The energy-level digram for the hypothetical one-electron element osbornium is s

Question

The energy-level digram for the hypothetical one-electron element osbornium is shown. If such an atom absorbs an 18.0 eV photon, the electron will jump from the n =1 ground level to the n = 4 level and subsequently decay.

n - 4 ------------------------------------ -2.00 eV
n - 3 ------------------------------------ -5.00 eV

n - 2 ------------------------------------ -10.0 eV


n - 1 ------------------------------------ -20.0 eV

A. How many different wavelength photons could be released by this atom?
B. Calculate the wavelength of the only such photon that would be in the visible light spectrum.

Explanation / Answer

A) 6 different photons can be released from 6 different drops in energy levels:

4 -> 3, E = 5eV - 2eV = 3eV
4 -> 2, E = 10eV - 2eV = 8eV
4 -> 1, E = 20eV - 2eV = 18eV
3 -> 2, E = 10eV - 5eV = 5eV
3 -> 1, E = 20eV - 5eV = 15eV
2 -> 1, E = 20eV - 10eV = 10eV

B) E = hf, where h = 4.136*10^-15 eVs

The only photon that is in the visible spectrum is the photon produced when the electron falls from n=4 to n-3,

3eV/h = f = (3eV)/(4.136*10^-15 eVs) = 7.25*10^14 Hz = 725 THz

This is the very upper edge of the violet spectrum, almost UV, which is at about 800THz.

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