Chapter 7 The Quantum-Mechanical Model of the Atom

A Theory that Explains Electron Behavior the quantum-mechanical model explains the manner electrons exist and behave in atoms helps us understand and predict the properties of atoms that are directly related to the behavior of the electrons why some elements are metals while others are nonmetals why some elements gain 1 electron when forming an anion, while others gain 2 why some elements are very reactive while others are practically inert and other Periodic patterns we see in the properties of the elements

One of the ways that energy travels through space: – Light from sun; microwave oven; radiowaves for MRI mapping • Exhibit the same type of wavelike behavior and travel at the speed of light in a vacuum • It has electric and magnetic fields that simultaneously oscillate in planes mutually perpendicular to each other and to the direction of propagation through space. Electromagnetic radiation has oscillating electric (E) and magnetic (H) fields in planes

The Nature of Light its Wave Nature light is a form of electromagnetic radiation composed of perpendicular oscillating waves, one for the electric field and one for the magnetic field an electric field is a region where an electrically charged particle experiences a force a magnetic field is a region where an magnetized particle experiences a force all electromagnetic waves move through space at the same, constant speed 3.00 x 108 m/s in a vacuum = the speed of light, c

Characterizing Waves the number of waves = number of cycles Waves are characterized by wavelength, frequency, and speed. – wavelength (λ) is the distance between two consecutive peaks or troughs in a wave. – frequency (ν) is defined as the number of waves (cycles) per second - is a measure of the distance covered by the wave the distance from one crest to the next the number of waves = number of cycles units are hertz, (Hz) or cycles/s = s-1 1 Hz = 1 s-1 the amplitude is the height of the waVe the distance from node to crest or node to trough the amplitude is a measure of how intense the light is – the larger the amplitude, the brighter the light

Amplitude & Wavelength Dim light Bright light

Interference the interaction between waves is called interference when waves interact so that they add to make a larger wave it is called constructive interference waves are in-phase when waves interact so they cancel each other it is called destructive interference waves are out-of-phase

Diffraction when traveling waves encounter an obstacle or opening in a barrier that is about the same size as the wavelength, they bend around it – this is called diffraction traveling particles do not diffract the diffraction of light through two slits separated by a distance comparable to the wavelength results in an interference pattern of the diffracted waves an interference pattern is a characteristic of all light waves

2-Slit Interference

The Relationship Between Wavelength and Frequency for waves traveling at the same speed, the shorter the wavelength, the more frequently they pass this means that the wavelength and frequency of electromagnetic waves are inversely proportional since the speed of light is constant, if we know wavelength we can find the frequency, and visa versa Calculate the wavelength of red light with a frequency of 4.62 x 1014 s-1 A laser dazzels the audience in a rock concert by emitting green light with a wave length of 515 nm. Calculate the frequency of the light

Color the color of light is determined by its wavelength or frequency white light is a mixture of all the colors of visible light a spectrum RedOrangeYellowGreenBlueViolet when an object absorbs some of the wavelengths of white light while reflecting others, it appears colored the observed color is predominantly the colors reflected

The Electromagnetic Spectrum visible light comprises only a small fraction of all the wavelengths of light – called the electromagnetic spectrum short wavelength (high frequency) light has high energy radiowave light has the lowest energy gamma ray light has the highest energy high energy electromagnetic radiation can potentially damage biological molecules ionizing radiation

The Photoelectric Effect it was observed that many metals emit electrons when a light shines on their surface this is called the Photoelectric Effect classic wave theory attributed this effect to the light energy being transferred to the electron according to this theory, if the wavelength of light is made shorter, or the light waves intensity made brighter, more electrons should be ejected in experiments with the photoelectric effect, it was observed that there was a maximum wavelength for electrons to be emitted called the threshold frequency regardless of the intensity it was also observed that high frequency light with a dim source caused electron emission without any lag time

Particlelike Properties of Electromagnetic Energy Refers to the phenomenon in which electrons are emitted from the surface of a metal when light strikes it: – No electrons are emitted by a given metal below a specific threshold frequency νo. – For light with frequency lower than the threshold frequency, no electrons are emitted regardless of the intensity of the light. – For light with frequency greater than the threshold frequency, the number of electrons emitted increases with the intensity of the light. – For light with frequency greater than the threshold frequency, the kinetic energy of the emitted electrons increases linearly with the frequency of the light.

