The proton mass is and the triton (tritium nucleus) mass is

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

Deriving the Spectrum, Ch The exact Coulomb problem and Rydberg states

Problem

The proton mass is

1836.15\,m_e

and the triton (tritium nucleus) mass is

5496.92\,m_e

. Take

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

and

a_0 = 0.052918\,\mathrm{nm}

. ((a)) Find the Lyman-alpha wavelength (

n=2\to1

) for ordinary hydrogen and for tritium, and report the isotope shift

\lambda_{\rm H}-\lambda_{\rm T}

in nm. ((b)) Find the

1s

contact density

|\psi_{100}(0)|^2

for tritium, in

\mathrm{m^{-3}}

. ((c)) The helium nucleus (alpha particle) mass is

7294.3\,m_e

. A radio recombination line from singly ionised helium (He

^+

Z=2

), of the same

\Delta n=1

type as hydrogen's H

n\alpha

series, is observed at

204.4\,\mathrm{GHz}

. Identify the lower level

n

of the transition.

Browse the problem library