The Wave Nature of Light: Understanding Wavelength, Frequency, and Electromagnetic Radiation

1. The Wave Nature of Light A wave is a continuously repeating change or oscillation in matter or in a physical field. Light is a wave, consisting of oscillations in electric and magnetic fields, traveling through space. 5- מבנה האטום

2. The Wave Nature of Light A wave can be characterized by its wavelength and frequency. Wavelength, symbolized by the Greek letter lambda, l, is the distance between any two identical points on adjacent waves. • Frequency, symbolized by the Greek letter nu, n, is the number of wavelengths that pass a fixed point in one unit of time (usually a second). The unit is 1/S or s-1 which is also called the Hertz (Hz). 5- מבנה האטום

3. The Wave Nature of Light • Wavelength and frequency are related, their product equals to speed of light. The speed of light, c, is 3.00 x 108 m/s. c = nl When the wavelength is reduced by a factor of two, the frequency increases by a factor of two. 5- מבנה האטום

4. The Wave Nature of Light What is the wavelength of blue light with a frequency of 5.09 1014/s? c = nl so l = c/n n = 5.09  1014/s c = 3.00  108 m/s 5- מבנה האטום

5. 5- מבנה האטום Electromagnetic Radiation E increasing, increasing, decreasing The range of frequencies and wavelengths of electromagnetic radiation is called the electromagnetic spectrum.

6. Quantum Effects and Photons Light consists of quanta(singular: quantum) or particles of electromagnetic energy, called photons. The energy of each photon is proportional to its frequency: E = hn h = 6.626  10−34 J  s (Planck’s constant) • Light, therefore, has properties of both waves and matter. Neither understanding is sufficient alone. This is called the wave-particle duality of light. 5- מבנה האטום

7. Photons 5- מבנה האטום • Photons with λ = 452 nm are blue. • What’s the frequency of this radiation? • What’s the energy of 1 of these photons? • What’s the energy of 1 mol of 452-nm photons? a) n = c 2.9979 x 108 ms-1 452 x 10-9 m n = = = 6.63 x 1014 s-1 b) E= hn c  E = 6.626 x 10-34Js (6.63 x 1014 s-1) = 4.39 x 10-19 J c) E/mol= 4.39 x 10-19 J (6.022 x 1023 mol-1) = 2.6 x 105 J mol-1

8. Spectra • When atoms or molecules absorb energy, that energy is often released as light energy. • Fireworks, neon lights, etc. • 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 or molecule; the pattern is called an emission spectrum. • Noncontinuous • Can be used to identify the material • Flame tests 5- מבנה האטום

9. Exciting Gas Atoms to Emit Light • Light is emitted when gas atoms are excited via external energy (e.g., electricity or flame). • Each element emits a characteristic color of light. 5- מבנה האטום

10. Emission Spectra 5- מבנה האטום

11. Examples of Spectra A line spectrum shows only certain colors or specific wavelengths of light. A continuous spectrum contains all wavelengths of light. 5- מבנה האטום

12. Na K Li Ba Identifying Elements with Flame Tests 5- מבנה האטום

13. 1 l 1 1 = R − m2 n2 Rydberg’s Spectrum Analysis Johannes Rydberg (1854–1919) Rydberg analyzed the spectrum of hydrogen and found that it could be described with an equation that involved an inverse square of integers. m: shell the transition is to (inner shell) R= 1.097 X 10-2 nm-1 n: shell the transition is from (outer shell) 5- מבנה האטום

14. The Bohr Theory of the Hydrogen Atom In 1913, Neils Bohr, a Danish scientist, set down postulates to account for: 1. The stability of the hydrogen atom. 2. The line spectrum of the atom. 5- מבנה האטום

15. Energy-Level Postulate An electron can have only specific energy values called energylevels. Energy levels are quantized. Energy levels of the hydrogen atom can be determined using the formula: RH = 2.179  10−18 J (Rydberg constant) n = principal quantum number 5- מבנה האטום

