Spectrum & energy level of neutral hydrogen

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SUMMARY

The energy levels of the doubly ionized Lithium atom (Li++) are directly related to those of neutral Hydrogen due to the Bohr model, with the formula E = 13.6 x Z2/n2 being applicable. The energy levels for Li++ are calculated using Z=3, resulting in higher energy levels compared to Hydrogen's Z=1. The radius of the Li++ ion in the ground state is smaller than that of neutral Hydrogen due to stronger electrostatic forces from the nucleus. The spectrum of Li++ will resemble that of neutral Hydrogen, as both have a single electron in their outer shell.

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  • Understanding of the Bohr model of the atom
  • Familiarity with the concept of ionization energy
  • Knowledge of electrostatic forces in atomic structure
  • Basic grasp of atomic spectra and electron transitions
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  • Explore the calculation of energy levels for multi-electron ions
  • Learn about the implications of nuclear charge on atomic radius
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Students studying atomic physics, particularly those focusing on ionized atoms and their energy levels, as well as educators teaching the principles of the Bohr model and atomic spectra.

Noirchat
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Would like to see if I've understood this question somewhat. :-)


Homework Statement



A doubly ionised Lithium atom (Li^++) has two of its normal complement of electrons removed. The energy levels of the remaining single electron ion are closely related to those of the neutral Hydrogen atom - since the nuclear charge of Lithium is +3 compared to +1 for Hydrogen. Assuming the Bohr model for the atoms:
(a) How are the energy levels of Li^++ ion related to neutral Hydrogen? Estimate values if possible.
(b) How is the radius of the Li^++ ion in the ground state related to neutral hydrogen in the ground satte? Estimate values if possible.
(c) How would the spectrum of the Li^++ ion be related to neutral Hydrogen.

Homework Equations




None given.

But i think E = 13.6 x Z^2/n^2 is used in part a ?

The Attempt at a Solution




(a) I think that the energy levels would be the same since they both have one electron in their shell.

(b) The radius of the Li^++ iom would be smaller than that of the neutral hydrogen as the protons and neutrons in the nucleus of the Li^++ would have stronger neutostatic forces and thus will be held more tightly.


(c) The spectrum would be similar as they both consist of one electron in their shell and thus only one electron would be ionised.
 
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