Review Chapter 8: The Quantum

Mechanical Atom

Chemistry: The Molecular Nature of Matter, 6th edition

By Jesperson, Brady, & Hyslop

2

Chapter 8 Concepts

Connect (& calculate) wavelength, frequency, and the energy of the wave.

Calculate the energy emitted or absorbed by an electron moving to or from an excited state

Understand & communicate the duel wave-partial duality of light and electrons

Understand & communicate the collapsing atom paradox Understand & communicate quantized energy of an electron Electron book-keeping: quantum numbers, e- configurations, & orbital

diagrams The Heisenberg Uncertainty Principle & electron density (probability) The shape of orbitals Calculate Zeff

Periodic trends dependent on Zeff

Memorize

l = cc = speed of light = 2.9979 × 108 m/s

E = h h = Planck’s constant = 6.626 × 10–34 J s

E = NAhNA = 6.02 × 1023 atoms/mole

22

21

111

nnRH

RH = 109,678 cm–1 = Rydberg constant

Zeff = # protons - # core electrons

Electromagnetic Radiation

high energy, short waveslow energy, long waves

Quantum Mechanics

http://abyss.uoregon.edu/~js/glossary/wave_particle.html

Neat Videos: • https://www.youtube.com/watch?v=

Xmq_FJd1oUQ (wave-particle, short)• https://www.youtube.com/watch?v=

a8FTr2qMutA (heisenburg uncertainty principle, short)

• https://www.youtube.com/watch?v=7vc-Uvp3vwg (heisenburg uncertainty principle, short)

• https://www.youtube.com/watch?v=QVPIGtGcYE0 (great NOVA episode ~ 1 hr)

• Light behaves as a particle & a wave• Photon is a particle of light

• Energy is Quantized: • Photoelectric effect• excited electron emit only specific frequencies of light (Energy)

• Electrons also behave as a particle & a wave• Double slit experiment: electrons behave as a wave! And a particle!

• Collapsing wave paradox• If E quantized an electron cannot have E = 0

Quantum Numbersn = principal quantum number = 1, 2, 3, 4, …, n Determine n by the row the element is in

ℓ = secondary quantum number = 0, 1, 2, …, n-1 Determine by the section of the periodic table: group 1A & 2A = s = 0, group 3A - 8A = p = 1, transition metals = d = 2, lanthanide & actinides = f = 3.

mℓ = magnetic quantum number = + ℓ, ..., 0, ..., - ℓDetermined by column element is in. Left to right positive to

negative, but remember each orbital has two electrons: Ex: p orbitals:

= +1 0 -1 +1 0 -1

+1 0 -1ms = magnetic spin quantum number = + ½ , - ½ First electron placed = + ½ and the second = - ½

__ __ __

e- Configurations & Orbital Diagrams

4s

3s

2s

1s

Energy

4p

3p

2p

3d

4d5s

5p6s

Aufbau Principle: Fill electrons in the orbital diagram in order of increasing energy:

s, (n-2)f, (n-1)d, pPauli Exclusion Principle: 2 electrons per orbital with opposite spinsHund’s Rule: Fill all orbitals of the same energy with one electron before pairing electrons.

__ __ __

__

Electron Configurations will follow the order: 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14 5d10 6p6 ….

Abbreviate: [Nobel gas] in n-1 row

Orbital Shapes

Orbitals & corresponding m

px pz py

dx2-y2 dxz dz2 dyz dxy

s

s: spherical nodes = n-1 0 planar nodesp: spherical nodes = n-1 1 planar noded: spherical nodes = n-1 2 planar nodesf: spherical nodes = n-1 3 planar nodes

Periodic TrendsElectron Affinity

INCREASING

Ionization EnergyINCREASING

Atom SizeINCREASING

Atom Size: Zeff the same down a column, but distance from valence e- to nucleus increases, therefore size increases. Zeff increases across a row therefore size decreases.

Ionization Energy (IE): The energy required to remove an electron from the valence shell increases with Zeff and decreases with increased distance between the nucleus and electron.

Electron Affinity (EA): This is the opposite of ionization energy, it is how easy it is to add an electron to an atom, and follows the same trend as IE energy.

Problem Set 8 A

1. Which electromagnetic radiation has a higher energy? Radio waves or microwaves? UV light or X rays?

2. How does thermal imaging work? (Use what you have learned about the electromagnetic spectrum to briefly explain).

3. Blue, red, and green lasers have wavelengths of 445 nm, 635 nm, and 532 nm respectively what are their frequencies, and what is the energy in Joules of a photon from each laser?

4. In Neon there is a line with the frequency of 4.546 x1014 Hz. What is its wavelength and color of the line? And what is the energy of each of its photons?

5. What is the wavelength of light (in nm) that is emitted when an excited electron in the hydrogen atom falls from n = 5 to n = 3? Would you expect to be able to see the light emitted?

6. How many grams of water could have its temperature raised by 7.000°C by a mole of photons that have a wavelength of 450.0 nm?

(sH2O @ 0C = 4.179 J/gC)

Problem Set 8 B

7. Would you expect the waves above to increase or decrease in amplitude when added together?

8. With the strong attractive force between the positively charged nucleus and an electron, why doesn’t the nucleus capture electrons?

9. Determine quantum numbers for Boron. It’s electron configuration is 1(s)2 2(s)2 2(p)1

10. What is the electron configuration for Nitrogen? N-3?

11. Is Selenium (Se) paramagnetic or diamagnetic?

12. Draw an orbital diagram for Indium (In).

Problem Set 8 C

13. What is the abbreviated electron configuration and abbreviated orbital diagram for the following elements:

a) Feb) Atc) Rad) Sb

14. What is the valence electron configuration for O and Se?

15. Which atom has the smallest radius? Ca, Na, Mg, Ar, K?

16. Which atom has the smallest ionization energy? C, Cs, K, Mg, Ba?

17. Which atom has the greatest electron affinity? O, I, Ne, Ar, Cl, K, Ga?

Problem Set 8 Solutions1. Microwaves. X-rays.

2. Thermal imaging detects infrared radiation, which is heat. Higher temperature bodies emit more infrared radiation.

3. Blue: 6.74 x1014 s-1; 4.74 x10-19 J Red: 4.72 x1014 s-1; 3.13 x10-19 J Green: 5.64 x1014 s-1; 3.74 x10-19 J

4. Wavelength = 660 Color = Red Energy = 1.467 x 1016 J

5. Wavelength = 1282 nm (1.282 x10-6 m) Not in visible range

6. Mass of water = 9093 g

7. Decrease amplitude

8. Lowest quantum number n = 1, and Energy of an electron is inversely proportional to n, therefore it can never have an energy of 0 because n cannot equal 0.

9. n = 2 l = 1 ml = 1 ms = + ½

10. 1(s)2 2(s)2 2(p)3. 1(s)2 2(s)2 2(p)6

11. Paramagnetic (2 unpaired electrons)

Problem Set 8 Solutions

12. .

13. Answers:a) [Ar] 4s2 3d6 [Ar] 3d __ __ __ __ __ 4s __b) [Xe] 6s2 4f14 5d10 6p5

c) [Xe] 4f __ __ __ __ __ __ __ 5d __ __ __ __ __ 6s __ 6p __ __ __

d) [Rn] 7s2 [Rn] 7s __e) [Kr] 5s2 4d10 5p3 [Kr] 4d __ __ __ __ __ 5s __ 5p __ __ __

14. O: 2s2 2p4 Se: 4s2 4p4

15. Ar 16. Cs 17. Cl

4s

3s

2s

1s

Energy

4p

3p

2p

3d

4d5s

5p6s