Chapter 7 notes
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This document discusses key concepts in quantum mechanics including: - Planck's quantum theory which established that atoms can only emit or absorb energy in discrete quanta. - Einstein's explanation of the photoelectric effect using the particle nature of light (photons). - Bohr's model of the hydrogen atom which explained its spectral lines by postulating discrete electron energy levels. - Quantum numbers which describe the state of an electron including its orbital, orientation, and spin. - Electron configuration which shows how electrons fill atomic orbitals according to the aufbau principle.
![[Ne]](https://image.slidesharecdn.com/chapter7notes-150901141243-lva1-app6892/85/Chapter-7-notes-42-320.jpg)
![The Aufbau principle (building-up)
• e- are added progressively to the atomic orbitals to build up
the element
• e- configuration of element are normally represented by a
noble gas core
[Ne]
[Ar]
=1s2
2s2
2p6
=1s2
2s2
2p6
3s2
3p6
e- configuration of Na
→1s2
2s2
2p6
3s1
or
→ [Ne] 3s1
• The aufbau principle works for nearly every element tested.
• There are exceptions to this principle, eg chromium and copper
Cr (Z=24), the e- configuration is [Ar] 4s1
3d5
instead of [Ar] 4s2
3d4
Cu (Z=29), the e- configuration is [Ar] 4s1
3d10
instead of [Ar]4s2
3d9
Because of greater stability associated with
half-filled (3d5
)and completely filled (3d10
)subshells](https://image.slidesharecdn.com/chapter7notes-150901141243-lva1-app6892/85/Chapter-7-notes-47-320.jpg)
![What is the electron configuration of Mg?
Mg 12 electrons
1s < 2s < 2p < 3s < 3p < 4s
1s2
2s2
2p6
3s2
2 + 2 + 6 + 2 = 12 electrons
Abbreviated as [Ne]3s2
[Ne] =1s2
2s2
2p6
What are the possible quantum numbers for the last
(outermost) electron in Cl?
Cl 17 electrons 1s < 2s < 2p < 3s < 3p < 4s
1s2
2s2
2p6
3s2
3p5
2 + 2 + 6 + 2 + 5 = 17 electrons
Last electron added to 3p orbital
n = 3 l = 1 ml = -1, 0, or +1 ms = ½ or -½](https://image.slidesharecdn.com/chapter7notes-150901141243-lva1-app6892/85/Chapter-7-notes-48-320.jpg)
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Chapter 7 notes
- 1. 1
- 2. 7.1 FROM CLASSICAL PHYSICS TO QUANTUM THEORY 7.2 THE PHOTOELECTRIC EFFECT 7.3 BOHR’S THEORY OF THE HYDROGEN ATOM 7.4 THE DUAL NATURE OF THE ELECTRON 7.5 QUANTUM NUMBERS 7.6 ELECTRON CONFIGURATION 7.9 THE BUILDING-UP PRINCIPLE
- 3. Properties of Waves Wavelength (λ) is the distance between identical points on successive waves. Unit= m/cm/nm. Amplitude is the vertical distance from the midline of a wave to the peak or trough. Frequency (ν) is the number of waves that pass through a particular point in 1s. Unit= Hz. (1Hz = 1 cycle/s). Speed of the wave (u) = λν Wave is the vibrating disturbance by which energy is transmitted.
- 4. Light consists of electromagnetic waves (electric +magnetic) Electromagnetic radiation is the emission and transmission of energy in the form of electromagnetic waves. Speed of light (c) = λν = 3.00 x 108 m/s Maxwell’s Electromagnetic Radiation Theory
- 5. Types of electromagnetic radiation
- 6. λ ν = c λ = c/ν λ = 3.00 x 108 m/s / 6.0 x 104 Hz λ = 5.0 x 103 m A photon has a frequency of 6.0 x 104 Hz. Convert this frequency into wavelength (nm). λ = 5.0 x 1012 nm λ = 3.00 x 108 m/s / 6.0 x 104 /s
- 7. • When solids are heated, they emit electromagnetic radiation over a wide range of wavelengths. Planck’s Quantum Theory Quantum = the smallest quantity of energy that can be emitted/absorbed in the form of electromagnetic radiation. •Atoms emit/absorb energy only in discrete units (quantum) Quantum energy, E = hν h = Planck’s constant = 6.63 x 10-34 Js v = frequency
- 8. 7.2 THE PHOTOELECTRIC EFFECT
- 9. Light has both wave and particle-like properties Photon = particle of light Photoelectric Effect = electrons are ejected from the surface of certain metals exposed to light of at least a minimum frequency(threshold frequency). Einstein’s light theory Energy α frequency Photon energy, E = hν
- 10. E = hν E = 6.63 x 10-34 (J•s) x 3.00 x 10 8 (m/s) / 0.154 x 10-9 (m) E = 1.29 x 10 -15 J E = h x c / λ When sodium is bombarded with high- energy electrons, X rays are emitted. Calculate the energy (in joules) associated with the photons if the wavelength of the X rays is 0.154 nm.