Einstein’s Explanation Energy is in fact quantized and can be transferred only in discrete units of size hν. A system can transfer energy only in whole quanta Einstein proposed that the light energy was delivered to the atoms in packets, called quanta or photons the energy of a photon of light was directly proportional to its frequency inversely proportional to it wavelength the proportionality constant is called Planck’s Constant, (h) and has the value 6.626 x 10-34 J∙s

Kinetic Energy = Ephoton – Ebinding Ejected Electrons 1 photon at the threshold frequency has just enough energy for an electron to escape the atom binding energy, f for higher frequencies, the electron absorbs more energy than is necessary to escape this excess energy becomes kinetic energy of the ejected electron Kinetic Energy = Ephoton – Ebinding KE = hn - f

Examples he blue color in fireworks is often achieved by heating copper(I) chloride (CuCl) to about 1200°C. The hot compound emits blue light having a wave- length of 450 nm. What is the increment of energy (the quantum) tha is emitted at 450 nm by CuCl? What is the energy (in kJ/mol) of photons of radar waves with ν = 3.35 x 108 Hz? Calculate the number of photons in a laser pulse with wavelength 337 nm and total energy 3.83 mJ What is the frequency of radiation required to supply 1.0 x 102 J of energy from 8.5 x 1027 photons?

Spectra when atoms or molecules absorb energy, that energy is often released as light energy fireworks, neon lights, etc. when that light is passed through a prism, a pattern is seen that is unique to that type of atom or molecule – the pattern is called an emission spectrum non-continuous can be used to identify the material Rydberg analyzed the spectrum of hydrogen and found that it could be described with an equation that involved an inverse square of integers However, his equation gave little information into why atomic spectra were discrete, why atoms are stable, or why his equation worked

Examples of Spectra Oxygen spectrum Neon spectrum

Emission vs. Absorption Spectra Spectra of Mercury

Bohr’s Model Neils Bohr proposed that the electrons could only have very specific amounts of energy fixed amounts = quantized the electrons traveled in orbits that were a fixed distance from the nucleus stationary states therefore the energy of the electron was proportional the distance the orbital was from the nucleus electrons emitted radiation when they “jumped” from an orbit with higher energy down to an orbit with lower energy the distance between the orbits determined the energy of the photon of light produced

Bohr Model of H Atoms

Wavelike Properties of Matter Chapter 5: Periodicity and Atomic Structure Wavelike Properties of Matter 11/25/2018 Energy is really a form of matter, and all matter exhibits both particulate and wave properties. –Large “pieces” of matter, such as base balls, exhibit predominantly particulate properties –Very small “pieces” of matter, such as photon, while showing some particulate properties through relativistic effects, exhibit dominantly wave properties –“Pieces” of intermediate mass, such as electrons, show both the particulate and wave properties of matter Louis de Broglie in 1924 suggested that, if light can behave in some respects like matter, then perhaps matter can behave in some respects like light. In other words, perhaps matter is wavelike as well as particlelike. mv h l = Copyright © 2008 Pearson Prentice Hall, Inc.

examples What velocity would an electron (mass = 9.11 x 10-31kg) need for its de Broglie wavelength to be that of red light (750 nm)? What is the velocity of an electron having a de Broglie wavelength that is approximately the length of a chemical bond? Assume this length to be 1.2 x 10-10 m Determine the wavelength of a neutron traveling at 1.00 x 102 m/s (Massneutron = 1.675 x 10-24 g)

Quantum Mechanics and the Heisenberg Uncertainty Principle Heisenberg Uncertainty Principle – both the position (Δx) and the momentum (Δmv) of an electron cannot be known beyond a certain level of precision 1. (Δx) (Δmv) > h 4π 2. Cannot know both the position and the momentum of an electron with a high degree of certainty 3. If the momentum is known with a high degree of certainty i. Δmv is small ii. Δ x (position of the electron) is large 4. If the exact position of the electron is known i. Δmv is large ii. Δ x (position of the electron) is small

Determinacy vs. Indeterminacy according to classical physics, particles move in a path determined by the particle’s velocity, position, and forces acting on it determinacy = definite, predictable future because we cannot know both the position and velocity of an electron, we cannot predict the path it will follow indeterminacy = indefinite future, can only predict probability the best we can do is to describe the probability an electron will be found in a particular region using statistical functions