1 Atomic Spectra Blackbody radiation is the visible glow that solid objects emit when heated. Max Planck (1858–1947): proposed the energy is only emitted in discrete packets called quanta. The amount of energy depends on the frequency:

2 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.

3 Atomic Spectra A photon’s energy must exceed a minimum threshold for electrons to be ejected. Energy of a photon depends only on the frequency.

4 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?

5 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. For Light :  h mc  h p For a Particle:  h mv  h p

6 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.

7 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.

8 Quantum Mechanics

9 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, .

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

11 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.

12 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 = 1 = p orbital l = 2 = d orbital l = 3 = f orbital l = 4 = g orbital

13 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…...

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

15 Quantum Numbers

16 Electron Radial Distribution

17 Electron Radial Distribution s Orbital Shapes:

18 Electron Radial Distribution p Orbital Shapes:

19 Electron Radial Distribution d and f Orbital Shapes:

20 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 ).

21 Effective Nuclear Charge Z eff is lower than actual nuclear charge. Z eff increases toward nucleus ns > np > nd > nf This explains certain periodic changes observed.

22 Effective Nuclear Charge

23 Electron Configuration of Atoms Pauli Exclusion Principle: No two electrons in an atom can have the same quantum numbers (n, l, m l, m s ). Hund’s Rule: When filling orbitals in the same subshell, maximize the number of parallel spins.

24 Electron Configuration of Atoms Rules of Aufbau Principle: 1. Lower n orbitals fill first. 2. Each orbital holds two electrons; each with different m s. 3. Half-fill degenerate orbitals before pairing electrons.

25 Electron Configuration of Atoms Assigning Electrons to Atomic Orbitals 1. The number of electrons in an atom is equal to the atomic number. 2. Assign electrons to the lowest energy orbitals first, then build up.

26 Electron Configuration of Atoms Assigning Electrons to Atomic Orbitals 3. No more than 2 electrons can occupy a single orbital: their spins must be paired. 4. If more than one orbital is available at the same energy, add single electrons with the same spin to each orbital before adding two electrons to one orbital. 5. Use the periodic table as a guide.

27 Electron Configuration of Atoms Writing Electron Configurations Name the occupied atomic orbitals in the atom with the number of electrons in each orbital written as a superscript. Li: 1s 2 2s 1 Na: 1s 2 2s 2 2p 6 3s 1 Fe: 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 6

28 Electron Configuration of Atoms Writing Electron Configurations One may also write the configuation as a noble gas closed shell plus the valence electrons present in the atom. Li: [He]2s 1 Na: [Ne]3s 1 Fe: [Ar]4s 2 3d 6

29 Electron Configuration of Atoms

30 Electron Configuration of Atoms Li   1s 2 2s 1 1s 2s Be   1s 2 2s 2 1s 2s B    1s 2 2s 2 2p 1 1s 2s 2p x 2p y 2p z C     1s 2 2s 2 2p 2 1s 2s 2p x 2p y 2p z

31 Electron Configuration of Atoms N      1s 2 2s 2 2p 3 1s 2s 2p x 2p y 2p z O      1s 2 2s 2 2p 4 1s 2s 2p x 2p y 2p z Ne      1s 2 2s 2 2p 5 1s 2s 2p x 2p y 2p z S [Ne]     [Ne] 3s 2 3p 4 3s 3p x 3p y 3p z

32 Electron Configuration of Atoms

33 Electron Configuration of Atoms

34 Electron Configuration of Atoms Anomalous Electron Configurations: Result from unusual stability of half-filled & full-filled subshells. Chromium should be [Ar] 4s 2 3d 4, but is [Ar] 4s 1 3d 5 Copper should be [Ar] 4s 2 3d 9, but is [Ar] 4s 1 3d 10 In the second transition series this is even more pronounced, with Nb, Mo, Ru, Rh, Pd, and Ag having anomalous configurations (Figure 5.20).

35 Periodic Properties

36 Electron Configuration of Atoms Metallic Radius: One half of the distance between neighboring atoms in a solid sample. Predicting Relative Atomic Radii: 1. The atom with the largest n is largest. 2. If n is equal, then the atom with the largest nuclear charge is smallest.

37 Atomic Radii

38 Atomic Radii

39 Atomic Radii