1. Wave-Particle Duality 2: The Quantum Mechanical Model

2. Explain the historical development of the Quantum Mechanical Model of the atom.
Describe the quantum arrangement of electrons in an atom.
Include: energy level, sublevel, and orbital.
Additional KEY Terms
quantum number (n)

3. de Broglie (1924) – developed an equation that predicts wave qualities for all matter.
Suggests electron orbits are fixed due to wavelength restrictions for quantized energies

5. Problems - World is 3D
- Bohr’s math failed to explain all spectra
- matter also have wave-particle duality
Heisenberg (1925) - it is impossible to know precisely the velocity and position of a particle at the same time – Heisenberg Uncertainty Principle

6. Schrödinger (1926) – developed a wave equation that describes the energies and behaviour of subatomic particles.
Determines the probability of finding an electron in a 3-D volume of space around the nucleus.

7. Each energy level's boundary is the area of electron location 90% of the time.

8. The (n) number indirectly describes the size and energy of an orbit.
Bohr’s orbits are now called labeled the principle quantum number (n)
The (n) number indirectly describes the size and energy of an orbit.

9. The probable location of every electron is now described by a set of 4 quantum numbers.
principal (n)
location from nucleus
2. orbital angular momentum (l)
shape of orbital
3. magnetic (m)
orientation in 3D space
4. spin angular momentum (s)
spin of the election

10. s p d f Sublevels (l) vary in shape
Principle quantum numbers (n) contain many places of probable electron location – sublevels
Sublevels (l) vary in shape
There are four types that appear in this order:
s p d f
Each sublevel can be made of multiple orbitals (m) in 3D space that hold two electrons (s).

11. NUCLEUS
n = 1 s
n = 2 s p
n = 3 s p d
Notice: number of sublevels (l) equals the principal quantum number (n) for the level

12. s sublevel (sphere) – 1 orbital orientation present.

13. p sublevel (dumbell) – 3 orbital orientations.

14. d sublevel (cloverleaf) – 5 orbital orientations.
f sublevel (indeterminate) – 7 orbital orientations.

15. n = 3 1s 2s 2p 3s 3p 3d
n = 2
n = 1

16. Energy Level (n)
Sublevels (l)
Total Orbitals 1 s 1s 2
s,p
1s+3p = 4 3
s,p,d
1s+3p+5d = 9 4
s,p,d,f
1s+3p+5d+7f = 16 n
n types n2

17. CAN YOU / HAVE YOU?
Explain the historical development of the Quantum Mechanical Model of the atom.
Describe the quantum arrangement of electrons in an atom.
Include: energy level, sublevel, and orbital.
Additional KEY Terms
quantum number (n)