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## LIGHT and Planck's Constant

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**LIGHT and Planck's Constant**DO NOW: Using your textbooks answer the following What is mass spectrometry and how is it used? Define light What is the formula for Planck’s constant and what does each variable represent**The study of light led to the development of the quantum**mechanical model. • Light is a kind of electromagnetic radiation. (radiant energy) • Electromagnetic radiation includes many kinds of waves • All move at 3.00 x 108 m/s ( c) Light**Crest**Wavelength Amplitude Trough Orgin Parts of a wave**Orgin - the base line of the energy.**• Crest - high point on a wave • Trough - Low point on a wave • Amplitude - distance from origin to crest • Wavelength - distance from crest to crest • Wavelength - is abbreviated l Greek letter lambda. Parts of Wave**Waves**• To understand the electronic structure of atoms, one must understand the nature of electromagnetic radiation. • The distance between corresponding points on adjacent waves is the wavelength().**Waves**• The number of waves passing a given point per unit of time is the frequency (). • For waves traveling at the same velocity, the longer the wavelength, the smaller the frequency.**Electromagnetic Radiation**• All electromagnetic radiation travels at the same velocity: the speed of light (c), 3.00 108 m/s. • Therefore, c = **The number of waves that pass a given point per second.**• Units are cycles/sec or hertz (hz) • Abbreviated n the Greek letter nu c = ln Frequency**Are inversely related**• As one goes up the other goes down. • Different frequencies of light is different colors of light. • There is a wide variety of frequencies • The whole range is called a spectrum Frequency and wavelength**High energy**Low energy Low Frequency High Frequency X-Rays Radiowaves Microwaves Ultra-violet GammaRays Infrared . Long Wavelength Short Wavelength Visible Light**Energy is quantized.**• Light is energy • Light must be quantized • These smallest pieces of light are called photons. • Energy and frequency are directly related. Light is a Particle**E = h x n**• E is the energy of the photon • n is the frequency • h is Planck’s constant • h = 6.6262 x 10 -34 Joules sec. • joule is the metric unit of Energy Energy and frequency**The Nature of Energy**• The wave nature of light does not explain how an object can glow when its temperature increases. • Max Planck explained it by assuming that energy comes in packets called quanta.**The Math**• Only 2 equations • c = λν • E = hν • Plug and chug.**The Nature of Energy**• Einstein used this assumption to explain the photoelectric effect. • He concluded that energy is proportional to frequency: E = h where h is Planck’s constant, 6.63 10−34 J-s.**The Nature of Energy**• Therefore, if one knows the wavelength of light, one can calculate the energy in one photon, or packet, of that light: c = E = h**What is the wavelength of blue light with a frequency of 8.3**x 1015hz? • What is the frequency of red light with a wavelength of 4.2 x 10-5 m? • What is the energy of a photon of each of the above? Examples**HW**6.11, 6.12, 6.14, 6.17, 6.18**The Nature of Energy**Another mystery involved the emission spectra observed from energy emitted by atoms and molecules.**The Nature of Energy**• One does not observe a continuous spectrum, as one gets from a white light source. • Only a line spectrum of discrete wavelengths is observed.**Waves**• To understand the electronic structure of atoms, one must understand the nature of electromagnetic radiation. • The distance between corresponding points on adjacent waves is the wavelength().**Waves**• The number of waves passing a given point per unit of time is the frequency (). • For waves traveling at the same velocity, the longer the wavelength, the smaller the frequency.**Electromagnetic Radiation**• All electromagnetic radiation travels at the same velocity: the speed of light (c), 3.00 108 m/s. • Therefore, c = **The Nature of Energy**• The wave nature of light does not explain how an object can glow when its temperature increases. • Max Planck explained it by assuming that energy comes in packets called quanta.**The Nature of Energy**• Einstein used this assumption to explain the photoelectric effect. • He concluded that energy is proportional to frequency: E = h where h is Planck’s constant, 6.63 10−34 J-s.