Chapter 7 QUANTUM THEORY & ATOMIC STRUCTURE Brooks/Cole - Thomson

Transcription

1 Chapter 7 QUANTUM THEORY & ATOMIC STRUCTURE 1

2 7.1 The Nature of Light 2 Most subatomic particles behave as PARTICLES and obey the physics of waves. Light is a type of electromagnetic radiation Light consists of energy particles called photons that travel as waves.

3 The Wave Nature of Light 3 Wavelength (λ) The distance a wave travels in one cycle The distance between two corresponding points on a wave Units are meters (m) or commonly nanometers (nm = 10-9 m) 3

4 The Wave Nature of Light 4 Frequency (ν) The number of wave cycles that move through a point in space in 1 sescond Units are hertz (Hz) which are the same as inverse seconds (1/s) Long wavelength --> low frequency Short wavelength --> high frequency 4

5 The Wave Nature of Light Amplitude - The height of the crest (or depth of a trough) - Indication of the light intensity or brightness 5

6 The Wave Nature of Light 6 Speed The distance the wave moves per unit time (m/s) The product of its frequency (cycles per second) and wavelength (m/s) = c In a vacuum, speed of light: c = 3.00 x 10 8 m/sec wavelength Long wavelength --> low freq. Short wavelength --> high freq. wavelength Node

7 Electromagnetic Spectrum arranges wavelength from shortest to longest arranges frequency from highest to lowest shows visible light with wavelengths from nm 7 7 7

8 Wavelength ( ), Frequency ( ) = C & Energy (E photon ) C = 3.00 x 10 8 m/s (speed of light) h = J. s (Planck s constant) Photons are packets of light energy 8 p. 273

9 Problem Red light has = 700. nm; calculate the frequency and energy of a photon nm 1 x 10-9 m 1 nm = 7.00 x 10-7 m Freq = 3.00 x 108 m/s 7.00 x 10-7 m 4.29 x 1014 sec -1 E photon = h = (6.63 x J s)(4.29 x s -1 ) = 2.85 x J per photon

10 The Particle Nature of Light Black body radiation 10 A solid object emits visible light when it is heated to about 1000 K. The intensity ) of the light changes as the temperature changes. Figure 7.6 Familiar examples of light emission related to blackbody radiation. Smoldering coal Electric heating element Lightbulb filament

11 The Particle Nature of Light 11 Black body radiation & the Quantum Theory of Energy - Any object (including atoms) can emit or absorb only certain quantities of energy. - Energy is quantized; it occurs in fixed quantities, rather than being continuous. Each fixed quantity of energy is called a quantum. - An atom changes its energy state by emitting or absorbing one or more quanta of energy. DE = n h n can only be a whole number h = x J s (the Planck s constant) Max Planck ( )

12 Problem Calculate the energy of 1.00 mol of photons of red light (wavelength 700. nm, frequency 4.29 x sec -1 ). 12 E photon = h = (6.63 x J s)(4.29 x s -1 ) = 2.85 x J per photon E per mol = (2.85 x J/ph)(6.02 x photons/mol) E = kj/mol

13 7.2 Atomic Spectra 13 Excited atoms can emit light characteristic of that element.

14 Spectrum of White Light 14 White light (sunlight, or light from regular light bulbs) that passes through a prism is separated into all colors that together are called a continuous spectrum gives the colors of a rainbow

15 Line Spectra of Excited Atoms & the Rhydberg Equation Excited atoms emit light of only certain wavelengths 15 Line Spectrum of Excited Hydrogen Gas

16 Line Spectra of Excited Atoms & the Rhydberg Equation 16 The wavelengths of emitted light are specific for the element. Line Spectra of Other Elements in the Gas Phase

17 The Rydberg Equation 17 is wavelength of the line R is Rydberg s constant: x 10 7 m -1 n 1 and n 2 are positive integers with n 2 > n 1 for the visible series, n 1 = 2 and n 2 = 3, 4, 5,... Three series of spectral lines of atomic hydrogen.

18 The Bohr Model of Hydrogen Atom Bohr s atomic model postulated the following: The H atom has only certain energy levels, which Bohr called stationary states. - Each state is associated with a fixed circular orbit of the electron around the nucleus. - The higher the energy level, the farther the orbit is from the nucleus. - When the H electron is in the first orbit, the atom is in its lowest energy state, called the ground state. 18

19 The Bohr Model of Hydrogen Atom 19 The atom does not radiate energy while in one of its stationary states. The atom changes to another stationary state only by absorbing or emitting a photon. ΔE = E final E initial - The energy of the photon (h ) equals the difference between the energies of the two energy states. E photon = ΔE = h When the E electron is in any orbit higher than n = 1, the atom is in an excited state.