16. Transitions Between Energy Levels An electron can change energy levels by absorbing energy to move to a higher energy level or by emitting energy in the form of a photon to move to a lower energy level. 5- מבנה האטום

17. Atomic Spectroscopy Explained • 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. • When an electron relaxes, a photon of light is released whose energy equals the energy difference between the orbitals. 5- מבנה האטום

18. Electron Transitions • To transition to a higher energy state, the electron must gain the correct amount of energy corresponding to the difference in energy between the final and initial states. • Electrons in high energy states are unstable and tend to lose energy and transition to lower energy states. • Each line in the emission spectrum corresponds to the difference in energy between two energy states. 5- מבנה האטום

19. 5- מבנה האטום

20. Bohr Model of H Atoms For a hydrogen electron, the energy lost is given by: If ni is the principal quantum number for of the initial energy level , and nf is the principal quantum number of the final energy level, then,  5- מבנה האטום

21. Bohr Model of H Atoms In general, hv equals –ΔE: That is, Recalling that v = c/λ, the above equation can be written as: 5- מבנה האטום

22. Bohr Model of H Atoms Light is absorbed by an atom when the electron transition is from lower n to higher n (nf > ni). In this case, DE will be positive. Light is emitted from an atom when the electron transition is from higher n to lower n (nf< ni). In this case, DE will be negative. An electron is ejected when nf = ∞. 5- מבנה האטום

23. Bohr Model of H Atoms Energy-level diagram for the electron in the hydrogen atom. 5- מבנה האטום

24. Bohr Model of H Atoms Electron transitions for an electron in the hydrogen atom. 5- מבנה האטום

25. Bohr Model of H Atoms Determine the wavelength of the light emitted when the electron in a hydrogen atom undergoes a transition from n = 4 to n = 2 It is known that: Subtracting the lower value from the higher value gives a positive result. If the result is negative, reverse the subtraction. 5- מבנה האטום

26. Bohr Model of H Atoms Equate the result to hν as it equals the energy of the photon. The frequency of the light emitted is: Since The color is blue-green. 5- מבנה האטום

27. 5- מבנה האטום Beyond Bohr: Quantum Mechanics Bohr’s model predicts the H-atom: • emission and absorption spectrum. • ionization energy. The model does not work for any other atom. e-do not move in fixed orbits.

28. The Quantum Mechanical Model of the Atom In 1926, Erwin Schrödinger proposed the quantum mechanical model of the atom, which focuses on the wavelike properties of the electron. In 1927, Werner Heisenberg stated that it is impossible to know precisely where an electron is and what path it follows—a statement called the Heisenberg uncertainty principle. 5- מבנה האטום

29. The Quantum Mechanical Model of the Atom Probability of finding electron in a region of space (Y2) Solve Wave function or orbital (Y) Wave equation Quantum mechanics allows us to make statistical statements about the regions in which we are most likely to find the electron. Solving Schrödinger’s equation gives us a wave function, represented by the Greek letter psi, y, which gives information about a particle in a given energy level. Psi-squared, y2, gives us the probability of finding the particle within a region of space. 5- מבנה האטום

30. Wave Function The wave function for the lowest level of the hydrogen atom is shown to the left. 5- מבנה האטום

31. Wave Function Two additional views are shown on the next slide. Figure A illustrates the probability density for an electron in hydrogen. Figure B shows the probability of finding the electron at various distances from the nucleus. The highest probability (most likely) distance is at 50 pm. 5- מבנה האטום

32. Wave Function B A 5- מבנה האטום

33. Quantum Numbers According to quantum mechanics, each electron is described by four quantum numbers: 1.Principal quantum number (n) 2. Angular momentum quantum number (l) 3. Magnetic quantum number (ml) 4. Spin quantum number (ms) The first three define the wave function for a particular electron. The fourth quantum number refers to the magnetic property of electrons. 5- מבנה האטום

