Wlesson 3 Sp 2020 electromagnetic spectra and atomic spectra PDF

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ELECTROMAGNETICRADIATION ANDBOHRMODELOFTHEATOM Pleasespendextratimeunderstandingandlearningthematerialontheslideswith*

DimensionalAnalysis Theprocessofunitconversionisfacilitatedusingdimensionalanalysis. Unit factors are utilized in this process and are made from any two equivalent factors. StudentProblem(thisproblemwillnotbedoneinlecture) Convert619nmtomknowingthat109nm=1m

ElectromagneticRadiationandElectromagneticSpectrum • Electromagnetic radiation is the emission and absorption of energy in the form of electromagnetic waves. This type of energy therefore has wavelength, frequency and speed.

• Theelectromagneticspectrumisacontinuous (uninterrupted)band ofvisibleandinvisiblelightthatrangesfromshorttolong wavelengths.

ElectromagneticSpectrum

Wavelength,FrequencyandAmplitude

* Wavelength (symbol: , pronounced lambda, units: m) is the distance between two peaks or troughs in the wave. Frequency (symbol: , pronounced nu, units: s‐1 which is called Hz) is the number of wavelengths per second that travel past a given point. Amplitude: Vertical distance from the midline of a wave to the peak or trough.

RelationshipbetweenFrequencyandWavelength

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The product of frequency () and wavelength () always equals a constant, c, the speed of light:

c=  c=2.998x108m/s

Attimes,cisrequiredintermsofnm:c=2.998x1017 nm/s

As frequency increases, the wavelength decreases; thus they are inversely related.

Problem A radio station broadcasts at 580. kHz. What is the wavelength (in meters) of this radio signal ? c = 2.998 x 108 m/s

1000 Hz = 1kHz

,units:s‐1 whichiscalledHz

c= 

QuantizedEnergyAnalogy Quantum: The smallest quantity of energy that can be emitted or absorbed in the form of electromagnetic radiation. ContinuousEnergy:Anyamountofenergycanbemeasured. Energyisquantized:onlycertainenergiesareallowed. A ramp is analogous to continuous energy – you can sit at any position along a ramp and thus be at any elevation between the two levels. Stairs, however, are analogous to quantized energy – you can only sit at certain elevations between the two levels and nowhere in between. You may sit only on the steps, not in between the steps. Only certain elevations are allowed.

QuantizedEnergy

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Max Planck postulated that energy could be gained or lost only in whole number multiples of the quantity h .

He related the energy of radiation emitted or absorbed to its frequency using the equation:

Planck’sEquation: Energyof radiation(J)

E=h

frequency

Planck’sconstant (h=6.626x10‐34J•s) (h=6.626x10‐34kg•m2/s)

Note:SometexthaveE=nh wherenisapositiveinteger(1,2,3,etc.)calledaquantumnumber

QuantizedEnergy

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• Each change in an atom’s energy occurs when the atom absorbs or emits one or more “packets” of energy. Each packet is called a quantum.

•

A quantum of energy is equal to h .

• An atom changes its energy state by emitting (or absorbing) one or more quanta (plural of quantum), and the energy of the emitted (or absorbed) radiation is equal to the difference in the atom’s energy states, i.e. E = h .

EnergyasParticles

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Albert Einstein proposed that electromagnetic radiation is itself quantized and can be viewed as a stream of “particles” called photons.

• Hededucedtheenergyofaphotonusing:

• Note that energy is inversely related to wavelength, and directly related to frequency.

Problem An electron emitted light having an energy of 3.025 x 10‐19 J. What is the wavelength of this light in nm? h=6.626x10‐ 34J•s,c=2.998x1017 nm/s,E=h =h(c/)

DualNatureofLight

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• Einstein and Planck proved that electromagnetic radiation exhibits wavelike AND particulate properties (wave‐particle duality). • de Broglie then proved that matter exhibits particulate AND wavelike properties. • Foraparticlewithvelocity,u:

• Wavelengthofaparticle: deBroglie’sEquation

Problem What is the deBroglie’s wavelength (in m) of a 142 g baseball thrown at 44 m/s?

h=6.626x10‐ 34J•s,1J=1kg(m2/s2), =h/(mu) ,1000g=1kg

Whatdowenowknowaboutmatterandenergy? MatterandenergyareNOTdistinct. Energy is a form of matter and all matter exhibits both the properties of waves AND of particles. Large pieces of matter exhibits particulate properties with an associated wavelength that is so small that it is not observed. Its wave‐like properties are not considered. Small pieces of matter exhibit wave properties predominantly and some particulate properties.

