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7.1.4 Atomic Spectra.notebook
October 13, 2014
7.1.4 Atomic Energy Levels
Niels Bohr & Atomic Spectra
Soilds emit very distinctive bands of color if they are incandesent and viewed through a spectroscope ­ an emission spectrum ­ something that Niels Bohr suggested was due to the excitation of electrons to jump from one electron energy level (specific orbit) to another and then fall back down, emitting a photon of specific wavelength. Specfic packets of energy (quanta) is needed for this to happen to electrons.
Planck's Constant
h= 4.14x10­15eVs
or
6.63 x 10­34 Js
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7.1.4 Atomic Spectra.notebook
October 13, 2014
7.1.4 Atomic Energy Levels
Emission spectra Absorption spectrum 2
7.1.4 Atomic Spectra.notebook
October 13, 2014
7.1.4 Atomic Energy Levels
Niels Bohr found that the excited state was a fraction of the energy of the ground state:
The Balmer Series describes mathematically the component wavelengths of the hydrogen spectra:
R = 1.097 x 107 m­1
if
then
&
or
This formula represnts the energy to remove an electron from ground state to infinity ­ ground state energy works out to E1 = ­13.6 eV, the ionization energy for hydrogen.
For Helium (atomic number Z = 2) the inozation energy is given by:
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7.1.4 Atomic Spectra.notebook
October 13, 2014
7.1.4 Atomic Energy Levels
When an excited electron drops from energy level n = j to a lower one n = i a photon of energy is emitted, the energy of the photon is the difference between the two energy levels:
Since
then the wavelength og the photon is:
Example:
The first five energy levels of an atom are given as:
­3eV ­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­ n = 5
­4eV ­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­ n = 4
­7eV ­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­ n = 3
­15eV ­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­ n = 2
a) If the atom begins in the n = 3 level, what photon energies could be emitted as it returns to the ground state?
b) What could happen if this atom, while in an undetermined energy state, were bombarded with a photon of energy 10 eV?
­62eV ­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­ n = 1
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7.1.4 Atomic Spectra.notebook
October 13, 2014
7.1.4 Atomic Energy Levels
Example:
The first five energy levels of an atom are given as:
a) If the atom begins in the n = 3 level, what photon energies could be emitted as it returns to the ground state?
­3eV ­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­ n = 5
­4eV ­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­ n = 4
In n= 3 the atom could return to ground state via 3 ­ 1, or from 3 ­ 2 and then 2 ­ 1.
­7eV ­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­ n = 3
E3­1 = E3 ­ E1 = (­7eV)­(­62eV) = 55eV
­15eV ­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­ n = 2
E3­2 = E3 ­ E2 = (­7eV)­(­15eV) = 8eV
E2­1 = E2 ­ E1 = (­15eV)­(­62eV) = 47eV
8ev+47eV = 55eV
b) What could happen if this atom, while in an undetermined energy state, were bombarded with a photon of energy 10 eV?
­62eV ­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­ n = 1
Since no two energy states in this atom are separated by 10eV, the atom could not absorb a 10eV photon, so nothing would happen.
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7.1.4 Atomic Spectra.notebook
October 13, 2014
7.1.4 Atomic Energy Levels
0eV
Example 2:
a) How much energy must a ground­state electron in a hydrogen atom absorb to be excited to the n = 4 energy level?
b) With the electron in the n = 4 level, what wavelengths are possible for the photon emitted when the electron drops to a lower energy level? In what regions of the EM spectrum do these photons lie?
­0.85eV
photon emitted
­1.5eV
­3.4eV
­13.6eV
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7.1.4 Atomic Spectra.notebook
October 13, 2014
7.1.4 Atomic Energy Levels
Example 2:
a) How much energy must a ground­state electron in a hydrogen atom absorb to be excited to the n = 4 energy level?
The energy absorbed from to go from ground state to 4th level:
E = E4 ­ E1 = (­0.85eV) ­ (­13.6eV) = 12.8 eV
b) With the electron in the n = 4 level, what wavelengths are possible for the photon emitted when the electron drops to a lower energy level? In what regions of the EM spectrum do these photons lie?
The electron can make several different transitions:
E4 ­ 3
E4 ­ 2
E4 ­1
E4 ­ 3 = E4 ­ E3 = (­0.85eV) ­ (­1.5eV) = 0.65eV
E4 ­ 2 = E4 ­ E2 = (­0.85eV) ­ (­3.4eV) = 2.55eV
E4 ­ 1 = E4 ­ E1 = (­0.85eV) ­ (­13.6eV) = 12.8eV
λ 4 − 3 = hc/E 4 ­ 3 = (4.14x10­15 eVs)(3.0x108m/s)/0.65eV = 1910 nm
λ 4 − 2 = hc/E 4 ­ 2 = (4.14x10­15 eVs)(3.0x108m/s)/2.55eV = 487 nm
λ 4 − 1 = hc/E 4 ­ 1 = (4.14x10­15 eVs)(3.0x108m/s)/12.8eV = 97 nm
0eV
­0.85eV
photon emitted
­1.5eV
­3.4eV
­13.6eV
(ultraviolet)
(blue­green)
(infrared)
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7.1.4 Atomic Spectra.notebook
October 13, 2014
7.1.4 Atomic Energy Levels
What is the ionization energy fro a hydrogen atom in the state n=3?
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