1. PRINCIPLES OF CHEMISTRY I CHEM 1211CHAPTER 7 DR. AUGUSTINE OFORI AGYEMAN Assistant professor of chemistry Department of natural sciences Clayton state university

2. CHAPTER 7 ELECTRONIC STRUCTURE OF ATOMS

3. ELECTROMAGNETIC RADIATION - Also known as radiant heat or radiant energy - One of the ways by which energy travels through space - Consists of electric and magnetic fields which are perpendicular to each other and to the direction of propagation Examples heat energy in microwaves light from the sun X-ray radio waves

4. ELECTROMAGNETIC RADIATION - Light properties is a key concept for understanding electronic structure - Studies of atomic structure has come from observations of the interaction of visible light and matter - To study the properties of electrons in atoms, it is helpful to understand waves and electromagnetic radiation

5. ELECTROMAGNETIC RADIATION Three Characteristics of Waves Wavelength (λ) - Distance for a wave to go through a complete cycle (distance between two consecutive peaks or troughs in a wave) Frequency (ν) - The number of waves (cycles) per second that pass a given point in space Speed (c) - All waves travel at the speed of light in vacuum (3.00 x 108 m/s)

6. ELECTROMAGNETIC RADIATION λ1 node amplitude ν1 = 4 cycles/second λ2 peak ν2 = 8 cycles/second λ3 ν3 = 16 cycles/second trough one second

7. ELECTROMAGNETIC RADIATION - Inverse relationship between wavelength and frequency λα 1/ν c = λ ν = 3.00 x 108 m/s λ = wavelength (m) ν = frequency (cycles/second = 1/s = s-1 = hertz = Hz) c = speed of light (3.00 x 108 m/s)

8. ELECTROMAGNETIC RADIATION Wavelength (m) 10-11 103 Radio frequency FM Shortwave AM Gamma rays Ultr- violet Infrared Microwaves Visible X rays Frequency (s-1) 104 1020 Visible Light: VIBGYOR Violet, Indigo, Blue, Green, Yellow, Orange, Red 400 – 750 nm - White light is a blend of all visible wavelengths - Can be separated using a prism

9. ELECTROMAGNETIC RADIATION An FM radio station broadcasts at 90.1 MHz. Calculate the wavelength (in m, nm, Ǻ) of the corresponding radio waves c = λ ν λ = ? ν = 90.1 MHz = 90.1 x 106 Hz = 9.01 x 107 Hz c = 3.00 x 108 m/s λ = c/ ν = [3.00 x 108 m/s]/[9.01 x 107 Hz] = 3.33 m = 3.33 x 109 nm = 3.33 x 1010Ǻ

10. QUANTIZATION OF ENERGY Max Planck’s Postulate - Energy can be gained or lost by whole-number multiples - Change in energy (E) = nhν n = an integer (1, 2, 3, …..) h = Planck’s constant (6.626 x 10-34 joule-second, J-s) ν = frequency of electromagnetic radiation absorbed or emitted

11. QUANTIZATION OF ENERGY Max Planck’s Postulate - Energy is quantized and can occur only in discrete units of size, hν - Matter is allowed to emit or absorb energy only in whole-number multiples - Each of these small quantities (packets) of energy is the quantum - Many scientists dismissed Planck’s idea

12. QUANTIZATION OF ENERGY Albert Einstein’s Proposal - Electromagnetic radiation is itself quantized - Electromagnetic radiation can be viewed as a stream of ‘tiny particles’ called photons h = Planck’s constant (6.626 x 10-34 joule-second, J-s) ν = frequency of the radiation λ = wavelength of the radiation

13. QUANTIZATION OF ENERGY Photoelectric Effect - A phenomenon in which electrons are emitted from the surface of a solid metal when light strikes Eo = hνo Eo = minimum energy required to remove an electron νo = threshold frequency below which electrons are not emitted by a given metal

14. QUANTIZATION OF ENERGY Photoelectric Effect Below νo - No electrons are emitted irrespective of the light intensity Above νo - Number of electrons emitted increases with light intensity - Kinetic energy increases linearly with frequency

15. QUANTIZATION OF ENERGY Photoelectric Effect m = mass of electron (kg) v = velocity of electron (m/s) hν = energy of incident electron (J) hνo = energy required to remove electron from metal’s surface (J)

16. QUANTIZATION OF ENERGY Einstein’s Equation E = mc2 E = energy m = mass c = speed of light

17. QUANTIZATION OF ENERGY Einstein’s Equation The Dual Nature of Light - Electromagnetic radiation exhibits wave properties and particulate properties

