Today’sConcepts:BohrAtomicModel

Electricity & MagnetismLecture 30

Presentation Created by Dr. Adam Lark

Things you asked about:

“ThisactuallykindofmadesenseconsideringIhavedonethisallinchemistry.”

“Isthisreallynecessarytolearnthisinthiscourse??““Couldyoupleaseexplaintherelationshipbetweenthewavelengthsandatomicorbitals??”“Ilikedthisone.”

Question

“Pleaseexplainall4quantumnumbersthattheylistedintheprelecture.”

Rutherford Scattering

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Ifpositiveandnegativechargesarerandomlydistributedinatoms

Apositivelychargedalphaparticlewillnotbedeflectedbecausethenetchargeisclosetozero.

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Ifthepositiveandnegativechargeareseparatedinanatom

Apositivelychargedalphaparticlewillbedeflectedsomeofthetime.

α+

+-α+

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ElectronsmustorbittheProtons!

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Bridge Question 1

Which of the following scattering patterns correspond to the model of the atom proposed by Rutherford?

Thealphaparticlesmustscatterinall

directions.

Diffraction Grating Spectrometer

Hydrogenlamp

Diffraction Grating spectrometer

VisibleSpectralLinesofHydrogen

BalmerSeries,n=2

m

Aregularpatternoflineswasobserved.

Rydberg Formula

RH=1.097x107m-1

ThewavelengthofthatlightcanbefoundusingtheRydbergformula:

m=initialorbit

n=finalorbit

Rydberg Formula

IntheBohrmodelforthehydrogenatom,whatisthewavelengthofthelightproducedbyanelectronfallingfromthestate,n=3,tothegroundlevel,n=1?.(A)102nm

(B)1367nm

(C)1823nm

(D)102nm

(E)Noneoftheabove

RH=1.097x107m-1

λ apx= 1x 10–7m

Bohr Atomic Model (Hydrogen)

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Electronsinanatomareconfinedtospecificorbits

Whenelectronsjumpfromoneorbittoanother,energyisgainedorlostintheformoflight!

Eachorbithasanenergyassociated

withit:

RydbergEnergy

forn=1:E=E0

E0=2.18x10-18J

forn=1:rn=a0

BohrRadius

Eachorbithasaradiusassociated

withit:

de Broglie orbits

Hypothesis:Wavelengthsofelectronsarerelatedtoenergyandonlyorbitswithintegerwavelengthsareallowed.

E=hf=hc/λλ=hc/E

Bohr Atomic Model

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RadiusandEnergyScalewithZ,thenumberofprotonsinthenucleus

Energy: Radius:

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E0=2.18x10-18J

Bridge Question 2

A drawing of the Bohr model of electron orbits in the Hydrogen atom is shown.

Bridge Question 2a

Which of the following will cause an electron transition from n = 1 to n = 2?

A. AphotonwithenergyEphoton=13.6eVB. AphotonwithenergyEphoton=3.4eVC. AnyphotonwithenergyEphoton<10.2eVD. AphotonwithenergyEphoton=11eVE. Noneoftheabove

Bridge Question 2a Explanation

EI=-13.6eV

EF=-3.4eV

Ephoton=10.2eV

AnswerC?

Thephotonmusthaveenergyexactlyequalto10.2eV

AnswerE!

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Bridge Question 2b

Which of the following transitions will emit a photon with the longest wavelength? Fromn=4ton=3

Fromn=3ton=2

Fromn=2ton=1

Lowerenergy=lowerfrequency

Ephoton=hf

lowerfrequency=longerwavelength

h=4.13×10−15eV⋅s=6.63×10−34 J⋅s

Bridge Question 3

How many possible wavelengths could be observed when a hydrogen atom initially excited to the n = 4 state returns to the ground state?

A. 2 B. 3 C. 4 D. 5 E. 6

n=4 ton=1n=4 ton=2

n=3 ton=1 n=3 ton=2

n=2 ton=1

n=4 ton=3Orbits: 4 3 2 1

Bridge Question 4

AccordingtotheBohrmodel,whichoftheionslistedinthetablebelowwouldhavethesmallestdistancebetweenanelectroninthelowestenergylevelandthenucleus?

A. He

B. Li

C. Be

D. B

LargestZ,smallestr!

Simulation

Hydrogenatomsimulation