PHYS 202. Lecture 23 Professor Stephen Thornton April 25, 2005

Transcription

1 PHYS 202 Lecture 23 Professor Stephen Thornton April 25, 2005

2 Reading Quiz The noble gases (He, Ne, Ar, etc.) 1) are very reactive because they lack one electron of being in a closed shell. 2) are very reactive because they have one extra electron in their outer shell. 3) are not reactive because their outer shell is completely full of electrons. 4) do not exist on Earth because they are lighter than air.

3 Answer: 3 Even the subshells of the noble gases are completely full of electrons. They neither want to gain an electron or give one up. They are nonreactive.

4 Last lecture de Broglie wavelengths Particles have wavelike properties Wave-particle duality Heisenberg uncertainty principle Tunneling Models of atoms Emission spectra Work problems

5 Today Review hydrogen spectra Rydberg equation Bohr model of the atom Quantum mechanics and quantum numbers Pauli exclusion principle Periodic table Atomic radiation Lasers Fluorescence and phosphorescence

6 Items of interest Exam 3: 83.6 ± 13.6 Outstanding! Last problem sessions are this week. Grades have been posted. Contact TAs about problem section corrections. Teaching evaluations start this week.

7 The Line Spectrum of an Atom

8 The Line Spectrum of Hydrogen Emission Absorption

9 Hydrogen energy levels Balmer series Emission Name n = 1, to E 1 Lyman n = 2, to E 2 Balmer n = 3, to E 3 Paschen n = 4, to E 4 Brackett

10 The Balmer Series = R n 3,4,5,... λ 2 2 = 2 n

11 The Lyman, Balmer, and Paschen Series of Spectral Lines

12 Rydberg equation = R ' 1,2,3,4,5,... *** 2 2 n = λ n' n n= n' + 1, n' + 2, n' + 3,... n = 1 Lyman series n = 2 Balmer series n = 3 Paschen series

13 Hydrogen energy levels n ' = 3 n ' = 2 Emission Name n = 1, to E 1 Lyman n = 2, to E 2 Balmer n = 3, to E 3 Paschen n = 4, to E 4 Brackett n ' = 1

14 How can we understand the quantum phenomena shown by hydrogen spectrum?? Niels Bohr Danish physicist Bohr tried to keep as many classical concepts as possible, but realized that the ideas of the new quantum physics (Planck and Einstein) would be needed. Bohr proposed four assumptions in his model to be able to explain the hydrogen spectrum.

15 Bohr model - assumptions 1) Electron in H atom moves in circular orbit. 2) Only certain orbits are allowed where angular momentum L n = nh/2π, where n = 1,2,3, This is quantization!! 3) Electrons do not radiate energy when in these allowed orbits. 4) Electromagnetic radiation is emitted and absorbed when electron changes from one of these orbits to another. E = hf

16 h A Bohr Orbit If we use Ln = mvr = nh/2π and classical results we have studied, we find: r n h 4π mke 2 = where = a = r = m is Bohr orbit 4π mke Quantized!!! n 2

17 The First Three Bohr Orbits

18 Energy-Level Diagram for the Bohr Model of Hydrogen We showed energy levels like this before, and now we want to calculate the values.

19 E = K + U Energy of Bohr orbit for electron in orbit kze E = mv + U = 2 2r where we are considering a hydrogen-like atom of charge Ze. (single electron atom) E E n n π mk e Z = n 1,2,3, h = n 2 Z = ( 13.6 ev) n= 1,2,3,... 2 n

20 The Origin of Spectral Series in Hydrogen E n = 13.6 ev ( ) Z n 2 2

21 Hydrogen spectrum If we take the energies for each of the Bohr orbits just found and find the E transitions between the various levels of quantum number n, we find hc 2π mk e 1 1 E = hf = = λ h nf n i π mk e = R 3 λ 2 2 = 2 2 h c nf n i nf n i π mk e 7-1 R = = m 3 hc Rydberg constant calculated!!

22 de Broglie Wavelengths and Bohr Orbits

23 Conceptual quiz: Electrons in Bohr orbits of the hydrogen atom 1) do not radiate electromagnetic energy because atoms are stable and Bohr assumed they didn t radiate. 2) produce electromagnetic radiation to generate laser radiation. 3) must radiate electromagnetic energy. 4) radiate energy only when > n.

