Physics 6C
Energy Levels
Bohr Model of the Atom
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Bohr’s Model of Hydrogen
•Positively charged nucleus at center
•Electrons occupy circular orbits around the nucleus
•Angular momentum of electrons is quantized (has to be a multiple of ħ)
•Radius values and energy levels are also quantized
This is the formula for calculating hydrogen energy levels.
The ‘Ground State’ is n=1.
This is the closest orbit and the lowest energy level.
e-
E1  13.6eV
E
En  21
n
rn
+
For larger values of n, the electron is farther
from the nucleus, and the energy is closer to
zero. The electron is ‘free’ when its energy is
zero (or positive).
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Example: Suppose a hydrogen atom is in its ground state. If a photon is absorbed, exciting
the atom to the n=3 state, what is the wavelength of the photon?
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: Suppose a hydrogen atom is in its ground state. If a photon is absorbed, exciting
the atom to the n=3 state, what is the wavelength of the photon?
The diagram shows the photon approaching,
and the electron jumping to the excited state
after the photon’s energy is absorbed.
n=3
n=1
+
e-
e-
photon
Prepared by Vince Zaccone
For Campus Learning
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Example: Suppose a hydrogen atom is in its ground state. If a photon is absorbed, exciting
the atom to the n=3 state, what is the wavelength of the photon?
The diagram shows the photon approaching,
and the electron jumping to the excited state
after the photon’s energy is absorbed.
n=3
The photon energy is the difference between
the energy levels.
n=1
Ephoton  E3  E1
+
 13.6eV
 1.5eV
32
Ephoton  (1.5eV)  (13.6eV)  12.1eV
E3 
e-
e-
photon
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: Suppose a hydrogen atom is in its ground state. If a photon is absorbed, exciting
the atom to the n=3 state, what is the wavelength of the photon?
The diagram shows the photon approaching,
and the electron jumping to the excited state
after the photon’s energy is absorbed.
n=3
The photon energy is the difference between
the energy levels.
n=1
Ephoton  E3  E1
+
 13.6eV
 1.5eV
32
Ephoton  (1.5eV)  (13.6eV)  12.1eV
E3 
e-
e-
photon
Now we can solve for the wavelength:
hc

(4.14  1015 eV  s)(3  108 ms )
12.1eV 

  103nm
Ephoton 
Note that this photon is in the ultraviolet range
Prepared by Vince Zaccone
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Example: Suppose a hydrogen atom is in its ground state. If a photon is absorbed, exciting
the atom to the n=3 state, what is the wavelength of the photon?
Now suppose the atom emits a photon and
drops down to the n=2 state. What is the
wavelength of this emitted photon?
Again, the photon energy is the
difference between the energy levels.
n=3
n=2
n=1
ee-
+
Emitted
photon
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: Suppose a hydrogen atom is in its ground state. If a photon is absorbed, exciting
the atom to the n=3 state, what is the wavelength of the photon?
Now suppose the atom emits a photon and
drops down to the n=2 state. What is the
wavelength of this emitted photon?
Again, the photon energy is the
difference between the energy levels.
n=3
n=2
n=1
ee-
+
Emitted
photon
Ephoton  E2  E3
 13.6eV
E2 
 3.4eV
2
2
Ephoton  (3.4eV)  (1.5eV)  1.9eV
Prepared by Vince Zaccone
For Campus Learning
Assistance Services at UCSB
Example: Suppose a hydrogen atom is in its ground state. If a photon is absorbed, exciting
the atom to the n=3 state, what is the wavelength of the photon?
Now suppose the atom emits a photon and
drops down to the n=2 state. What is the
wavelength of this emitted photon?
Again, the photon energy is the
difference between the energy levels.
n=3
n=2
n=1
ee-
+
Emitted
photon
Ephoton  E2  E3
 13.6eV
E2 
 3.4eV
2
2
Ephoton  (3.4eV)  (1.5eV)  1.9eV
Now we can solve for the wavelength:
Ephoton 
1.9e V 
hc

(4.14  1015 e V  s)(3  108
m)
s

  654nm
This one is visible, so we would see this in an emission spectrum.
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