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Copyright©2000 by Houghton Mifflin Company. All rights reserved. 4 Waves Waves have 3 primary characteristics: 1. λ Wavelength: distance between two peaks in a wave. 2. ν Frequency: number of waves per second that pass a given point in space. 3. cSpeed: speed of light is 2.9979 10 8 m/s.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 6 Wavelength and frequency can be interconverted. = c/ = frequency (s 1 ) = wavelength (m) c = speed of light (m s 1 ) Inverse Proportion. c = λ υ

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 8 Problem An FM radio station broadcasts at 99.5 MHz. Calculate the wavelength of the corresponding radio waves. λ = 2.9979 x 10 8 m/s 99.5 MHz x 10 6 Hz/ 1 MHz = 3.01296 m = 3.01 m

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 10 At the end of the 1800s Matter & Energy were thought to be Distinct. Section 7.2 The Nature of Matter

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 11 Matter: - Thought to consist of Particles - Particles have mass & specified position in space. Energy: - In the form of light (Electromagnetic Radiation), thought to be Continuous & Wavelike. - Mass-less & unspecified position in space.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 12 Max Planck (Early 1900s) Studied Radiation emitted by solid bodies heated to incandescence. Thought of the day: Matter could absorb or emit any quantity of energy. He could not explain his results based on this!!! So, he proposed that energy can be gained or lost only in whole number intervals of h.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 13 Plancks Constant E = change in energy, in J h = Plancks constant, 6.626 10 34 J s = frequency, in s 1 = wavelength, in m Transfer of energy is quantized, and can only occur in discrete units, called quanta.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 14 Energy can be gained or lost only in Integer multiples of h. E = n h where n = an integer (1,2.3,…) h = 6.626 x 10 -34 Jsec

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 15 Energy is Quantized Discrete units of h. Each small packet of energy is called a Quantum. Energy is transferred in Whole Quanta.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 17 Problem A photon of ultraviolet light possess enough energy to mutate a strand of human DNA. What is the energy of a single photon having a wavelength of 25 nm? What is the energy of a mole of photons having a wavelength of 25 nm?

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 18 Problem 25 nm x 1 m____ = 25 x 10 -9 m 1 x 10 -9 nm ν = c/ λ = 2.9979 x 10 8 m/s 25 x 10 -9 m = 1.19916 x 10 16 s -1 (or Hz)

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 19 E = h ν = (6.626 x 10 -34 J · s) ( 1.19916 x 10 16 s -1 ) = 7.9 x 10 -18 J per photon Thus (7.9 x 10-18 J/ photon) x (6.022 x 10 23 photons/mole) = 4.8 x 10 6 J/mole

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 20 Albert Einstein Proposed that electromagnetic Radiation is itself Quantized, that is, It can be viewed as a stream of Particles called Photons. Energy of a photon: E = h = h c/

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 21 Energy and Mass Also, Einstein proposed that Energy has mass E = mc 2 E = energy m = mass c = speed of light

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 22 Rearrange equation: m = E/ c 2 That is, mass is associated with a given quantity of energy. Therefore, the apparent mass of a photon can be calculated.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 26 Light thought to be purely wavelike was found to have particulate properties. Matter thought to be purely particulate Does it exhibit wave properties?

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 27 Wavelength and Mass = wavelength, in m h = Plancks constant, 6.626 10 34 J s = 6.626 10 34 kg m 2 s 1 m = mass, in kg = velocity, in m/s de Broglies Equation (1923): Allows one to calculate a wavelength for a particle.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 28 For an electron, = 6.626 x 10 -34 J sec (9.11 x 10 -31 kg) (1.0 x 10 7 m/s) = 7.27 x 10 -11 m Small wavelength, but on the same order as the spacing between atoms in a typical crystal.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 29 For a ball, = 6.626 x 10 -34 J sec (0.10 kg) (35 m/s) = 1.9 x 10 -34 m So very small that it is not observed.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 30 Today, Matter and energy are not distinct. All matter exhibits both particulate a and wave properties. Large matter (balls) exhibits predominately Particulate properties. Very small bits of matter (photons) exhibit Predominately wave properties.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 31 Atomic Spectrum of Hydrogen Section 7.3 Continuous spectrum: Contains all the wavelengths of light. Line (discrete) spectrum: Contains only some of the wavelengths of light.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 33 Sample of H 2 gas (HH) Introduce a high energy spark H 2 molecules absorb energy Some of the HH bonds break Resulting H atoms are EXCITED, i.e. contain excess energy. They will eventually relax & will release excess energy by emitting light of various wavelengths. LINE SPECTRUM

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 34 Line Spectrum Line spectrum results because only certain energies are allowed for the electron in H atom. That is, energy of electron in H atom is QUANTIZED. E = h ν = h c/ λ

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 36 If any energy were allowed then we would see a Continuous Spectrum (a) and When only certain energies are possible we see only a discrete Line Spectrum (b)

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 38 Section 7.4 Niels Bohr (1913) Developed Quantum Model for the Hydrogen Atom. The Electron in a Hydrogen Atom moves around the nucleus only in certain allowed circular orbits.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 39 Figure 7.8 Electronic Transitions in the Bohr Model for the Hydrogen Atom He calculated the radii for the allowed circular orbits. Only certain electron energies allowed. Energy levels consistent with the Hydrogen line-emission spectrum.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 40 The Bohr Model E = energy of the levels in the H-atom z = nuclear charge (for H, z = 1) n = an integer The electron in a hydrogen atom moves around the nucleus only in certain allowed circular orbits.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 41 The Bohr Model If n = (infinite distance), then E = 0. Negative sign - Energy of electron bound to nucleus is lower than electron further away.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 44 Suppose electron in a higher energy level (n=6) returns to the ground state. Calculate E = E f – E i = E 1 – E 6 E = - 2.178 x 10 -18 J (1 2 / 1 2 ) - (- 2.178 x 10 -18 J (1 2 / 6 2 ) = - 2.117 x 10 -18 J Negative sign indicates that atom has lost energy and is now in a more stable state.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 45Wavelength? Energy carried away from the atom by emission of a photon. Calculate the wavelength of light (in nm) associated with this transition. λ = 93.83 nm Lets Do # 50 a & 56.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 46 TWO IMPORTANT POINTS Bohr Model correctly fits Quantized Energy Levels of the H-atom. Postulates only certain allowed circular orbits. As electron is brought closer to the nucleus, Energy is released from the system.

Copyright©2000 by Houghton Mifflin Company. All rights reserved. 47 Bohrs Model Appeared promising. Calculations worked well for hydrogen. Didnt work when applied to other atoms. Something fundamentally incorrect. Important for its introduction of the concept of Quantization of energy in atoms.