24 Answer: 1 Bohr had to make this assumption because obviously atoms are stable.

25 Quantum physics The fact that Bohr s angular momentum condition could be understood using de Broglie s matter waves encouraged physicists to follow the notion. Bohr model only works for hydrogenlike atoms. Versions of a full fledged quantum physics theory were soon proposed by Erwin Schrödinger Max Born Werner Heisenberg

26 Quantum mechanical hydrogen atom Quantum physics is characterized by a series of quantum numbers similar to the n of Bohr: Principal quantum number n: n = 1,2,3, primarily determines energy and major orbits Orbital angular momentum quantum number, = 0,1,2,...,( n 1) States with lower h are lower in L = + energy. ( 1) 2 π

27 Quantum numbers, continued Magnetic quantum number ; depends on magnetic field. m = + specifies one direction of Electron spin quantum number electron spin up or down m, 1,..., 2, 1, L h Lz = m 2 π m s m s = 1 1, 2 2

28 Energy Level Structure of Hydrogen First number gives the number of electrons in the particular state. For example, 6e - means 6 electrons.

29 Pauli exclusion principle Wolfgang Pauli: No two electrons can have the same set of quantum numbers ( n m m ).,,, s Now we can explain most of the subject of chemistry!

30 States of Hydrogen for n = 1 and n = 2 n = 1, l = 0 Two States n = 1 l = 0 m l = 0 m s = 1/2 n = 1 l = 0 m l = 0 m s = 1/2 n = 2, l = 0 Two States n = 2 l = 0 m l = 0 m s = 1/2 n = 2 l = 0 m l = 0 m s = 1/2 n = 2, l = 1 Six States n = 2 l = 1 m l = 1 m s = 1/2 n = 2 l = 1 m l = 1 m s = 1/2 n = 2 l = 1 m l = 0 m s = 1/2 n = 2 l = 1 m l = 0 m s = 1/2 n = 2 l = 1 m l = 1 m s = 1/2 n = 2 l = 1 m l = 1 m s = 1/2

31 Probability Cloud for the Ground State of Hydrogen

32 Probability as a Function of Distance

33 Shell and Subshell Designations n Shell 1 K 2 L 3 M 4 N l Subshell 0 s 1 p 2 d 3 f 4 g

34 Energy Levels in Multielectron Atoms 4s is lower than 3d. Rules: Smallest values of n have lowest energies. Smallest values of have lowest energies.

35 Designation of Electronic Configuration

36 Electronic Configuration of the Elements Hydrogen through Potassium Atomic Number Element Electronic configuration 1 Hydrogen (H) 2 Helium (He) 3 Lithium (Li) 4 Beryllium (Be) 1s 1 1s 2 1s 2 2s 1 1s 2 2s 2 5 Boron (B) 1s 2 2s 2 2p 1 6 Carbon (C) 1s 2 2s 2 2p 2 7 Nitrogen (N) 8 Oxygen (O) 1s 2 2s 2 2p 3 1s 2 2s 2 2p 4 9 Fluorine 1s 2 2s 2 2p 5

37 Electronic Configuration of the Elements Hydrogen through Potassium Atomic Number Element Electronic configuration 10 Neon (Ne) 1s 2 2s 2 2p 6 11 Sodium (Na) 12 Magnesium (Mg) 13 Aluminum (Al) 1s 2 2s 2 2p 1 3s 1 1s 2 2s 2 2p 1 3s 2 1s 2 2s 2 2p 1 3s 2 3p 1 14 Silicon (Si) 1s 2 2s 2 2p 1 3s 2 3p 2 15 Phosphorus (P) 1s 2 2s 2 2p 1 3s 2 3p 3 16 Sulfur (S) 1s 2 2s 2 2p 1 3s 2 3p 4 17 Chlorine (Cl) 1s 2 2s 2 2p 1 3s 2 3p 5 18 Argon (Ar) 1s 2 2s 2 2p 1 3s 2 3p 6 19 Potassium 1s 2 2s 2 2p 1 3s 2 3p 6 4s 1 Note: 2p 1 here should be 2p 6. These are ground state configurations. Excited states have electrons moved up to other subshells.

38 Designation of Elements in the Periodic Table

39 Periodic table

40 Conceptual Quiz: An atom has the configuration 1s 2 2s 2 2p 1 3s 1. What best describes this atom? 1) It is the ground state of carbon. 2) It is the ground state of boron. 3) It is an excited state of boron. 4) It is an excited state of carbon. 5) It is an excited state of nitrogen.

41 Answer: 4 It is an atom, not an ion, and there are six electrons. The atom is carbon. Because the 2p subshell is not filled, and there is one electron in the 3s subshell, the atom is in an excited state.

42 X-Ray Tube show x-ray example

43 X-Ray Spectrum

44 Stimulated Emission - lasers

45 The Helium Neon Laser

46 The Helium Neon Laser

47 Holography

48 The Mechanism of Fluorescence

49 Work Problem 31-45