18. QUANTIZATION OF ENERGY De Broglie’s Equation For a particle with velocity, v - Particles have wavelength associated with them - Wavelength is inversely proportional to mass - In conclusion, matter and energy are not distinct

19. QUANTIZATION OF ENERGY De Broglie’s Equation Calculate the wavelength of an electron of mass 8.81 x 10-31 kg, traveling at a speed of 1.5 x 107 m/s λ = ? v = 1.5 x 107 m/s m = 8.81 x 10-31 kg λ = (6.626 x 10-34 j-s)/[(8.81 x 10-31 kg)(1.5 x 107 m/s)] = 5.0 x 10-11 m

20. THE ATOMIC SPECTRUM Spectrum Intensity of light as a function of wavelength Transmission - Electromagnetic radiation (EM) passes through matter without interaction Absorption - An atom (or ion or molecule) absorbs EM and moves to a higher energy state (excited) Emission - An atom (or ion or molecule) releases energy and moves to a lower energy state

21. THE ATOMIC SPECTRUM - The excited atoms release energy by emitting light - The emitted light has various wavelengths called emission spectrum - The emission spectrum of an atom is called line spectrum - Lines corresponding to discrete wavelengths are seen when passed through a prism - Implies electron energy levels are quantized - The emission spectrum of the sun (white light) is a continuous spectrum when passed through a prism (ROYGBIV-rainbow)

22. RYDBERG EQUATION - A study of the wavelengths from the line spectra of the hydrogen atom RH = Rydberg constant = 1.097 x 107 m-1 n1 and n2 are positive integers n1 < n2

23. THE BOHR MODEL - An electron in a hydrogen atom moves around the nucleus in certain allowed circular orbits - Negatively charged electrons are attracted to the positively charged nucleus - Electrons are charged particles under acceleration and hence radiate energy (emit light and lose energy)

24. THE BOHR MODEL n = integer (the larger the n value, the larger the orbital radius) Z = nuclear charge (Z = 1 for hydrogen, one photon) - If n is infinitely large (n = ∞), E = 0 As the electron gets closer to the nucleus - E becomes more negative - Energy is released from the system

25. THE BOHR MODEL - Energy required to excite the H electron from one level to another level (Z = 1) E = Efinal – Einitial = energy level n2 – energy level n1

26. THE BOHR MODEL Limitations - Bohr’s model does not work for any other atoms apart from H - Electrons do not move in circular orbits around the nucleus

27. THE BOHR MODEL Calculate the energy required to excite the hydrogen electron from level n = 1 to level n = 3. Calculate the wavelength of light that must be absorbed by a H atom in its ground state to reach its excited state

28. THE BOHR MODEL

29. QUANTUM MECHANICS - Developed by Heisenberg, de Broglie, and Schrödinger - An electron bound to a nucleus seems to be a standing wave (stationary waves such as those from guitar strings)

30. QUANTUM MECHANICS Schrödinger’s Equation Ĥψ = Eψ ψ = wave function (coordinates x, y, z function) ψ2 = probability of finding an electron at a given point in space Ĥ = operator E = total energy of atom (sum of potential and kinetic energies)

31. THE WAVE FUNCTION - A specific wave function is called the orbital - It is difficult to know precisely the pathway (position and momentum) of an electron in a given time

32. THE WAVE FUNCTION Heisenberg Uncertainty Principle x = uncertainty in a particle’s position (mv) = uncertainty in a particle’s momentum Momentum = product of mass and velocity of an object

33. QUANTUM NUMBERS - Describes various properties of the orbital Principal Quantum Number (n) - Called the electron shell - Related to the size and energy of the atomic orbital - Has integral values 1, 2, 3, …… - Orbital becomes larger as n increases (electron is farther from the nucleus) - Electron energy increases with increasing n (electron is less tightly bound and energy is less negative) - Orbitals with the same energy (same n value) are said to be degenerate

34. QUANTUM NUMBERS - Describes various properties of the orbital Angular Momentum (Azimuthal) Quantum Number (l) - Called electron subshell - Related to the shape of the atomic orbitals - Has integral values 0, 1, 2, 3, ……, n-1 (for each value of n) - The values of l are assigned letters Value of l 0 1 2 3 4 Letter used s p d f g

35. QUANTUM NUMBERS - Describes various properties of the orbital Magnetic Quantum Number (ml) - Related to the orientation of the orbital in space relative to the other orbitals in the atom - Has integral values between l and –l, including 0 (ml = 2l + 1) Value of l 0 1 2 3 4 Letter used s p d f g # of orbitals (ml) 1 3 5 7 9

