1. 禪： 見山不是山 見水不是水 見山又是山 見水又是水

2. The Beginnings of Quantum Mechanics
Quantum-mechanical model: A model that explains the behavior of absolutely small particles such as electrons and photons.
Until the beginning of the twentieth century it was believed that all physical phenomena were deterministic.
Work done at that time by many famous physicists discovered that for sub-atomic particles, the present condition does not determine the future condition.
Albert Einstein, Neils Bohr, Louis de Broglie, Max Planck, Werner Heisenberg, P. A. M. Dirac, and Erwin Schrödinger

3. Quantum mechanics forms the foundation of chemistry
Continuous
Quantum mechanics forms the foundation of chemistry
Explaining the periodic table
The behavior of the elements in chemical bonding
Provides the practical basis for lasers, computers, and countless other applications

4. The Nature of Light (1) Its Wave Nature 1) Definition
Light: a form of electromagnetic radiation
composed of perpendicular oscillating waves, one for the electric field and one for the magnetic field.
require no medium for their propagation

5. 2) Characterizing Waves
*****
Amplitude: the height of the wave, a measure of light intensity—the larger the amplitude, the brighter the light.
Wavelength (l, lambda): a measure of the distance covered by the wave.
Frequency (n, nu): the number of waves that pass a point in a given period of time. Unit = cycles/s or s–1 (Hz, hertz).
The relationship between wavelength and frequency:
c = 3.00 × 108 m/s (speed of light)

7. 3) Electromagnetic Spectrum
*****

8. Continuous
The main regions of the electromagnetic spectrum ranging in wavelength from m (gamma rays) to 105 m (radio waves).
The shorter wavelength (high-frequency) light has higher energy. (high-energy electromagnetic radiation can potentially damage biological molecules-Ionizing radiation)
The electromagnetic spectrum is largely invisible to the eye.
White light is a mixture of all the colors of visible light:
Red Orange Yellow Green Blue Indigo Violet

9. 4) Interference and Diffraction (characteristics of wave)

10. The Nature of Light (2) Its Particle Nature The Photoelectric Effect
The metals emit electrons when a light shines on their surface called photoelectric effect.

11. Continuous
*****
A minimum frequency, called threshold frequency, was needed before electrons would be emitted regardless of the intensity.
Einstein proposed that the light energy was delivered to the atoms in packets, called quanta or photons.
Threshold: 門檻、臨界
The energy of a photon of light is directly proportional to its frequency:
Planck’s Constant h = × 10−34 J ∙ s.
Energy can be absorbed or emitted only as whole multiples of a quantum, that is, 1 hv, 2 hv, 3 hv etc.

12. Kinetic Energy = Ephoton – Ebinding
Continuous
*****
One photon at the threshold frequency gives the electron just enough energy for it to escape the atom - Binding energy, f.
When irradiated with a shorter wavelength photon, the electron absorbs more energy than is necessary to escape. This excess energy becomes kinetic energy of the ejected electron.
Kinetic Energy = Ephoton – Ebinding
KE = hn − f

14. No electrons would be ejected.
Suppose a Metal Will Eject Electrons from Its Surface When Struck by Yellow Light. What Will Happen If the Surface Is Struck with Ultraviolet Light?
No electrons would be ejected.
Electrons would be ejected, and they would have the same kinetic energy as those ejected by yellow light.
Electrons would be ejected, and they would have greater kinetic energy than those ejected by yellow light.
Electrons would be ejected, and they would have lower kinetic energy than those ejected by yellow light.
Ans: 3
Ans: 3

15. Atomic Spectroscopy
When atoms absorb energy, that energy is often released as energy as light.
When that emitted light is passed through a prism, a pattern of particular wavelengths of light is seen that is unique to that type of atom

16. The Bohr Model of the Atom
Bohr’s major idea: The energy of the atom was quantized, the amount of energy in the atom was related to the electron’s position in the atom (particle like behavior).
Quantized means that the atom could only have very specific amounts of energy.
The electrons travel in orbits that are at a fixed distance from the nucleus-stationary states, the energy of the electron in a particular orbit was proportional to the distance from the nucleus.
Electrons emit radiation when they “jump” from an orbit with higher energy down to an orbit with lower energy.
The emitted radiation was a photon of light and the distance between the orbits determined the energy of the photon of light produced.

17. Bohr’s Hydrogen Atom: A Planetary Model
Bohr proposed the electron energy of hydrogen atom is quantized
Each specified electron energy value, called an energy level (En), of the atom:
n: an integer, RH = 2.18 x 10–18 J (Rydberg constant)
When the electron is located infinitely far from nucleus: En = 0
The “–” sign : represents attraction forces

18. Bohr Model of H Atoms

19. Bohr’s Explanation of H atom Line Spectra
*****
Bohr’s Equation:
E: energy change of an electron from initial energy level to final energy level
Efinal: final energy level
Einitial: initial energy level
RH: 2.18 x 10–18 J
Energy of H(g) from n = 1 to n = ∞, E = 2.18 x 10–18 J/atom, It is the ionization energy of the H(g)
The emitted photon E = h
Bohr’s theory is limited for one-electron species, such as H, He+, and Li2+

21. Hydrogen Energy Transitions and Radiation

22. Wave Behavior of Electrons
*****
de Broglie proposed that particles could have wavelike character just like light
The wavelength of a particle (such as an electron) given by:
λ: wavelength
h: Planck’s constant
m: mass of the particle
v: moving speed of the particle

24. Electron Diffraction
Proof that the electron had wave nature came a few years later with the demonstration that a beam of electrons would produce an interference pattern the same as waves do.
Electrons actually present an interference pattern, demonstrating they behave like waves.

