The existence of spectral lines is another important aspect of the atom that finds no explanation in classical physics

atomic spectra

1. Introduction to hydrogen atom spectrum
ATOMIC SPECTRA
Atomicstabilityisnottheonlythingthatasuccessfultheoryofthe
atommustaccountfor.
Theexistenceofspectrallinesisanotherimportantaspectofthe
atomthatfindsnoexplanationinclassicalphysics.
Condensedmatter(solidsandliquids)atalltemperaturesemitsem
radiationinwhichallwavelengthsarepresent,thoughwith
differentintensities.Theobservedfeaturesofthisradiationwere
explainedbyPlanckwithoutreferencetoexactlyhowitwas
producedbytheradiatingmaterialortothenatureof
thematerial.

2. Introduction to hydrogen atom spectrum

3. Introduction to hydrogen atom spectrum
Whenanatomicgasorvaporatsomewhatlessthanatmospheric
pressureissuitably“excited,”usuallybypassinganelectriccurrent
throughit,theemittedradiationhasaspectrumwhichcontains
certainspecificwavelengthsonly.Anidealizedarrangementfor
observingsuchatomicspectraisshowninFig.;

4. Introduction to hydrogen atom spectrum

5. Introduction to hydrogen atom spectrum

6. Introduction to hydrogen atom spectrum
Abovefigureshowstheemissionlinespectraofseveral
elements.Everyelementdisplaysauniquelinespectrumwhena
sampleofitinthevaporphaseisexcited.
Spectroscopyisthereforeausefultoolforanalyzingthe
compositionofanunknownsubstance.

7. Introduction to hydrogen atom spectrum
Whenwhitelightispassedthrougha
gas,thegasisfoundtoabsorblightof
certainofthewavelengthspresentin
itsemissionspectrum.
Theresultingabsorptionline
spectrumconsistsofabright
backgroundcrossedbydarklinesthat
correspondtothemissing
wavelengths(Fig.);emissionspectra
consistofbrightlinesonadark
background.
Thespectrumofsunlighthasdark
linesinitbecausetheluminouspart
ofthesun,whichradiatesverynearly

8. Introduction to hydrogen atom spectrum
likeablackbodyheatedto5800K,issurroundedbyanenvelopeof
coolergasthatabsorbslightofcertainwavelengthsonly.Most
otherstarshavespectraofthiskind.
Thenumber,intensity,andexactwavelengthsofthelinesinthe
spectrumofanelementdependupontemperature,pressure,the
presenceofelectricandmagneticfields,andthemotionofthe
source.
Itispossibletotellbyexaminingitsspectrumnotonlywhat
elementsarepresentinalightsourcebutmuchabouttheirphysical
state.
Anastronomer,forexample,canestablishfromthespectrumofa
starwhichelementsitsatmospherecontains,whethertheyare
ionized,andwhetherthestarismovingtowardorawayfromthe
earth.

9. Introduction to hydrogen atom spectrum
Spectral Series
Acenturyagothewavelengthsinthespectrumofanelementwere
foundtofallintosetscalledspectralseries.
SuchserieswasdiscoveredbyJ.J.Balmerin1885inthecourseofa
studyofthevisiblepartofthehydrogenspectrum.Figureshowsthe
Balmerseries.
Thelinewiththelongestwavelength,656.3nm,isdesignatedH!,
thenext,whosewavelengthis486.3nm,isdesignatedH",andso
on.
Asthewave-lengthdecreases,thelinesarefoundclosertogether
andweakerinintensityuntiltheserieslimitat364.6nmisreached,
beyondwhichtherearenofurtherseparatelinesbutonlyafaint
continuousspectrum.Balmer’sformulaforthewavelengthsofthis
seriesis

10. Introduction to hydrogen atom spectrum

11. Introduction to hydrogen atom spectrum
TheBalmerseriescontainswavelengthsinthevisibleportionofthe
hydrogenspectrum.
Thespectrallinesofhydrogenintheultravioletandinfraredregions
fallintoseveralotherseries.IntheultraviolettheLyman
seriescontainsthewavelengthsgivenbytheformula,

12. Introduction to hydrogen atom spectrum
Thesespectralseriesofhydrogenareplottedinterms
ofwavelengthinFig.
TheBrackettseriesevidentlyoverlapsthePaschenand
Pfundseries.
ThevalueofRisthesameinEqs.(4.6)to(4.10).

13. Introduction to hydrogen atom spectrum
ENERGY LEVELS AND SPECTRA
The various permitted orbits involve different electron energies. The
electron energy Enis given in terms of the orbit radius rnby Eq. as
Substituting for rnfrom Eqabove, we see that
TheenergiesspecifiedbyEq.(4.15)arecalledtheenergylevelsof
thehydrogenatomandareplottedinFig.4.15.Theselevelsareall
negative,whichsignifiesthattheelectrondoesnothaveenough
energytoescapefromthenucleus.Anatomicelectroncanhaveonly
theseenergiesandnoothers.Ananalogymightbeapersonona
ladder,whocanstandonlyonitsstepsandnotinbetween.

14. Introduction to hydrogen atom spectrum
ThelowestenergylevelE1iscalledthe
groundstateoftheatom,andthe
higherlevelsE2,E3,E4,...arecalled
excitedstates.
Asthequantumnumbernincreases,
thecorrespondingenergy
Enapproachescloserto0.Inthelimitof
n=∞,E∞=0andtheelectronisnolonger
boundtothenucleustoformanatom.
Apositiveenergyforanucleus-electron
combinationmeansthattheelectronis
freeandhasnoquantumconditionsto
fulfill;suchacombinationdoesnot
constituteanatom,ofcourse.

15. Introduction to hydrogen atom spectrum
Theworkneededtoremoveanelectronfromanatominitsground
stateiscalleditsionizationenergy.
Theionizationenergyisaccordinglyequalto-E1,theenergythat
mustbeprovidedtoraiseanelectronfromitsgroundstatetoan
energyofE=0,whenitisfree.Inthecaseofhydrogen,theionization
energyis13.6eVsincethe
ground-stateenergyofthehydrogenatomis-13.6eV.

16. Introduction to hydrogen atom spectrum
OriginofLineSpectra
Wemustnowconfronttheequationsdevelopedabovewith
experiment.Anespeciallystrikingobservationisthatatomsexhibit
linespectrainbothemissionandabsorption.Dosuchspectrafollow
fromourmodel?
Thepresenceofdiscreteenergylevelsinthehydrogenatomsuggests
theconnection.Letussupposethatwhenanelectroninanexcited
statedropstoalowerstate,thelostenergyisemittedasasingle
photonoflight.Accordingtoourmodel,electronscannotexistinan
atomexceptincertainspecificenergylevels.Thejumpofanelectron
fromoneleveltoanother,withthedifferenceinenergybetweenthe
levelsbeinggivenoffallatonceinaphotonratherthaninsome
moregradualmanner,fitsinwellwiththismodel.

17. Introduction to hydrogen atom spectrum
Spectral lines originate in transitions between
energy levels. Shown are the spectral series
of hydrogen. When n=∞ , the electron is free.

18. Introduction to hydrogen atom spectrum