrogen is 285http://ethesis.unifr.ch/theses/downloads.php?file=LudhovaL.pdf

Many more peer reviewed papers say it is 256 fm, or 255 fm though. (search for '256 fm muonic' in teh googlez).

So who is right? And more importantly, why is there such a massive descripancy?

Any help will be greatly appreciated. Thanks.
 
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  • #2
seattle.truth said:
Some places say (including this paper) claim the bohr radius of muonic hydrogen is 285http://ethesis.unifr.ch/theses/downloads.php?file=LudhovaL.pdf

Many more peer reviewed papers say it is 256 fm, or 255 fm though. (search for '256 fm muonic' in teh googlez).

So who is right? And more importantly, why is there such a massive descripancy?

Any help will be greatly appreciated. Thanks.

They are both correct under different contexts. 256 fm is the correct Bohr radius for an infinitely heavy nucleus. 285fm is the Bohr radius for a proton-muon atom. This is because the reduced mass of muon when it forms an atom with a proton is 0.89879 times its rest mass. The first value is constant (but it is not accurate for a real system), while the second value is physical and accurate, but it is only valid for a proton nucleus. The physical value is different from 285 for a Deutoron for example (and it is in between 256 and 285, because the reduced muon mass is larger.)
 
  • #3
Thank you very much, sir.

I didn't know about reduced mass in Newtonian physics.

Now I'm enlightened (after doing a bit more research).
 
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Related to Why the discrepancy in muonic H Bohr radius? 285 fm or 256 fm?

1. Why is there a discrepancy in the muonic H Bohr radius?

The discrepancy in the muonic H Bohr radius is due to the difference in mass between an electron and a muon. The muon is approximately 200 times more massive than an electron, which causes it to have a smaller orbit and therefore a smaller Bohr radius.

2. How does the mass of the muon affect the Bohr radius?

The Bohr radius is inversely proportional to the mass of the particle. Therefore, since the muon is more massive than an electron, it has a smaller Bohr radius.

3. Can the discrepancy in the muonic H Bohr radius be explained by quantum effects?

No, the discrepancy is not due to quantum effects. While quantum effects do play a role in the behavior of particles, they do not account for the significant difference in mass between an electron and a muon.

4. Are there any other factors that could contribute to the discrepancy in the muonic H Bohr radius?

Other factors, such as the energy levels of the muonic hydrogen atom or experimental error, could also play a role in the observed discrepancy. However, the main factor is the difference in mass between the electron and muon.

5. How is the muonic H Bohr radius measured and verified?

The muonic H Bohr radius is measured and verified through experiments using particle accelerators and other high-energy physics techniques. These experiments involve observing the behavior and interactions of muons and measuring their properties, such as their mass and orbit size, to determine the Bohr radius.

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