Hydrogen atom: A muonic hydrogen atom is a proton orbited by a muon (a particle with the same charge as an electron and 207 times its mass) in which the mass of the muon is significant relative to the mass of the proton. What would be the radius of the smallest muon orbit in a muonic hydrogen atom?

Question

Quizplus · Accepted Answer

The radius of the smallest muon orbit can be calculated using the formula for the Bohr radius:

a = ε₀h²/(πμe²)

where ε₀ is the electric constant, h is Planck's constant, μ is the reduced mass of the system (muon-proton), and e is the elementary charge.

For a muonic hydrogen atom, the reduced mass is:

μ = m_pm_μ/(m_p + m_μ) = m_p/208

where m_p is the mass of the proton and m_μ is the mass of the muon.

Substituting in the values and solving, we get:

a = 2.84 × 10^-13 m

Therefore, the answer is D.

Hydrogen Atom: a Muonic Hydrogen Atom Is a Proton Orbited