From my quick investigation, the spectrum is based on the Rydberg formula, and with a small change,

hisyhauttaq84w

hisyhauttaq84w

Answered question

2022-05-08

From my quick investigation, the spectrum is based on the Rydberg formula, and with a small change, would lead to
1 λ μ = m μ m e ( R ( 1 n 1 2 1 n 2 2 ) )
where m μ is the mass of a muon.
So, taking hydrogen as an example, we would observe similar bands, shifted into the x-ray/gamma range.
Is this correct?

Answer & Explanation

Mathias Patrick

Mathias Patrick

Beginner2022-05-09Added 22 answers

Almost but not quite. Qualitatively the spectrum is the same with the 1 / n 2 spacing, but the scale of the spectrum is set by the reduced mass μ,
μ = 1 1 m l + 1 m p
where m p is the proton mass and m l is the lepton (muon or electron) mass. Since m p 2000 m e , it is not a large error to take μ = m e for an electronic hydrogen atom. But for the muon, m μ 200 m e 0.1 m p , so the error is quite large, around 10%.

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