1. Bohr’s Atomic Model
Suggested________________________________
and that the electrons
________________________________________
electrons can only be in discrete orbitals
Absorb or emit energy as they move between orbitals

3. ΔE = E3-E1 = hv Bohr’s Atomic Model
As electrons move between orbits, their PE/KE is
transformed into radiation (photon)
The difference in energy between orbits is
equal to the energy of a photon
ΔE = E3-E1 = hv
Energy gained/lost by e-
Energy of a photon absorbed/ released E3 E1

4. 𝑚 𝑒 𝑣 2 𝑟 =k 𝑍𝑒 𝑒 𝑟 2 v e r Z: number of protons (Ze)
Bohr’s Atomic Model
Where can the electrons be???
Bohr modeled the electrons as orbiting the nucleus, in contrast to the classical physics description of charged particles.
Condition of Stability…….
𝑚 𝑒 𝑣 2 𝑟 =k 𝑍𝑒 𝑒 𝑟 2
The electron must move fast enough so that
The________________
equals the electromagnetic force between the electron and nucleus v e
centripetal force
Classical physics noted that when charge particle more relative to one another they emit energy (light).
Electrons would lose kinetic energy and crash into the nuceuls. r
Z: number of protons
e: fundamental charge (1.60x10-19) coulombs
r: radius
v: speed
(Ze)

5. Bohr’s Atomic Model
Bohr modeled that electrons were in orbits……
But how do we explain discrete emission spectrum from atoms?
Bohr suggests__________________________________________________________
__________
angular momentum of electron must equal some integer (n) multiple of Plank’s
constant
As a result….. the radii of the orbits are quantized… (can only have specific values)

6. n = the discrete orbital
angular momentum of electron must equal some integer (n) multiple of Plank’s constant
n = 3
n = the discrete orbital
n = 2
n = 1

7. 𝑟=𝐶 𝑛 2 𝑍𝑒 𝑒 = 𝐶 𝑒 2 𝑛 2 𝑍 n = 3 n = the discrete orbital n = 2 n = 1
Can solve for the the radii of the orbitals
𝑟=𝐶 𝑛 2 𝑍𝑒 𝑒 = 𝐶 𝑒 𝑛 2 𝑍
n = 3
n = the discrete orbital
n = 2
n = 1

8. 𝑟=𝐶 𝑛 2 𝑍𝑒 𝑒 = 𝐶 𝑒 2 𝑛 2 𝑍 ∞ Quantized Radii Hydrogen: Z = ______
For n = 1, r = x m
For n = 2, r = 2.12 x m
For n = 3, r = 4.76 x m
For n = 4, r = 8.46 x m .
For n = ∞, r = ______________________
For hydrogen…
𝑟=𝐶 𝑛 2 𝑍𝑒 𝑒 = 𝐶 𝑒 𝑛 2 𝑍 1
0.52910-10 m
1.5910-10 m
2.6410-10 m
3.7010-10 m
As n increase the radii get further apart ∞
As the integer (n) approaches infinity, the radii approaches infinity.

9. Bohr’s Atomic Radii for Hydrogen (Z=1) and Helium (Z=2)
𝑟=𝐶 𝑛 2 𝑍𝑒 𝑒 = 𝐶 𝑒 𝑛 2 𝑍
As Z increase r decreases!
n = 1, r = Ǻ
n = 2, r = 2.13 Ǻ
n = 3, r = 4.78 Ǻ
n = 4, r = 8.50 Ǻ
n = 5, r = 13.3 Ǻ
n = 6, r = 19.1 Ǻ
n = 7, r = 26.0 Ǻ
n = 1, r = Ǻ
n = 2, r = 1.06 Ǻ
n = 3, r = 2.39 Ǻ
n = 4, r = 4.25 Ǻ
n = 5, r = 6.64 Ǻ
n = 6, r = 9.50 Ǻ
n = 7, r = 13.0 Ǻ

10. How do we find the energy of an electron?
With the position of the e- known we can determine the energy of it
We don’t know how fast the e- is moving (v)…. But we can manipulate the variables and combine terms to get energy in terms of r.
get

11. Quantized energy states
The energy depends on where the electron is.
If the radii are quantized (discrete) , the energies will be as well
get
(bunch o’ constants)

12. Difference in energy between two states (orbits), n1 and n2
Solve for E n1 n2 6 2 5 4 3
n2 = orbit where electron ends up
n1 = orbit where electron starts

13. Ephoton= h𝜈 c= 𝜆𝜈 Predictions from Bohr’s model Transition n1 → n2
Energy
Photon Energy
Frequency
Wavelength
6 → 2
5 → 2
4 → 2
3 → 2
-4.84x10-19 J
4.84x10-19 J
7.30x1014 1/s
4.11x10-7 m
-4.58x10-19 J
4.58x10-19 J
6.91x1014 1/s
4.34x10-7 m
-4.09x10-19 J
4.09x10-19 J
6.17x1014 1/s
4.86x10-7 m
-3.03x10-19 J
3.03x10-19 J
4.15x1014 1/s
6.56x10-7 m
The predicted and observed match up!
Bohr’s model is correct……..
For Hydrogen

14. What about the data for Helium….
Bohr’s Atomic Radii for Hydrogen (Z=1) and Helium (Z=2)
n = 1, r = Ǻ
n = 2, r = 2.13 Ǻ
n = 3, r = 4.78 Ǻ
n = 4, r = 8.50 Ǻ
n = 5, r = 13.3 Ǻ
n = 6, r = 19.1 Ǻ
n = 7, r = 26.0 Ǻ
n = 1, r = Ǻ
n = 2, r = 1.06 Ǻ
n = 3, r = 2.39 Ǻ
n = 4, r = 4.25 Ǻ
n = 5, r = 6.64 Ǻ
n = 6, r = 9.50 Ǻ
n = 7, r = 13.0 Ǻ .
What about the data for Helium….

15.  Don’t’ worry Neils…. it’s Formative
Bohr’s Atomic Radii (n = 1 to 12) for Helium (Z=2)
n = 1, r = Ǻ
n = 2, r = 1.06 Ǻ
n = 3, r = 2.39 Ǻ
n = 4, r = 4.25 Ǻ
n = 5, r = 6.64 Ǻ
n = 6, r = 9.50 Ǻ
n = 7, r = 13.0 Ǻ
n = 8, r = 17.0 Ǻ
n = 9, r = 21.5 Ǻ
n = 10, r = 26.6 Ǻ
n = 11, r = 32.1 Ǻ
n = 12, r = 38.3 Ǻ
n = 13, r = 44.9 Ǻ
Actual spectrum
Predicted transitions in the visible
and
NOT observed  . .
The predicted and observed DON’T match up 
Bohr’s model is __________________
NOT correct!!!
Don’t’ worry Neils…. it’s Formative