# Quantum Mechanics Chapter 7 §4-5. The de Broglie Relation 1924 1924 All matter has a wave-like nature… All matter has a wave-like nature… Wave-particle.

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Quantum Mechanics Chapter 7 4-5 Slide 2 The de Broglie Relation 1924 1924 All matter has a wave-like nature All matter has a wave-like nature Wave-particle duality Wave-particle duality All matter and energy exhibit wave-like and particle- like properties. Slide 3 The de Broglie Relation The de Broglie Equation relates the wavelength of a particle to its momentum. The de Broglie Equation relates the wavelength of a particle to its momentum. Wavelength Plancks constant 6.626x10 -34 Js Velocity, m/s Mass, kg Slide 4 The de Broglie Relation Compare the wavelengths of (a) an electron traveling at a speed of one-hundredth the speed of light with (b) that of a baseball of mass 0.145 kg having a speed of 26.8 m/s (60.0 mi/hr). Compare the wavelengths of (a) an electron traveling at a speed of one-hundredth the speed of light with (b) that of a baseball of mass 0.145 kg having a speed of 26.8 m/s (60.0 mi/hr). (a) the electron What is the mass of an electron? What is the electron speed if it is one-hundredth the speed of light? Slide 5 The de Broglie Relation Compare the wavelengths of (a) an electron traveling at a speed of one-hundredth the speed of light with (b) that of a baseball of mass 0.145 kg having a speed of 26.8 m/s (60.0 mi/hr). Compare the wavelengths of (a) an electron traveling at a speed of one-hundredth the speed of light with (b) that of a baseball of mass 0.145 kg having a speed of 26.8 m/s (60.0 mi/hr). (b) the baseball Slide 6 The de Broglie Relation Compare the wavelengths of (a) an electron with (b) that of a baseball. Compare the wavelengths of (a) an electron with (b) that of a baseball. What does that mean? (a)The electron (2.43x10 -10 m) (a)The baseball (1.71x10 -34 m) Slide 7 The Schroedinger Equation Schroedinger combined Plancks photons, Einsteins wave-particle duality, and de Broglies idea that all energy and matter follow the wave particle duality into one equation (the wave function) for the electron: Schroedinger combined Plancks photons, Einsteins wave-particle duality, and de Broglies idea that all energy and matter follow the wave particle duality into one equation (the wave function) for the electron: No, you dont have to memorize it. This created the basis for Quantum mechanics. Slide 8 Quantum Mechanics Quantum Mechanics of an atom are divided into four quantum numbers: Quantum Mechanics of an atom are divided into four quantum numbers: n m m s m s Principle Quantum Number the number that represents the energy level Angular Momentum Quantum Number Azimuthal the number that represents the subshell Magnetic Quantum Number the number that represents the orbital within the subshell Spin Quantum Number the number that represents the electrons spin Slide 9 Quantum Mechanics Quantum Mechanics of an atom are divided into four quantum numbers: Quantum Mechanics of an atom are divided into four quantum numbers: n m m s m s Electron Spin: m s = 1 / 2 OR + 1 / 2 Energy level: n = 1 - Subshell: Based on which energy level the electron is in; = 0 - (n-1) Orbital: Based on which subshell the electron is in; m = - + Slide 10 Quantum Mechanics Energy level n SubshellOrbital m Electron Spin m s 10 (s)0 1 / 2 OR + 1 / 2 20 (s)0 1 / 2 OR + 1 / 2 21 (p)1, 0, +1 1 / 2 OR + 1 / 2 30 (s)0 1 / 2 OR + 1 / 2 31 (p)1, 0, +1 1 / 2 OR + 1 / 2 32 (d)2, 1, 0, +1, +2 1 / 2 OR + 1 / 2 40 (s)0 1 / 2 OR + 1 / 2 41 (p)1, 0, +1 1 / 2 OR + 1 / 2 42 (d)2, 1, 0, +1, +2 1 / 2 OR + 1 / 2 43 (f)3, 2, 1, 0, +1, +2, +3 1 / 2 OR + 1 / 2 Slide 11 Lets Practice Determine the quantum numbers for Determine the quantum numbers for Na Na First, write out the electron configuration. 1s 2 2s 2 2p 6 Next, write out the four quantum numbers for the last electron in the electron configuration: n = = m = m s = 3s 1 3 Since the energy level is 3 0 Since the subshell is s, which is indicated by the number 0 0 Since the orbital is in the s subshell, so the only possible value is 0. 1 / 2 Spin must follow Paulis exclusion principle Slide 12 Lets Practice Determine the quantum numbers for Determine the quantum numbers for W First, write out the electron configuration. 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 5s 2 4d 10 5p 6 6s 2 4f 14 Next, write out the four quantum numbers for the last electron in the electron configuration: n = = m = m s = 5d 4 5 Since the energy level is 5 2 Since the subshell is d, which is indicated by the number 2 +1 Since the orbital is in the 4 th orbital in the d subshell: 2. 1, 0 +1, +2. 1 / 2 Spin must follow Paulis exclusion principle Slide 13 Lets Practice Determine the quantum numbers for Determine the quantum numbers for Br Br First, write out the electron configuration. 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 Next, write out the four quantum numbers for the last electron in the electron configuration: n = = m = m s = 4p 5 4 Since the energy level is 4 1 Since the subshell is p, which is indicated by the number 1 0 Since the orbital is in the 2 nd orbital in the p subshell: 1, 0 +1. 1 / 2 Spin must follow Paulis exclusion principle

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