1. Solid Sphere Model or Billiard Ball Model John Dalton
Planetary Model or Nuclear Model Ernest Rutherford
Plum Pudding Model J.J. Thomson
Bohr Model or Orbit Model Neils Bohr
Electron Cloud Model or Quantum Mechanical Model Louis de Broglie & Erwin Schrodinger

2. Ĥ = E
Solutions to the Schrodinger equation yields a set of wavefunctions called orbitals
Each orbital has a characteristic shape and energy
Describe an orbital with 4 quantum numbers

3. Orbitals According to Quant Mech.
Describe by 4 quantum numbers
n: principle quantum number
Gives relative E of orbital (as n increase, E increase)
Relative distance from nucleus
All orbitals with same n make up a shell
l: angular momentum
Gives relative shape or orbital
Values are from 0 to n-1
s has l = 0, p has l = 1, d has l = 2, f has l = 3
All values with same n and different l, are subshells

4. Quant Numbers ctd. ml: magnetic quantum number ms: spin quantum number
orientation in 3-D
px vs. py for ex
Values are +l to –l
ms: spin quantum number
Spin of electron: ±1/2

8. Energy of Orbitals What influences the energy of an orbital?
Hint: n and l

9. Energy of Orbitals What influences the energy of an orbital?
Hint: n and l
As n increases, so does E
as you get further from nucleus, E increases
Shape: s < p < d < f (more on this later)

10. Probability, 2
If we know something about the E of the orbital, then we can say something about the probability of finding the e- there.
As E increases, 2 decreases
Probability density maps (next slide) give a sense of where we are likely to find an e- in an orbital
Most likely near the nucleus

12. Coulomb’s Law describes the force of attraction between charged particles (in this case the nucleus and the e-):
F = kQ1Q2 d2
e- is more attracted to nucleus when
it is closer to it (low n value or small d)
nucleus has more + charge
charge of the nucleus is called nuclear charge, Z, and depends on #p in nucleus

13. Probability density maps seem to imply that the e- is most likely to be found at the nucleus
This is not necessarily true
A more realistic plot is a radial distribution curve which represents the total probability of finding the e- within a space at a distance, r, from the nucleus
Radial Probability = 2 x volume shell at r
Recall, 2 is best near nucleus, small r value,
but volume shell increases with r (onion analogy)

14. Radial Probability = 2 x volume shell at r
When r = 0 (at nucleus), volume shell = 0 and so radial probability = 0
As increase r, volume of shell increases, so radial probability goes up
Hit a max: as move further from nucleus (increase r), 2 gets less and less and eventually tapers to 0
From this plot, an e- is most likely to be found 52.9 pm from the nucleus in a 1s orbital
radial

15. # pks increases with n (# pks = n value)
# nodes = n-1
e- density is more spread out with increasing n

16. e- is likely to be found a certain distance from the nucleus (but still uncertain as to exact location)
More likely to be found in lower n value and lower l value (if not occupied)
Means that lower n and lower l are lower in energy