CHEMISTRY T HIRD E DITION Gilbert | Kirss | Foster | Davies © 2012 by W. W. Norton & Company CHAPTER 7-B Quantum Numbers

2 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:

3 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.

4 Atomic Spectra

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

6 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?

7 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

8 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.

9 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.

10 Quantum Mechanics

11 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, .

12 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 )

13 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.

14 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

15 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…...

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

17 Quantum Numbers