25. Uncertainty Principle
Heisenberg stated that the product of the uncertainties in both the position and speed of a particle was inversely proportional to its mass.
x = position, Dx = uncertainty in position
v = velocity, Dv = uncertainty in velocity
m = mass
This means that the more accurately you know the position of a small particle, such as an electron, the less you know about its speed, and vice versa.

26. Trajectory versus Probability

27. Quantum Mechanics (Wave Mechanics)
Schrödinger (wave) equation:
An acceptable solution to Schrödinger equation that states the location of an electron at a given point in space and each wave function  is associated with a particular energy E.
A plot of distance versus 2 represents an orbital, a probability distribution map of a region where the electron is likely to be found.
Quantum mechanics is applied to explain the wave-particle duality behavior for many-electron atoms
Principle quantum number (n): 主量子數
Angular Momentum Quantum Number (ι): 角動量量子數
Magnetic Quantum Number (mι): 磁量子數
Electron spin Quantum Number (ms): 電子自旋量子數

28. Quantum Numbers and Atomic Orbitals Quantum Numbers
Solving a Schrödinger equation, in other words, a wave function contain three parameters that have specific integral values called quantum numbers (n, l, and ml).
A wave function with a given set of three quantum numbers is called an atomic orbital.
These orbitals allow us to visualize a three-dimension region which describe the probability of finding an electron.
A fourth quantum number, called electron spin quantum number (ms), describe the orientation of the spin of the electron.
Each electron in a atom is described by its unique set of four quantum number.
Principle quantum number (n): 主量子數
Angular Momentum Quantum Number (ι): 角動量量子數
Magnetic Quantum Number (mι): 磁量子數
Electron spin Quantum Number (ms): 電子自旋量子數

29. The Principal Quantum Number (n)
*****
The Principal Quantum Number (n)
n = 1, 2, 3, .....(positive integer)
Determines the size and the energy level of the atomic orbital
All orbitals with same value of n constitute a principal level (shell)
The Angular Momentum Quantum Number (ι)
ι = = 0, 1, 2,...., n–1
Determines the shape of the orbital
All orbitals with the same value of n and the same value of ι constitute a sublevel (subshell)
Value of ι :
Orbital (subshell) designation: s p d f
(Principle) shell: 主殼層
K shell: n = 1, L shell: n = 2, M shell: n = 3, N shell: n = 4
Subshell: 次殼層

30. The Magnetic Quantum Number (mι )
*****
The Magnetic Quantum Number (mι )
mι = –ι , –ι+1, ..., 0, ..., ι–2, ι–1, ι
Determines the orientation in space of the orbitals of any given type in a sublevel

31. Energy Levels and Sublevels
*****
the number of sublevels within a principal level = n.
the number of orbitals within a sublevel = 2l + 1.
the number of orbitals in a principal level = n2.

34. Quantum Mechanical Explanation of Atomic Spectra
Each wavelength in the spectrum of an atom corresponds to an electron transition between orbitals.
When an electron is excited, it transitions from an orbital in a lower energy level to an orbital in a higher energy level.
When an electron relaxes, it transitions from an orbital in a higher energy level to an orbital in a lower energy level.
Electrons in high energy states are unstable, a photon of light is released whose energy equals the energy difference between the orbitals.
Each line in the emission spectrum corresponds to the difference in energy between two energy states.

35. Quantum Leaps

36. Probability Density Function (1s for example)
The probability density function represents the total probability of finding anlectron at a particular point in space.

37. Radial Distribution Function (1s for example)

38. 2s and 3s The S Orbitals (l = 0, mι= 0)
Node: the region of zero electron probability

39. The Three p Orbitals (l = 1, mι= –1, 0, +1)
Three values of mι gives three p orbitals in the p subshell
mι= –1
mι= 0
First principal shell to have p subshell correspond to n = 2.

40. The Five d Orbitals (l = 2, mι= –2, –1, 0, +1, +2)
Five values of mι gives five d orbitals in the d subshell
First principal shell to have d subshell correspond to n = 3.

41. The Seven f Orbitals (l = 3, mι= –3, –2, –1, 0, +1, +2, +3)

42. The Shapes of Atomic Orbitals
The l quantum number primarily determines the shape of the orbital.
l can have integer values from 0 to (n – 1).
Each value of l is called by a particular letter that designates the shape of the orbital.
s orbitals are spherical.
p orbitals are like two balloons tied at the knots.
d orbitals are mainly like four balloons tied at the knots.
f orbitals are mainly like eight balloons tied at the knots.

44. End of Chapter 7