- 11. 7.3 BOHR’S THEORY OF THE HYDROGEN ATOM
- 12. Emission spectra •Continuous/line spectra of radiation emitted by substances •Every element has a unique emission spectrum. continuous spectra = light emission at all wavelengths, eg sun, heated solid line spectra = light emission only at specific wavelengths, eg H atom
- 13. Line Emission Spectrum of Hydrogen Atoms 411nm 434nm 486nm 656nm
- 14. 14
- 15. Bohr’s Theory of Atom En = -RH ( ) 1 n2 n = principal quantum number = 1,2,3,… RH = Rydberg constant = 2.18 x 10-18 J (energy hv) •explained the line spectrum of H •postulated a “solar system” model (e- travel in circular orbits around the nucleus) Ground level = lowest energy level(n=1) Excited level = higher energy level than ground level (n=2,3,…) 1. e- have specific (quantized) energy level 2. light is emitted as e- moves from higher energy orbit to a lower-energy orbit
- 16. E = hν E = hν Ephoton = ∆E = Ef - Ei Ef = -RH ( ) 1 n2 f Ei = -RH ( ) 1 n2 i i f ∆E = RH( ) 1 n2 1 n2 i f ∆E = hν = RH ( ) 1 n2 1 n2 ni > nf ∆E -ve Energy lost (photon emitted)
- 17. Ephoton = 2.18 x 10-18 J x (1/25 - 1/9) Ephoton = ∆E = -1.55 x 10-19 J λ = 6.63 x 10-34 (J•s) x 3.00 x 108 (m/s)/1.55 x 10-19 J λ = 1280 nm Calculate the wavelength (in nm) of a photon emitted by a hydrogen atom when its electron drops from the n = 5 state to the n = 3 state. Ephoton = h x c / λ λ = h x c / Ephoton i f ∆E = RH( ) 1 n2 1 n2 Ephoton =
- 18. 7.4 THE DUAL NATURE OF THE ELECTRON
- 19. De Broglie postulated that e- is both particle and wave. u = velocity of e- m = mass of e- λ = h mu De Broglie Relation m in kg h in J•s u in (m/s)
- 20. λ = h/mu λ = 6.63 x 10-34 / (2.5 x 10-3 x 15.6) λ= 1.7 x 10-32 m λ= 1.7 x 10-23 nm What is the de Broglie wavelength (in nm) associated with a 2.5 g Ping-Pong ball traveling at 15.6 m/s?
- 22. Quantum numbers Quantum numbers are a set of values that describes the state of an electron including its distance from the nucleus, the orientation and type of orbital where it is likely to be found, and its spin. 1)Principal quantum number (n) 2)Angular momentum quantum number (l) 3)Magnetic quantum number (ml) 4)Spin quantum number (ms)
- 23. Principal quantum number (n) n=1 n=2 n=3 • Energy of an orbital • distance of e- from the nucleus • n = 1, 2, 3, 4, …. • n ↑ - orbital energy ↑ - distance of e- (in orbital) from nucleus ↑ - orbital size ↑ - orbital stability ↓
- 24. Angular momentum quantum number (l) Shape of an orbital Possible values = 0 to (n-1) possible values = 0 1 2 3 4 5............ n-1 etter designation = s p d f g h............. shells → subshells → orbitals
- 25. l = 0 (s orbitals)
- 26. 26 l = 1 (p orbitals)
- 27. l = 2 (d orbitals)
- 28. Magnetic quantum number (ml) • Orientation of an orbital • Possible values = -l,……,0,…….,+l • Possible values = (2l+1) • Number of orbitals within a subshell with a particular l
- 29. ml = -1, 0, or 1 3 orientations is space n= 2 l=1
- 30. ml = -2, -1, 0, 1, or 2 5 orientations is space n= 3 l= 2
- 31. Electron spin quantum number (ms) • Spinning motion of e- • Possible values = +1/2 or -1/2
- 32. 32
- 33. Atomic orbital
- 34. Energy of Orbitals in a single e- atom Ground state (most stable condition) Excited state n=2 n=1 n=3 → Energy only depends on principal quantum number n Eg. orbitals energy levels in H atom
- 35. Energy of orbitals in a multi-electron atom Eg. orbitals energy levels in many-electron atom n=1 l = 0 n=2 l = 0 n=2 l = 1 n=3 l = 0 n=3 l = 1 n=4 l = 0 •e- will fill orbitals by the sum of n and l. •Orbitals with equal values of (n+l) will fill with the lower n values first. → depend on n & l n=3 l = 2 n=4 l = 1 n=5 l = 0 n=4 l =2 (atom containing two or more e-) (n+l)
- 36. Order of orbitals (filling) in multi-electron atom 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s
- 38. Electron configuration of an atom = how the e- are distributed among various atomic orbitals in an atom Orbital diagram Quantum numbers: (n, l, ml, ms) principal quantum number n angular momentum quantum number l number of e- in the orbital or subshell Each electron's quantum numbers are unique and cannot be shared by another electron in that atom.
