Positronium is an electron and a positron (equal mass ) orbiting their common centre…

PHYSICS · Multi-part · Fermi University Physics · Atomic, Molecular & Optical Physics · One-electron atoms and the origins of atomic structure · One-electron atoms and the origins of atomic structure

Reading the Spectrum, Ch The nuclear atom and the Bohr-Sommerfeld model

Problem

Positronium is an electron and a positron (equal mass

m_e

) orbiting their common centre of mass under their mutual Coulomb attraction. Using

R_\infty = 109737.32\,\mathrm{cm^{-1}}

and hydrogen's Balmer-

\alpha

vacuum wavelength,

656.47\,\mathrm{nm}

(computed with

R_{\rm H}

), ((a)) find the electron-positron reduced mass

\mu

in units of

m_e

; ((b)) find

R_{\rm Ps}

, the Rydberg constant for positronium; ((c)) predict the vacuum wavelength of positronium's

n = 3 \to n = 2

line, the analogue of hydrogen's Balmer-

\alpha

, and say whether it is exactly twice hydrogen's Balmer-

\alpha

wavelength.

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