Homework # 10 Worksheet: Quantum Numbers Assign quantum numbers to the valence electron of a lithium. 3. Assign quantum numbers for the tenth electron to fill a neon atom.

Aim 10: How can you describe the quantum mechanical model?

Quantum #’s are like an Address. What do you need to know to find out where you live? State City Street House Principle Quantum number (n) Angular Quantum number (ℓ) Magnetic Quantum number (mℓ) Spin Quantum number (ms)

1. Quantum Numbers Modern atomic theory states that any electron in an atom can be completely describe by four quantum numbers: n, l, ml ,ms

1st Quantum Number: Principal Quantum Number (n) Refers to the principal energy levels. n 1 2 3 4

2nd Quantum Number: Azimuthal or Angular Momentum Quantum Number (ℓ)

Letter s p d f ℓ can be any integer from 0 to n-1 Sublevel (s,p,d,f) Describe the shape of the orbital Letter s p d f ℓ 1 2 3

letter s p d f ℓ 1 2 3 Example: n = 3 ℓ = n-1 ℓ = 3-1 ℓ = 2

S,P,D,F s: Sharp p: Principal d: Diffuse f: Fundamental The s, p, d, and f stand for "sharp," "principal," "diffuse," and "fundamental," respectively, and are so named because they categorize the spectral lines generated by those types of orbitals: Electron configuration

3rd Quantum Number: Magnetic Quantum Number (mℓ) Designates the specific three dimensional orientation of the orbital ℓ.

s subshell: spherical 1 S 2 S 3 S

p subshell : dumbbell shape 3 orbitals z x y x y z

d subshell

mℓ can be any integer from: - ℓ to + ℓ Example: ℓ= 2 mℓ = -2, -1, 0, +1, +2

S ___ p ___ ____ ____ -1 0 1 d ____ ____ ____ ____ ____ -2 -1 0 1 2 f ____ ____ ____ ____ ____ ____ ____ -3 -2 -1 0 1 2 3

4th Quantum Number: Spin Quantum Number (ms ) the spin of the electron. Electrons in the same orbital must have opposite spins. 1 2 1 2 + - or The value of ms =

+ ½ - ½ 2 S

z ° + ½ - ½ y x

Empty PARAMAGNETIC are attracted to a magnetic field Half-Filled Filled MAGNETIC

The Pauli exclusion principle (Wolfgang Pauli, Nobel Prize 1945) states that: no two electrons in the same atom can have identical values for all four of their quantum numbers. What this means is that no more than two electrons can occupy the same orbital, and that two electrons in the same orbital must have opposite spins.

Summary

Quantum Numbers n, l, ml, ms ORBITAL PEL SPIN SUBLEVEL SHAPE

l = sublevel (s,p,d,f) S = 0 P = 1 d = 2 F = 3

ml = orbital s ___ 0 p ___ ___ ___ - 1 0 1 d ___ ___ ___ ___ ___ - 1 0 1 d ___ ___ ___ ___ ___ -2 - 1 0 1 2 f ___ ___ ___ ___ ___ ___ ___ -3 -2 - 1 0 1 2 3

ms = +1/2, -1/2 Spin!

TEST YOUR UNDERSTANDING

Oxygen s= 0 P = 1 d =2 f= 3 ___ ___ ___ ___ ___ 1s2 2 s2 2p4 s ___ n l n l ml ms 1 1/2

Oxygen s= 0 P = 1 d =2 f= 3 ___ ___ ___ ___ ___ 1s 2 s 2p s ___ n l ml n l ml ms 1 - 1/2

Oxygen s= 0 P = 1 d =2 f= 3 ___ ___ ___ ___ ___ 1s 2 s 2p - 1 0 1 n l ml ms 2 1 1 1/2

3. What are the four quantum numbers that represent an electron in 2 s orbital d =2 f= 3 n = 2 ℓ= 0 mℓ= 0 ms= +½ -½

4. What are the four quantum numbers that represent an electron in 3 p orbital d =2 f= 3 n = 3 ℓ= 1 ms= +½ -½ mℓ= -1

5. What are the four quantum numbers that represent an electron in 5 d orbital ℓ= 2 mℓ= -2 -1 0 +1 +2 ms= +½ -½

6. What are the four quantum numbers that represent an electron in 4 f orbital d =2 f= 3 n = 4 ℓ= 3 mℓ= - 3 -2 -1 0 +1 +2 + 3 ms= +½ -½

7. Where is an electron with the quantum numbers: P = 1 d =2 f= 3 n = 4 mℓ = 0 ℓ = 2 ms = +½ 4 d

8. Where is an electron with the quantum numbers: ℓ= 0 ms= -½ 2 s2

s p sharp principal d f diffuse fundamental

9. Assign quantum numbers for the tenth electron to fill a neon atom. [He] 2s2 2p6 1s2 2s2 2p6 1 2 2 p p p s s

10. Assign quantum numbers for the tenth electron to fill a neon atom. 1s2 2s2 2p6 1 2 2 p p p s s Ml = 1 ms = - 1/2 n = 2 L = 1

For each of the quantum numbers, state which one is invalid and why?

Practice: MCQ Questions http://www.ualr.edu/rebelford/chem1402/q1402/X3/c7/7-3/7-3.htm#JUMP_11

Value of l Sub shell Values of ml Possible orbitals s S 1 p -1 , 0 , 1 Px,Py,Pz 2 d -2, -1, 0, 1, 2 dxy,dxz,dyz,dx2y2, dz2 3 f -3, -2, -1, 0, 1, 2,3