Chm2045 Exam 3 Study Guide-2 PDF

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Exam 3 Study Guide CHM 2045 - Spring 2019

Chapter 7 7.1 Schrodinger’s Cat -

Electrons are small, and an atoms electrons determine many of its physical and chemical properties Scientists discovered that the absolutely small (or quantum) world of the electron behaves differently than the large (or macroscopic) world that we are used to observing Quantum- Mechanical Model: A model that explains the behavior of absolutely small particles such as electrons and photons

7.2 The Nature of Light -

Electromagnetic radiation: a type of energy embodied in oscillating electric and magnetic fields. - Described as a wave composed of oscillating, mutually perpendicular electric and magnetic fields propagating through space. - Light is electromagnetic radiation.

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Magnetic field: a region of space where a magnetic particle experiences a force (think of the space around a magnet). Electric field: a region of space where an electrically charged particle experiences a force. - Proton has a electric field around it. In a vacuum, these waves move at a constant speed of 3.00 x 10^8 m/s (186,000) Waves are characterized by amplitude and wavelength Amplitude: the vertical height of a crest ( or depth of a trough) - Determines the light’s intensity or brightness (greater amp, greater intensity) Wavelength: the distance between adjacent crest (or any two analogous points) - Measured in units such as meters, micrometers, or nanometers. Amplitude and wavelength can vary independently of one another. Frequency(v): the number of cycles (wave crest) that pass through a stationary point in a given period of time - Units of frequency are cycles per second or simply s^-1 or hertz (Hz), defined as 1 cycle/s. - Frequency of wave is directly proportional to the speed at which the wave is traveling. - Frequency is inversely proportional to the wavelength.

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Light equation: ν=cλ Nano= 10^-9 wavelengths determines color Electromagnetic spectrum: range of the wavelengths of all possible electromagnetic radiation.

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Gamma ray: the shortest wavelength on the electromagnetic radiation - High energy of gamma rays can damage biological molecules. X-rays: pass through many substances that block visible light and therefore used to image bones and internal organs. - Too much exposure to X-rays increases cancer risk. Ultraviolet (UV) radiation: the component of sunlight that produces a sunburn or suntan. Visible light: ranging from to red. Infrared (IR) radiation: the heat you feel when you place your near a hot object - Invisible to our eyes, infrared sensors can detect it. Microwaves: used for radar and in microwave ovens - Has longer wavelengths and therefore lower energies than visible or infrared light Radio waves: transmits the signals responsible for AM and FM radio, cellular telephone, television, and other forms of communication. Interference: how waves interact with each other Constructive interference: interaction of waves from two sources that align with overlapping crest, resulting in a waves of greater amplitude.

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Destructive interference: interaction of waves from two sources that are aligned so the crest of one overlaps the trough of the other, resulting in cancellation.

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Diffraction: also exhibit a characteristic

waves

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behavior. Photoelectric effect: the observation that many metal emit electrons when light shines upon them. The rate at which electrons leave the metal due to the photoelectric effect increases with increasing intensity of the light. The lag time would be the minimum amount of time required for the dim light to transfer sufficient energy to the electron to dislodge it. A packet of light is called a photon or a quantum. The energy of a photon can also be expressed in terms of wavelengths: E=hcλ

The kinetic energy (KE) of the ejected electron, therefore, is the difference between the energy of the photon (hv ), and the binding energy of the electron, as given by the equation: -

KE=hv−ϕ

7.3 Atomic Spectroscopy and Bohr Model -

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Atomic spectroscopy: the study of the electromagnetic radiation absorbed and emitted by atoms When an atom absorbs energy, in the form of heat, light, or electricity, it often re-emits that energy as light Atoms of each element emit light of a characteristic color - Ex: mercury emits blue, helium emits violet, hydrogen emits red The color of visible light is determined by its wavelength Emission Spectrum: the range of wavelengths emitted by a particular element; used to identify an element - Emission spectrum of a particular element is always the same The white light spectrum is continuous, there are no sudden interruptions in the intensity

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of the light as a function of wavelengths - The spectrum consists of light of all wavelengths The emission spectra of hydrogen, helium, and barium, however, are not continuous— they consist of bright lines at specific wavelengths, with complete darkness in between. Johannes Rydberg, a swedish mathematician, analyzed many atomic spectra and developed an equation that predicts the wavelengths of the hydrogen emission spectrum. The Rydberg equation is 1/λ=R(1/m^2−1/n^2), where R is the Rydberg constant (1.097×10^7m^−1) and m and n are integers. The Danish physicist Niels Bohr (1885–1962) attempted to develop a model for the atom that explained atomic spectra. - In his mode, electrons travel around the nucleus in circular orbits, however, these orbits only exist at specific, fixed distances from the nucleus. Bohr called these orbits stationary states - The energy of each Bohr orbit is also fixed, or quantized - Bohr also proposed that, in contradiction to classical electromagnetic theory, an electron orbiting the nucleus in a stationary state emits no radiation. It is only when an electron jumps, or makes a transition, from one stationary state to another that radiation is emitted or absorbed. - The electron is never observed between states, it is only observed in one state or another - The energy of the photon emitted when an electron makes a transition from one stationary state to another is the energy difference between the two stationary states. Transitions between stationary states that are closer together, therefore, produce light of lower energy (longer wavelength) than transitions between stationary states that are farther apart.

