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UMass Amherst CHEM 110 - Light and Structure of Atom

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Light and Structure of Atom● Energy associated with movement of electrons can be converted to light. The location ofelectrons in an atom are described in terms of a wave model and probabilities.● Light is an electromagnetic wave, that travels in a manner similar to the waves in theocean● Wavelength: The distance from one peak to the next.● Frequency: The number of complete waves/peaks that pass a point in space in a giventime.● The longer the wavelength, the lower the frequency; the higher the frequency, theshorter the wavelength.● Speed is the same for frequencies.● Electromagnetic Spectrum○ Violet:■ Frequency: 7.5 x 10^14■ Wavelength: 400 nm○ Indigo:■ Wavelength: 425 nm○ Blue:■ Wavelength: 470 nm○ Green:■ Frequency: 5.4 x 10^14■ Wavelength: 550 nm○ Yellow:■ Wavelength: 600 nm○ Orange:■ Frequency: 4.8 x 10^14■ Wavelength: 630 nm○ Red:■ Frequency: 4.5 x 10^14■ Wavelength: 665 nm● λν = c, λ = c/v, v = c/λ○ λ: wavelength, [ m ]○ ν: frequency, [ sec^-1(events per second), or Hz(hertz) ]■ 1 kHz = 10^3 sec^-1■ 1 MHz = 10^6 sec^-1○ c: speed of light [3.0 x 10^8 m/s]● Amplitude: Intensity of light.● Photoelectric Effect: The ejection of electrons from the metal does not depend on theintensity of the light, but only on the frequency of the light.● Photons: Packets of energy.○ Max Planck proposed that, light travels in discrete packets of energy, calledphotons○ The energy of a single packet is related to the frequency of the light● Ephoton = hν, v = E/h○ Ephoton: energy of the photon [ J ]■ 1 kJ = 1000 J○ ν: frequency, [s-1, Hz]○ h: Planck’s constant [6.626 x 10^-34 J*s]● λ = hc/E, E= hc/λ○ λ: Wavelength [ m ]■ Meters to nanometers, multiply by 10^9■ Nanometers to meters, divide by 10^9■ Wavelength is always positive, so take absolute value of answer.○ h: Planck’s constant [6.626 x 10^-34 J*s]○ c: speed of light [3.0 x 10^8 m/s]○ E: energy of the photon [ J ]● If a photon has low energy, it will be unable to knock an electron out of the metal. Aphoton of high energy (high frequency) can lead to the ejection of electrons.● The higher the frequency the higher the energy and shorter the wavelength.● Heisenberg Uncertainty Principle: “The position and the velocity of an electron cannotboth be measured exactly, at the same time”● Energy is Quantized:○ Energy can only exist at specific energy levels, like steps and not anywherebetween them. Instead of a smooth transition, there are certain steps thatmolecules have to go through from one energy level to another.○ These fixed levels are called quanta (plural quantum)● Quantum Mechanics: de Broglie Wavelength○ All matter and radiation display both wavelike and particle-like properties○ The characteristic wavelength of matter is given by the de Broglie equation○ De Broglie equation: λ = h / mv■ λ: wavelength, [ m ]■ m: mass of particle, [ kg ]■ v: velocity of particle, [ m/s ]■ h: Planck’s constant, [6.626 x 10-34 J.s or kg x m^2 / s]● The Schrodinger Equation: Cloud Model of Atom○ An electron is described by a wave function (Ψ)○ The probability of finding an electron around the nucleus is given by square of thewave function (Ψ2)○ If we solve the Schrodinger equation for electrons at different energy levels, ittells us where electrons are most likely located around the nucleus.● Quantum Numbers○ Quantum numbers: A series of numbers that result from solving theSchrodinger equation.○ Each electron can be described by using four different quantum numbers (theseare kind of like an electron’s address)○ Each orbital can be described by using 3 different quantum numbers.● n (principal quantum number): Describes the size, energy of the shell and how far theelectron is from the nucleus. Tells us the shell number.○ Allowed values of n are positive integers (n = 1, 2, 3, 4, 5,……)○ Number of Orbitals in a Shell = n^2○ShellSubshell1L = 02L = 0, & 13L = 0, 1, 2○● L (angular momentum quantum number): Describes what kind of subshell theelectron is in. Each subshell has a different l value For a given value of n, I can rangefrom 0 to (n-1)●LSubshell# ofPlanarNodes0s01p12d23f3● S orbitals are spherical● P orbitals are dumbbell or figure 8 shaped● D orbitals are cloverleaf shaped● Atomic orbitals are regions of space around the nucleus where an electron is most likelyto be found● There are four different types of orbitals: s,p,d,f● Planar Nodes in Atomic Orbitals○ Nodes are regions of space where there is zero probability of finding an electron● ml (magnetic quantum number): Describes the orbital three dimensional orientation inspace● For a specific value of l, ml can have values that range from -L to +L● Number of Orbitals in a Sub shell = 2L + 1● ms (electron spin quantum number): Describes the spin of the electron● Allowed values of ms are +1/2 or -1/2● Any two electrons occupying the same orbital must have opposite spins● Electrons in atoms occupy only certain energy levels● Each energy level is assigned a number, known as the principal quantum number (n)● Atomic Absorption and Emission○ The energy of each quantum level is given by:■ En = - Rhc/n^2■ En = - Rhc x (1 / n^2final - 1 / n^2 initial)● En: energy of level n● R: Rydberg constant, [ 1.097x10^7 m-1 ]● h: Planck’s constant, [6.626 x 10-34 J.s]● c: speed of light [3.0 x 10^8 m/s]● n: Energy level● Hydrogen Atomic Line Spectra○ ν = c/λ■ Energy and wavelength are inversely related, the larger the energydifference the smaller the wavelength and the higher the frequency.○ The change in energy for each of the transition is given by:■ ΔE = Efinal – Einitial■ The sign of ΔE for absorption is (+) and (-) for emission■ ΔE = -Rhc(2.179 x 10^-18 J) x (1 / n^2final - 1 / n^2 initial)■ E_n = -Rhc / n^2● Emission:○ When going down levels, energy = Negative and smaller,longer wavelength and lower frequency.○ Long wavelength = low frequency = low energy transition =short line on the diagram.○ Longer the line, higher the energy.■ Negative answer indicates emission● Absorption:○ When going up levels, energy = Positive and larger,smaller wavelength, and higher frequency.○ Short wavelength = high frequency = high energy transition= long line on the diagram.■ Positive answer indicates

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