34. Wave Function A wave function for an electron in an atom is called an atomic orbital (described by three quantum numbers—n, l, ml). It describes a region of space where there is high probability of finding the electron. 5- מבנה האטום

35. Principal Quantum Number, n This quantum number is the one on which the energy of an electron in an atom primarily depends. The smaller the value of n, the lower the energy and, in some cases, the smaller the orbital. The principal quantum number can have any positive value: 1, 2, 3, . . . Orbitals with the same value for n are said to be in the same shell. 5- מבנה האטום

36. Angular Momentum Quantum Number, l This quantum number distinguishes orbitals of a given n (shell) having different shapes. It can have any integer value from 0 to n–1. For a given n, there will be n different values of orbitals with a distinctive shape, l. Orbitals with the same values for n but different l are said to be in different subshells of a certain shell. 5- מבנה האטום

37. Quantum Numbers • Subshells are sometimes designated by lowercase letters: 5- מבנה האטום

38. Magnetic Quantum Number, ml This quantum number distinguishes orbitals of a given n and l—that is, of a given energy and shape but having different orientations. For l = 0, ml = 0. For l = 1, ml = –1, 0, and +1. Orbitals have the same shape but different orientations in space. ,(mℓ = -ℓ to +ℓ ) 5- מבנה האטום

39. Spin Quantum Number, ms This quantum number refers to the two possible orientations of the spin axis of an electron. It may have a value of either +1/2 or -1/2. 5- מבנה האטום

40. Summary of Quantum Numbers 5- מבנה האטום

41. Orbital Energies of the Hydrogen Atom 5- מבנה האטום

42. Quantum Numbers State whether each of the following sets of quantum numbers is permissible for an electron in an atom. If a set is not permissible, explain why. • n = 1, l = 1, ml = 0, ms = ½ • n = 3, l = 1, ml = –2, ms = –1/² c. n = 2, l = 1, ml = 0, ms = ½ d. n = 2, l = 0, ml = 0, ms = 1 5- מבנה האטום

43. Quantum Numbers • Not permissible The l quantum number is equal to n. It must be lesser than n. b. Not permissible The magnitude of the mlnumber must not be greater than 1. c. Permissible d. Not permissible The ms quantum number can be only +1/2 or –1/2. 5- מבנה האטום

44. Probability and Radial Distribution Functions • y 2 is the probability density. • The probability of finding an electron at a particular point in space • For s orbital maximum at the nucleus • Decreases as you move away from the nucleus • The radial distribution function represents the total probability at a certain distance from the nucleus. • Maximum at most probable radius • Nodes in the functions are where the probability drops to 0. 5- מבנה האטום

45. Probability Density for s Orbitals (l = 0) The probability density function represents the total probability of finding an electron at a particular point in space. 5- מבנה האטום

46. Radial Distribution Function The radial distribution function represents the totalprobability of finding an electron within a thin spherical shell at a distancerfrom the nucleus. The probability at a point decreases with increasing distance from the nucleus, but the volume of the spherical shell increases. The net result is a plot that indicates the most probable distance of the electron in a 1s orbital of H is 52.9 pm. 5- מבנה האטום

47. l = 0, the s Orbital • Each principal energy level has one s orbital. • Lowest energy orbital in a principal energy state • Spherical • Number of nodes = (n – 1) 5- מבנה האטום

48. Probability Densities and Radial Distributions for 2s and 3s Orbitals 5- מבנה האטום

49. l = 1, p orbitals • Each principal energy state above n = 1 has three p orbitals. • ml = −1, 0, +1 • Each of the three orbitals points along a different axis. • px, py, pz • The second-lowest energy orbitals in a principal energy state • Two-lobed • One node at the nucleus; total of n nodes 5- מבנה האטום

50. p Orbitals (l = 1) 5- מבנה האטום