7.4 The Wave Nature of Matter -

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The heart of quantum-mechanical theory is the wave nature of the electrons. The interference pattern is not caused by pairs of electrons interfering with each other, but rather by single electrons interfering with themselves. The wave nature of the electron is an inherent property of individuals electrons. De Broglie relation: wavelength of an electron of mass(m) moving at velocity(v) is given by this: λ=hmv de Broglie relation H is Planck’s constant. 6.626x10^-36 Complementary properties: wave nature and particle nature of the electrons. - Exclude on another- the more we know about one, the less we know about other. Position of electron is related to particle nature. Velocity of an electron is related to its wave nature.

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Heisenberg’s uncertainty principle: states that the product of Δx and mΔv must be greater than or equal to a finite number(h/4pi). - Δx×mΔv≥h4π Heisenberg’s uncertainty principle

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Particles move in a trajectory that is determined by the particle’s velocity (the speed and direction of travel), its position, and the forces acting on it. Deterministic: characteristic of the classical laws of motion, which imply the present circumstances determine future events. In quantum mechanics, trajectories are replaced with probability distribution maps. A probability distribution map is a statistical map that shows where an electron is likely to be found under a given set of conditions. Indeterminacy: asserting that present circumstances do not necessarily determine future events in the quantum mechanical realm.

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7.5 Quantum Mechanics and the Atom

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The position and velocity of the electron are complementary properties. Since velocity is directly related to energy (recall that kinetic energy equals 1/2mv^2), position and energy are also complementary properties—the more we know about one, the less we know about the other. Orbital: A probability distribution map, based on the quantum-mechanical model of the atom, used to describe the likely position of an electron in an atom; also an allowed energy state for an electron. The mathematical derivation of energies and orbitals for electrons in atoms comes from solving the Schrödinger equation for the atom of interest. The general form of Schrodinger’s equation is

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Hψ=Eψ

The symbolℋ is the Hamiltonian operator, a set of mathematical operations that represents the total energy (kinetic and potential) of the electron within the atom. The symbol E is the actual energy of the electron. The symbol ψ is the wave function Wave Function: a mathematical foundation that describes the wavelike nature of the electron - A plot of the wave function squared represents an orbital Quantum Numbers (n): An integer that specifies the overall size and energy of an orbital. The higher the quantum number n, the greater the average distance between the electron and the nucleus and the higher its energy. Principal quantum number (n): An integer that specifies the overall size and energy of an orbital. Angular momentum quantum number (l): sometimes called the azimuthal quantum number… is an integer that specifies the overall size and energy of an orbital. Magnetic quantum number (ml): An integer that specifies the orientation of an orbital Spin quantum number (ms): denotes the electron’s spin as either ½ (up arrow) or -½ (down arrow)

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The principal quantum number is an integer that determines the overall size and energy of an orbital. Its possible values are n=1,2,3,...and so on. Notice that orbitals with higher values of n have greater (less negative) energies. Notice also that, as n increases, the spacing between the energy levels decreases. The possible values of l are 0,1,2,… ,(n−1). In other words, for a given value of n, l can be any integer (including 0) up to n−1.

The possible values of ml are the integer values (including zero) ranging from −l to +l. Electron spin is a fundamental property of an electron (like its negative charge). The orientation of the electron’s spin is quantized, with only two possibilities: that we can call spin up (ms=+1/2) and spin down (ms=−1/2).

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Each specific combination of the first three quantum numbers (n, l, and mlml) specifies one atomic orbital. Principal level: The group of orbitals with the same value of n. Sublevel (or Subshell): Those orbitals in the same principle level with the same value of n and l The number of sublevels in any level is equal to n, the principal quantum number. The number of orbitals in any sublevel is equal to 2l + 1 The number of orbitals in a level is equal to n^2 Each wavelength in the emission spectrum of an atom corresponds to an electron transition between quantum-mechanical orbitals. When an atom absorbs energy, an electron in a lower-energy orbital is excited or promoted to a higher-energy orbital The difference in energy between two levels

ninitial and nfinal is given by

ΔE=Efinal−Einitial -

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the atom is unstable, and the electron quickly falls back or relaxes to a lower-energy orbital. As it does so, it releases a photon of light containing an amount of energy precisely equal to the energy difference between the two energy levels. Since the wavelength of the photon is related to its energy as E=hc/λ, we calculate

the wavelength of the photon as: - λ=hc/E

7.6 The Shapes of Atomic Orbitals

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Probability density: three-dimensional plot of the wave function squared, the probability (per unit volume) of finding the electron at a point in space. - ψ2=probability density=probability/unit volume As you move away from the nucleus, the probability density decreases. Radial distribution function: a mathematical function (corresponding to a specific orbital) that represents the total probability of finding an electron within a thin spherical shell at a distance r from the nucleus. - Represents, not probability density at a point r, but total probability at a radius r. At the nucleus (r=0), for example, the probability density is at a maximum. Node: a point where the wave function and therefore the probability density and radial distribution function, and therefore the probability density and radial distribution function, all pass through zero. Phase: the sign of the amplitude of wave- positive or negative.