- 39. Pauli exclusion principle - no two electrons in an atom can have identical values of all 4 quantum numbers a single orbital can hold a "pair " of e- with opposite "spins" a single e- in an orbital is called "unpaired" atomic number (Z) = # protons = # electrons (in neutral atom) s orbitals have 1 possible value of ml to hold 2 electrons p orbitals have 3 possible value of ml to hold 6 electrons d orbitals have 5 possible value of ml to hold 10 electrons f orbitals have 7 possible value of ml to hold 14 electrons → ∴ maximum of 2 electrons per orbital
- 40. • atoms with 1 or more unpaired electrons are paramagnetic, (attracted by a magnetic) • atoms with all spins paired are diamagnetic (repelled by magnet) Paramagnetism and Diamagnetism → paramagnetic → diamagnetic
- 41. Hund's Rule - the most stable arrangement of electrons in subshells is the one with the greatest number of parallel spins. e- configuration of C (Z=6)
- 42. [Ne]
- 43. How many electrons can a 3rd shell (n=3) have ? Or use formula
- 44. 44 How many 2p orbitals are there in an atom? 2p n=2 l = 1 If l = 1, then ml = -1, 0, or +1 3 orbitals How many electrons can be placed in the 3d subshell? 3d n=3 l = 2 If l = 2, then ml = -2, -1, 0, +1, or +2 5 orbitals which can hold a total of 10 e-
- 45. Determine the electron configuration of silicon Silicon has 14 protons and 14 electrons The electron configuration of silicon is 1s2 2s2 2p6 3s2 3p2
- 46. 7.9 THE BUILDING-UP PRINCIPLE
- 47. The Aufbau principle (building-up) • e- are added progressively to the atomic orbitals to build up the element • e- configuration of element are normally represented by a noble gas core [Ne] [Ar] =1s2 2s2 2p6 =1s2 2s2 2p6 3s2 3p6 e- configuration of Na →1s2 2s2 2p6 3s1 or → [Ne] 3s1 • The aufbau principle works for nearly every element tested. • There are exceptions to this principle, eg chromium and copper Cr (Z=24), the e- configuration is [Ar] 4s1 3d5 instead of [Ar] 4s2 3d4 Cu (Z=29), the e- configuration is [Ar] 4s1 3d10 instead of [Ar]4s2 3d9 Because of greater stability associated with half-filled (3d5 )and completely filled (3d10 )subshells
- 48. What is the electron configuration of Mg? Mg 12 electrons 1s < 2s < 2p < 3s < 3p < 4s 1s2 2s2 2p6 3s2 2 + 2 + 6 + 2 = 12 electrons Abbreviated as [Ne]3s2 [Ne] =1s2 2s2 2p6 What are the possible quantum numbers for the last (outermost) electron in Cl? Cl 17 electrons 1s < 2s < 2p < 3s < 3p < 4s 1s2 2s2 2p6 3s2 3p5 2 + 2 + 6 + 2 + 5 = 17 electrons Last electron added to 3p orbital n = 3 l = 1 ml = -1, 0, or +1 ms = ½ or -½
- 50. Outermost subshell being filled with e- •alkali metals and alkaline earth metals fill the s orbitals last •main group elements fill the p orbitals last •transition metals fill the d orbitals last •lanthanides (4f) and actinides (5f) fill the f orbitals last
- 51. 51