36. QUANTUM NUMBERS - Describes various properties of the orbital Electron Spin Quantum Number (ms) - Can have only one of the two values +1/2 and -1/2 - Electrons can spin in one of two opposite directions - Two electrons with the same spin are parallel - Two electrons with different spins are paired (one +1/2 and the other -1/2)

37. QUANTUM NUMBERS - The value of n and the letter for l are used to designate orbitals # of subshells # of electrons n Orbital designation ml l 0 Shell 1 1 subshell 0 1s 2 electrons 0 1 2s 2p 0 -1,0,+1 2 electrons 6 electrons Shell 2 2 subshells 0 -1,0,+1 -2,-1,0,+1,+2 2 electrons 6 electrons 10 electrons 0 1 2 3s 3p 3d Shell 3 3 subshells 2 electrons 6 electrons 10 electrons 14 electrons 0 1 2 3 4s 4p 4d 4f 0 -1,0,+1 -2,-1,0,+1,+2 -3,-2,-1,0,+1,+2,+3 Shell 4 4 subshells

38. QUANTUM NUMBERS For shell n - The number of orbitals = n2 - The maximum number of electrons = 2n2

39. QUANTUM NUMBERS n 1 2 3 4 Subshell s s, p s, p, d s, p, d, f Number of orbitals 1 1 + 3 = 4 1 + 3 + 5 = 9 1 + 3 + 5 + 7 = 16 Maximum number of electrons 2 8 18 32

40. PAULI EXCLUSION PRINCIPLE - In a given atom, no two electrons can have the same set of four quantum numbers (n, l, ml, and ms) - Electrons in the same orbital has the same n, l, and ml - These electrons should have different values of ms - Implies an orbital can hold a maximum of two electrons - The two electrons in any orbital must have opposite spins

41. ORBITAL SHAPES AND ENERGIES - An orbital is a region of space within an electron subshell - The electron with a specific energy has a high probability of being found - An orbital can accommodate a maximum of 2 electrons - The orbitals contain areas of high probability separated by areas of low probability - The areas of low probability are called nodes

42. ORBITAL SHAPES AND ENERGIES The s orbital - The number of nodes for s orbitals = n-1 - The s orbital is spherical - Its function always has a positive sign

43. ORBITAL SHAPES AND ENERGIES The p orbital - Note that there are no 1p orbitals - p orbitals have 2 lobes separated by a node at the nucleus - Labeled according to the xyz cordinate axis system 2p orbital with lobes centered along the x-axis is 2px orbital 2p orbital with lobes centered along the y-axis is 2py orbital 2p orbital with lobes centered along the z-axis is 2pz orbital - The p orbital has positive and negative signs (phases) - Size of lobes increase with increasing n

44. ORBITAL SHAPES AND ENERGIES The d orbital - Note that there are no 1d nor 2d orbitals - The d orbitals have two different fundamental shapes - dxy, dxz, dyz, dx2-y2: four lobes centered in the indicated planes - dz2: two lobes along the z axis and a belt centered in the xy plane - Size of lobes increase with increasing n

45. ORBITAL SHAPES AND ENERGIES The f orbital - Note that there are no 1f, 2f, nor 3f orbitals - Shapes are more complex than the d orbitals

46. POLYELECTRONIC ATOMS - Atoms with more than one electron Three energy contributions - The kinetic energy of the electrons as they move around the nucleus - The potenital energy of attraction between the nucleus and the electrons - The potenital energy of repulsion between the electrons - Electron repulsion cannot be calculated exactly since electron pathways are not exactly known (electron correlation problem)

47. POLYELECTRONIC ATOMS - Orbitals in a given principal quantum level for H atoms are degenerate - No orbitals are degenerate in polyelectronic atoms - Order of increasing energy levels s < p < d < f

48. ELECTRON CONFIGURATION - Elements in the periodic table are arranged in order of increasing atomic number (number of protons) - Similar to protons, electrons are added one by one to the nucleus to build up elements (Aufbau Principle)

49. ELECTRON CONFIGURATION Rules for assigning electrons - Electron subshells are filled in order of increasing energy (s, p, d, f) - All orbitals of a subshell acquire single electrons before any orbital acquire a second electron (Hund’s rule) - All electrons in singly occupied orbitals must have the same spin - A maximum of 2 electrons can exist in a given orbital and must have opposite spins (Pauli principle)

50. ELECTRON CONFIGURATION - Ordering of electron subshells is often complicated due to overlaps For instance, the 3d subshell has higher energy than the 4s subshell - Use of mnemonic for subshell filling is essential 1s The (n+1)s orbitals always fill before the nd orbitals 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 7s 7p