Bohr’sModeloftheAtom ContinuousSpectrum

white light prism

White light passed through a prism produces a spectrum of color that contains all of the wavelengths of visible light. This is why the spectrum is called continuous.

LineEmissionSpectrumofHydrogen

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*

TheBohrModeloftheAtom

Bohrpostulated:

• Theelectroninahydrogenatomcirclesthe

Bohrmodelof hydrogenatom

nucleusoftheatomincircularorbits(energylevels)thatarequantized. • Theenergyoftheelectroninhydrogenisquantizedanddependson theorbititoccupies.

• The energy of the electron in a given orbit is proportional to its distance from the nucleus.

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TheBohrModeloftheHydrogenAtom:EnergyLevels

• Energylevels:n=1< n=2< n=3... n=1

ground energystate

stable

n>1

excited energystates

unstable

n=∞

electronleavesatom

n= Quantumnumber

LineEmissionSpectrumofHydrogen

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TransitionsresponsibleforBalmer/visibleseries The Balmer series of lines is caused by electrons dropping from outer orbits to the n = 2 orbit.

Fourlinesinthevisibleregion: • red (656nm)(32) • blue‐green (486nm)(42) • blue‐violet (434nm)(52) • violet(410nm)(62)

These lines provide evidence that changes in energy between discrete energy levels in hydrogen will produce only certain wavelengths of light, i.e. the energy of the electron is quantized.

SpectralLinesEmittedbytheHatom

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NameofSeries

Causedbyelectrons droppingfromouter orbitsto

LymanorUVseries

n=1orbit

Balmerorvisibleseries

n=2orbit

Paschen orinfrared series

n=3orbit

Brackettseries

n=4orbit

Pfund series

n=5orbit

WhatHappensWhenanElectronAbsorbsEnergy?

* photon Electronabsorbsphoton andgoestoahigherenergy level,inthiscase,n=3

n=1

nucleus n=2 n=3

WhatHappensWhenanElectronEmitsEnergy?

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Electronemitsphoton andgoestoalower energylevel,inthis case,n=1

photon

n=1

nucleus n=2

n=3

EnergyAbsorptionandEmission Orbitwithenergy,E2

Energyabsorbed= Energyemitted =E2‐ E1

Orbitwithenergy,E1

Whenenergyis

When energy is

absorbed, Ehas

emitted, E has

apositive value.

a negative value.

Frequencyoflightabsorbed= = Frequencyoflightemitted= =

୉ଶି୉ଵ ୦

୉ଶି୉ଵ ୦

E=E2 – E1 E=h

CalculatingEnergyChanges

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The energy change when the electron in a hydrogen atom moves from one energy level to another can be calculated with:

2.178x10‐18J (Ryberg constant)

ni =initialenergylevel nf =finalenergylevel

nuclearcharge=atomicnumber (H=+1)

Problem: What is the wavelength, in nm, of light emitted when the electron in the hydrogen atom moves from n = 4 to n = 2 ? Give your answer to 3 sig. figs.

ΔE=‐ 2.178x10 – 18JZ2

1 1 nf2 ni2

E=h =hc/  h=6.626x10‐ 34J•s c=2.998x1017 nm/s

CalculatingEnergyChanges

* Thisequationcanonlybeusedforoneelectronspecies,likehydrogen.

Example:He+ andC5+ bothhaveoneelectron,thereforethisformulacould beusedtocalculateenergychanges.ThevalueofZthatwouldbeusedin thisformulaforHe+ andC5+ wouldbe+2and+6,respectively.

LineSpectra

He Ne Na Hg Everyelementhasauniquelineoremissionspectrum

Bohr’sModeloftheAtomisFundamentallyIncorrect

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Bohr’s model cannot account for the emission spectra of atoms containing more than one electron. Thismodelonlyworksfor1electronsystems. Example:H,He+,Li2+,etc.

It is important to note however, that the current theory of atomic structure, despite not being derived from the Bohr model, does include his postulate that the energy levels in atoms are quantized....