# Energy levels of a hydrogen-like ion.

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I need full explanation of each step. Please help.

1. The helium ion, He+, has energy levels similar to those of the hydrogen atom, since both species have only one electron. The energy levels of the He+ ion are given by the equation

En = - 5248.16 kj/mole n = 1, 2, 3, ...

n2

? Calculate the energies in kj/mole for the four lowest energy levels of the He+ ion.

E1 = kj/mole

E2 = kj/mole

E3 = kj/mole

E4 = k/mole

? One of the most important transition for the He+ ion involves a jump from the n = 2 to the n = 1 level. Delta(Change)E for this transition equals E2 - E1, where these two energies are obtained as in part a. Find the value of Delta(change)E in kJ/mole. Find the wavelength in nm of the line emitted when this transition occurs; use Equation 4 to make the calculation.

Delta(change)E = kJ/mole; Wavelength = nm

? Three of the strongest lines in the He+ ion spectrum are observed at the following wavelength: (1) 121.57 nm; f(2) 164.12 nm; (3) 468.90nm. Find the quantum numbers of the initial and final states for the transitions that give rise to these three lines. Do this by calculating, using Equation 4, the wavelengths of lines that can originate from transitions involving any two of the four lowest levels. You calculated one such wavelength in part b. make similar calculations with the other possible pairs of levels. When a calculated wavelength matches an observed one, write down nhi and nlo for that line. Continue until you have assigned all three of the lines. Make your calculations on the other side of this page.

(1) -> (2) -> (3) ->

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#### Solution Summary

The solution describes the relations between energy levels in Helium ion and the photon's frequency and wavelength which results from electronic transitions between levels.