IPhO_2025_Q1-03

Bohr radius (A.2)

IPhO · 2025 · Fisika Modern

Hydrogen and galaxies (Part A — Introduction; official 2025 IPhO question). This problem studies hydrogen and the mass distribution of galaxies. In the Bohr model, a non-relativistic electron of mass m_{e} orbits a fixed proton on a circular path. Throughout this part, use ℏ = h / (2 π) . The electron is non-relativistic and orbits a fixed proton on a circular orbit. The Bohr model quantizes angular momentum as L = n ℏ, where n is a positive integer; α = e^{2} / (4 π ϵ_{0} ℏ c) \approx_{7} .27 \times 1 0^{- 3} . Show that the radius of each orbit is given by r_{n} = n^{2} r_{1} .

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