Chapter 8 8.1 Nerve Signal Transmission -

Periodic Property: A property of an element that is predictable based on an element’s position in the periodic table. The relative size of sodium and potassium ions is an example of a periodic property. The arrangement of elements in the periodic table—originally based on similarities in the properties of the elements—reflects how electrons fill quantummechanical orbitals.

8.2 The development of The Periodic Table -The first attempt to organize these elements according to similarities in their properties was made by the German chemist Johann Döbereiner (1780–1849), who grouped elements into triads: three elements with similar properties. -For example, Döbereiner formed a triad out of barium, calcium, and strontium, three fairly reactive metals -About 50 years later, English chemist John Newlands (1837–1898) organized elements into octaves, in analogy to musical notes. -The modern periodic table is credited primarily to the Russian chemist Dmitri Mendeleev, even though a similar organization had been suggested by the German chemist Julius Lothar Meyer (1830–1895). -Mendeleev’s table is based on the periodic law, which states that when elements are arranged in order of increasing mass, certain properties recur periodically. Mendeleev

arranged the elements in a table in which mass increases from left to right and elements with similar properties fall in the same columns. -The theory that explains the reasons behind the periodic law is quantum-mechanical theory. 8.3 Electron Configurations: How Electrons Occupy Orbital Quantum-mechanical theory- describes the behavior of electrons in atoms. -since chemical bonding involves the transfer or sharing of electrons, quantummechanical theory helps us understand and describe chemical behavior. Electron Configuration- a notation that shows the particular orbitals that electrons occupy for that atom. Ground State- The lowest energy state of an atom, ion, or molecule. -Electrons generally occupy the lowest energy orbitals available. The effects of electron spin- a fundamental property of all electrons that affects the number of electrons allowed in any one orbital. Sublevel energy splitting-which determines the order of orbital filling within a level Orbital Diagram-which gives similar information but symbolizes the electron as an arrow and the orbital as a box. -In an orbital diagram, the direction of the arrow (pointing up or pointing down) represents the orientation of the electron’s spin. Pauli exclusion principle,formulated by Wolfgang Pauli (1900–1958) in 1925:no two electrons in an atom can have the same four quantum numbers. Degenerate- A term describing two or more electron orbitals with the same value of n that have the same energy. -The orbitals within a principal level of a multielectron atom, in contrast, are not degenerate—their energy depends on the value of l. -In general, the lower the value of l within a principal level, the lower the energy (E) of the corresponding orbital. Coulomb’s law-which states that the potential energy (E) of two charged particles depends on their charges (q1q1 and q2q2) and on their separation (r). -In this equation, ε0ε0 is a constant (ε0=8.85×10−12 C2/J⋅mε0=8.85×10−12 C2/J⋅m). -The potential energy is positive for charges of the same sign (plus ×× plus, or minus ×× minus) and negative for charges of opposite sign (plus ×× minus, or minus ×× plus). -The magnitude of the potential energy depends inversely on the separation between the charged particles. -For like charges, the potential energy (E) is positive and decreases as the particles get farther apart (as r increases).

-For opposite charges, the potential energy is negative and becomes more negative as the particles get closer together (as r decreases). -The magnitude of the interaction between charged particles increases as the charges of the particles increase. Shielding(screening)-repulsion of one electron by other electrons. Effective Nuclear Charge- The actual nuclear charge experienced by an electron, defined as the charge of the nucleus plus the charge of the shielding electrons. Penetration-The phenomenon of some higher-level atomic orbitals having significant amounts of probability within the space occupied by orbitals. -as the outer electron undergoes penetration into the region occupied by the inner electrons, it experiences a greater nuclear charge and therefore (according to Coulomb’s law) a lower energy. FIGURE 8.3 Radial Distribution Functions for the 1 s, 2s, and 2p Orbitals

-Because of penetration, the sublevels of each principal level are not degenerate for multielectron atoms. -In the fourth and fifth principal levels, the effects of penetration become so important that the 4s orbital lies lower in energy than the 3d orbitals and the 5s orbital lies lower in energy than the 4d orbitals. -The energy separations between one set of orbitals and the next become smaller for 4s orbitals and beyond, and the relative energy ordering of these orbitals can actually vary among elements. FIGURE 8.4 Radial Distribution Functions for the 3 s, 3p, 3d Orbitals

ny -The 3s electrons penetrate most deeply into the inner orbitals, are least shielded, and experience the “greatest” effective nuclear charge. The 3 d electrons penetrate least. This accounts for the energy ordering of the sublevels: s...