1 Chapter 7: Periodicity and Atomic Structure Renee Y. Becker Valencia Community College CHM 1045

2 Light and Electromagnetic Spectrum Several types of electromagnetic radiation make up the electromagnetic spectrum

3 Light and Electromagnetic Spectrum Frequency, : The number of wave peaks that pass a given point per unit time (1/s) Wavelength, : The distance from one wave peak to the next (nm or m) Amplitude: Height of wave Wavelength x Frequency = Speed (m) x (s -1 ) = c (m/s)

4 Light and Electromagnetic Spectrum

5 The Planck Equation E = h E = hc / h = Planck’s constant, x J s 1 J = 1 kg m 2 /s 2

6 Example1: Light and Electromagnetic Spectrum The red light in a laser pointer comes from a diode laser that has a wavelength of about 630 nm. What is the frequency of the light? c = 3 x 10 8 m/s

7 Atomic Spectra Atomic spectra: Result from excited atoms emitting light. Line spectra: Result from electron transitions between specific energy levels. Blackbody radiation is the visible glow that solid objects emit when heated.

8 Atomic Spectra Max Planck (1858–1947): proposed the energy is only emitted in discrete packets called quanta. The amount of energy depends on the frequency: E = energy = frequency = wavelengthc = speed of light h = planck’s constant E  h  hc h   10  34 J  s

9 Atomic Spectra Albert Einstein (1879–1955): Used the idea of quanta to explain the photoelectric effect. He proposed that light behaves as a stream of particles called photons A photon’s energy must exceed a minimum threshold for electrons to be ejected. Energy of a photon depends only on the frequency. E = h

10 Atomic Spectra

11 Example 2: Atomic Spectra For red light with a wavelength of about 630 nm, what is the energy of a single photon and one mole of photons?

12 Wave–Particle Duality Louis de Broglie (1892–1987): Suggested waves can behave as particles and particles can behave as waves. This is called wave– particle duality. m = mass in kgp = momentum (mc) or (mv) For Light :  h mc  h p For a Particle:  h mv  h p

13 Example 3: Wave–Particle Duality How fast must an electron be moving if it has a de Broglie wavelength of 550 nm? m e = x 10 –31 kg

14 Quantum Mechanics Niels Bohr (1885–1962): Described atom as electrons circling around a nucleus and concluded that electrons have specific energy levels. Erwin Schrödinger (1887–1961): Proposed quantum mechanical model of atom, which focuses on wavelike properties of electrons.

15 Quantum Mechanics Werner Heisenberg (1901–1976): Showed that it is impossible to know (or measure) precisely both the position and velocity (or the momentum) at the same time. The simple act of “seeing” an electron would change its energy and therefore its position.

16 Quantum Mechanics Erwin Schrödinger (1887–1961): Developed a compromise which calculates both the energy of an electron and the probability of finding an electron at any point in the molecule. This is accomplished by solving the Schrödinger equation, resulting in the wave function

17 Quantum Numbers Wave functions describe the behavior of electrons. Each wave function contains four variables called quantum numbers: Principal Quantum Number (n) Angular-Momentum Quantum Number (l) Magnetic Quantum Number (m l ) Spin Quantum Number (m s )

18 Quantum Numbers Principal Quantum Number (n): Defines the size and energy level of the orbital. n = 1, 2, 3,  –As n increases, the electrons get farther from the nucleus. –As n increases, the electrons’ energy increases. –Each value of n is generally called a shell.

19 Quantum Numbers Angular-Momentum Quantum Number (l): Defines the three-dimensional shape of the orbital. For an orbital of principal quantum number n, the value of l can have an integer value from 0 to n – 1. This gives the subshell notation: l = 0 = s orbital l = 3 = f orbital l = 1 = p orbital l = 4 = g orbital l = 2 = d orbital

20 Quantum Numbers Magnetic Quantum Number (m l ): Defines the spatial orientation of the orbital. For orbital of angular-momentum quantum number, l, the value of m l has integer values from –l to +l. This gives a spatial orientation of: l = 0 giving m l = 0 l = 1 giving m l = –1, 0, +1 l = 2 giving m l = –2, –1, 0, 1, 2, and so on…...

21 Quantum Numbers Magnetic Quantum Number (m l ): –l to +l S orbital 0 P orbital D orbital F orbital

22 Quantum Numbers Spin Quantum Number: m s The Pauli Exclusion Principle states that no two electrons can have the same four quantum numbers.

23 Quantum Numbers

24 Example 4: Quantum Numbers Why can’t an electron have the following quantum numbers? (a) n = 2, l = 2, m l = 1 (b) n = 3, l = 0, m l = 3 (c) n = 5, l = –2, m l = 1

25 Example 5: Quantum Numbers Give orbital notations for electrons with the following quantum numbers: (a)n = 2, l = 1 (b) n = 4, l = 3 (c) n = 3, l = 2

26 Electron Radial Distribution s Orbital Shapes: Holds 2 electrons

27 Electron Radial Distribution p Orbital Shapes: Holds 6 electrons, degenerate

28 Electron Radial Distribution d and f Orbital Shapes: d holds 10 electrons and f holds 14 electrons, degenerate

29 Effective Nuclear Charge Electron shielding leads to energy differences among orbitals within a shell. Net nuclear charge felt by an electron is called the effective nuclear charge (Z eff ). Z eff is lower than actual nuclear charge. Z eff increases toward nucleus ns > np > nd > nf

30 Effective Nuclear Charge