20 Features of the Bohr Model Quantum numbers are integers: n = 1, 2, 3, Radius of electron orbit directly relates to the electron s energy: the lower the n value, the smaller the electron orbit, and the lower the energy level. 20 If electrons are in quantized energy states, then E of states can have only certain values. This explains sharp line spectra.

21 Features of the Bohr Model 21 Ground state: when the electron is in the lowest possible orbit, which is closest to the nucleus. Excited state: when the electron is any orblt farther from the nucleus.

22 Features of the Bohr Model Absorption when H atom absorbs a photon whose energy equals the difference between the lower and higher energy levels, then the electron moves to the higher orbit. Emission when H atom in a higher energy level returns to a lower energy level, then the atom emits a photon whose energy equals the difference between the two levels. 22

23 The Bohr explanation of three series of spectral lines emitted by the H atom 23

24 The Energy Levels of the Hydrogen Atom 24 For an energy level n: For a transition between two energy levels The Bohr Equation:

25 Problem What is the wavelength corresponding to the transition of electron from n =2 to n = 1? 25 Solution: Energy of transition: E = E final - E initial = x J [(1/1 2 ) - (1/2) 2 ] = x J ==> EMISSION PROCESS Energy of emitted light E photon = hc/ = x J Wavelength of this light: = nm This is exactly in agreement with experiment!

26 7.3 The Wave-Particle Duality of Matter and Energy Matter and Energy are alternate forms of the same entity. E = mc 2 All matter exhibits properties of both particles and waves. Electrons have wave-like motion and therefore have only certain allowable frequencies and energies. Matter behaves as though it moves in a wave, and the de Broglie wavelength for any particle is given by: 26 λ mu h m = mass in kg u = speed in m/s L. de Broglie ( )

27 Problem Determine the de Broglie wavelength of (a) an electron with a speed of 1.00 x 10 6 m/s. [electron mass = 9.11 x kg]. (b) a lithium atom moving at 2.5 x 10 5 m/s Solution: (a) (b) h 6.626x10 J. s 1kgm. / s x10 m 31 6 mv (9.11x10 kg)(1.00x10 m / s) 1J mass of a lithium atom: g 1mol 1.152x10 23 g 23 1molLi 6.023x10 atomsli h 6.626x10 J. s 1kgm. / s x10 m 26 5 mv (1.152x10 kg)(2.5x10 m/ s) 1J This wavelength is within the range of g-rays ( m) 27

28 7.4 The Quantum-Mechanical Model of the Atom - Electron behaves simultaneously as a wave and a particle. The matter-wave of the electron occupies the space near the nucleus and is continuously influenced by it. - The Schrödinger wave equation allows us to solve for the energy states associated with a particular atomic orbital. The wave function (or atomic orbital) is a mathematical description of the electron s matter-wave in 3-D the region of 3D-space within which an electron is most likely to be found, and NOT the path the electron follows. - The square of the wave function 2 gives the probability density, a measure of the probability of finding an electron of a particular energy in a particular region of the atom. It describes the shape of an orbital. 28

29 Figure Electron probability density in the ground-state H atom.

30 Quantum Numbers of an Atomic Orbital 30 An atomic orbital is specified by three quantum numbers: n (principal): 1, 2, 3,. l (angular momentum): 0 to n-1 m l (magnetic): -l to 0 to +l

31 Quantum Numbers 31

32 Quantum Numbers & Energy Levels The energy states and orbital of an atom are associated with one or more quantum numbers: Level (or shell) given by the n values. Each designates the energy (size) of the electron. The lower the n value means the greater probability that the electron is closer to the nucleus. Sublevel (or subshell) given by the l values. Each designates the orbital shape with a letter: l = 0 is an s sublevel l = 2 is a d sublevel l = 1 is a p sublevel l = 3 is an f sublevel Name a subshell by its n value with the designated subshell letter. Orbital given by the m l values. Each designates the orbital orientation. 32

33 Problems a) What are the n, l, m l values for the 3d and 5f sublevels? b) Identify the incorrect quantum numbers: n l m l Sublevel name a) p b) s c) d c) Fill in the quantum numbers or sublevel names: n l m l Sublevel name a) ? b)? 3-2 6f c) 5 0? 5s 33

34 Shapes of Atomic Orbitals 34 s orbital l=0, no node p orbital l=1, 1 nodal plane d orbital l=2, 2 nodal planes f orbital l=3, 3 nodal planes

35 35 Size and Shape of Atomic Orbitals

36 The Special Case: Energy Level in Hydrogen Atom 36 Hydrogen is the only atom whose energy state depends completely on the principal quantum number n. Figure 7.21 Energy levels of the H atom.