**The Nature of Energy**• Therefore, if one knows the wavelength of light, one can calculate the energy in one photon, or packet, of that light: c = E = h**The Nature of Energy**Another mystery involved the emission spectra observed from energy emitted by atoms and molecules.**The Nature of Energy**• One does not observe a continuous spectrum, as one gets from a white light source. • Only a line spectrum of discrete wavelengths is observed.**The Nature of Energy**• Niels Bohr adopted Planck’s assumption and explained these phenomena in this way: • Electrons in an atom can only occupy certain orbits (corresponding to certain energies).**Atomic Spectrum**How color tells us about atoms**Atomic Spectrum**How color tells us about atoms**Prism**• White light is made up of all the colors of the visible spectrum. • Passing it through a prism separates it.**If the light is not white**• By heating a gas with electricity we can get it to give off colors. • Passing this light through a prism does something different.**Atomic Spectrum**• Each element gives off its own characteristic colors. • Can be used to identify the atom. • How we know what stars are made of.**These are called discontinuous spectra**• Or line spectra • unique to each element. • These are emission spectra • The light is emitted given off.**The Nature of Energy**Another mystery involved the emission spectra observed from energy emitted by atoms and molecules.**The Nature of Energy**• One does not observe a continuous spectrum, as one gets from a white light source. • Only a line spectrum of discrete wavelengths is observed.**The Nature of Energy**• Niels Bohr adopted Planck’s assumption and explained these phenomena in this way: • Electrons in an atom can only occupy certain orbits (corresponding to certain energies).**The Nature of Energy**• Niels Bohr adopted Planck’s assumption and explained these phenomena in this way: • Electrons in permitted orbits have specific, “allowed” energies; these energies will not be radiated from the atom.**The Nature of Energy**• Niels Bohr adopted Planck’s assumption and explained these phenomena in this way: • Energy is only absorbed or emitted in such a way as to move an electron from one “allowed” energy state to another; the energy is defined by E = h**1**nf2 ( ) - E = −RH 1 ni2 The Nature of Energy The energy absorbed or emitted from the process of electron promotion or demotion can be calculated by the equation: where RH is the Rydberg constant, 2.18 10−18 J, and ni and nf are the initial and final energy levels of the electron.**h**mv = • Louis de Broglie posited that if light can have material properties, matter should exhibit wave properties. • He demonstrated that the relationship between mass and wavelength was The Wave Nature of Matter**h**4 (x) (mv) • Heisenberg showed that the more precisely the momentum of a particle is known, the less precisely is its position known: • In many cases, our uncertainty of the whereabouts of an electron is greater than the size of the atom itself! The Uncertainty Principle**Quantum Mechanics**• Erwin Schrödinger developed a mathematical treatment into which both the wave and particle nature of matter could be incorporated. • It is known as quantum mechanics.**Quantum Mechanics**• The wave equation is designated with a lower case Greek psi (). • The square of the wave equation, 2, gives a probability density map of where an electron has a certain statistical likelihood of being at any given instant in time.**Solving the wave equation gives a set of wave functions, or**orbitals, and their corresponding energies. • Each orbital describes a spatial distribution of electron density. • An orbital is described by a set of three quantum numbers. Quantum Numbers**The principal quantum number, n, describes the energy level**on which the orbital resides. • The values of n are integers ≥ 0. Principal Quantum Number, n**This quantum number defines the shape of the orbital.**• Allowed values of l are integers ranging from 0 to n − 1. • We use letter designations to communicate the different values of l and, therefore, the shapes and types of orbitals. Azimuthal Quantum Number, l**Describes the three-dimensional orientation of the orbital.**• Values are integers ranging from -l to l: −l ≤ ml≤ l. • Therefore, on any given energy level, there can be up to 1 s orbital, 3 p orbitals, 5 d orbitals, 7 f orbitals, etc. Magnetic Quantum Number, ml