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

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SUMMARY

The discussion centers on calculating the wavelength of the Lyman-α line for hydrogen and positronium, specifically the transition from the first excited state to the ground state. It concludes that the emission lines observed from a star, which coincide with the Lyman series of hydrogen, indicate that the ion responsible for the pattern is likely positronium due to its reduced mass being half that of hydrogen. The relationship between mass and energy levels is pivotal in understanding the differences in emission lines between these two entities.

PREREQUISITES
  • Understanding of atomic structure and energy levels
  • Familiarity with the Lyman series of hydrogen
  • Knowledge of reduced mass calculations
  • Basic principles of spectroscopy
NEXT STEPS
  • Research the calculation of wavelengths for hydrogen and positronium transitions
  • Learn about the concept of reduced mass in quantum mechanics
  • Explore the implications of emission lines in astrophysics
  • Study the differences between hydrogen and positronium in terms of energy levels
USEFUL FOR

Astronomy students, physicists, and anyone interested in atomic physics and the spectral analysis of celestial bodies.

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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.

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