What ion is this? even emission lines matches lyman series of hydrogen

[unscientific]

Homework Statement

Calculate the wavelength of the Lyman-α line (the transition from the 1st excited
state to the ground state) for (a) hydrogen atoms and (b) positronium e+e-, and explain
the origin of their difference.

In the light emitted from a star, a pattern of emission lines is found with every
second line coinciding with a line of the Lyman series of hydrogen. Identify which ion
causes this pattern and identify the observed transitions [assume the star is stationary
with respect to the Earth].

Homework Equations

The Attempt at a Solution

(a) the positronium is simply a particle of reduced mass μ = m₁m₂/(m₁+m₂) orbiting a central particle of m₁+m₂. μ = m/2.

Is the ion a positronium? Since the E1 is proportional to m, and that positronium has half the mass of hydrogen..

 

[unscientific]

anyone?