Ukukhanya nama-spectrum e-athomu: ama-photon, amazinga amandla nemigqa ye-hydrogen

Ubude begagasi, i-frequency nejubane lokukhanya

Ukukhanya kuyigagasi le-electromagnetic. Ubude bayo begagasi λ yibanga phakathi kweziqongo, kanti i-frequency yayo ν yinani leziqongo ezidlula endaweni ethile ngomzuzwana ngamunye, ngama-hertz (s⁻¹). Ku-vacuum bonke ubude begagasi buhamba ngejubane elifanayo, c = 2.99792458 × 10⁸ m/s, inani eliqondile elichaziwe elibhalwe yi-NIST. La manani amathathu axhunywe ngo-c = λν, ngakho ubude begagasi ne-frequency kuhambisana ngokuphambene: yehlisa okukodwa kube yingxenye, okunye kuphindeke kabili.

Ukukhanya okubonakalayo kusuka cishe ku-400 nm (i-violet) kuya ku-700 nm (okubomvu). Ukukhanya kwe-ultraviolet kunobude begagasi obufushane nama-frequency aphakeme; i-infrared inobude begagasi obude nama-frequency aphansi. Guqula ama-nanometer abe amamitha ngaphambi kokusebenzisa u-c = λν: 1 nm = 10⁻⁹ m.

Amandla e-photon nomphumela we-photoelectric

Ukukhanya kumunywa futhi kukhishwe ngamaphakethe abizwa ngokuthi ama-photon. I-photon ngayinye iphethe amandla E = hν = hc/λ, lapho h = 6.62607015 × 10⁻³⁴ J·s eyi-Planck constant, nayo eqondile. Ubude begagasi obufushane busho amandla amaningi nge-photon ngayinye. Ukukhanya okugqame kakhulu kombala ofanayo kusho ama-photon amaningi, hhayi anamandla amakhulu.

Isibonelo esisebenzile 1. Ukukhanya okuphuzi kwesibani se-sodium kuseduze no-589.0 nm. I-frequency yakho ingu-ν = c/λ = (2.998 × 10⁸ m/s)/(589.0 × 10⁻⁹ m) = 5.090 × 10¹⁴ Hz. I-photon eyodwa iphethe u-E = hν = (6.626 × 10⁻³⁴ J·s)(5.090 × 10¹⁴ s⁻¹) = 3.373 × 10⁻¹⁹ J. Phindaphinda ngenombolo ka-Avogadro, 6.022 × 10²³ mol⁻¹, ukuze uthole i-mole yama-photon: 2.031 × 10⁵ J, noma 203.1 kJ/mol. Lokho kuqhathaniseka namandla esibopho samakhemikhali esibuthakathaka, yingakho ukukhanya okubonakalayo nokwe-ultraviolet kungaqhuba ukusabela kwe-photochemical.

Umphumela we-photoelectric ukhombisa umqondo we-photon ngqo. Ukukhanya kukhipha ama-electron ensimbini kuphela uma i-photon ngayinye iphethe okungenani i-work function yensimbi, Φ. Noma yimaphi amandla angeziwe aba amandla e-kinetic e-electron: KEmax = hν − Φ.

Isibonelo esisebenzile 2. Ake sithi ingaphezulu lensimbi linobude begagasi bomkhawulo obungu-540 nm (inani elinikeziwe kulo msebenzi). I-work function yalo ingu-Φ = hc/λ = (6.626 × 10⁻³⁴ J·s)(2.998 × 10⁸ m/s)/(540 × 10⁻⁹ m) = 3.679 × 10⁻¹⁹ J. Ukukhanya kwe-violet ku-405 nm kunama-photon angu-4.905 × 10⁻¹⁹ J, ngakho KEmax = 4.905 × 10⁻¹⁹ J − 3.679 × 10⁻¹⁹ J = 1.226 × 10⁻¹⁹ J. Uma kuyiswe ezinombolweni ezibalulekile ezintathu, lokho kungu-1.23 × 10⁻¹⁹ J, noma 0.765 eV. Ukukhanya okubomvu ku-650 nm, noma kunamandla kangakanani, akukhiphi ama-electron, ngoba i-photon ngayinye inokungu-3.06 × 10⁻¹⁹ J kuphela.

Kungani ama-athomu enikeza ama-line spectrum esikhundleni sothingo lwenkosazane

Into eqinile eshisayo, njenge-filament yesibani, ikhipha i-spectrum eqhubekayo. Igesi yama-athomu eshisayo enengcindezi ephansi ikhipha ubude begagasi obuthile kuphela. Ama-electron ku-athomu angahlala emazingeni athile amandla kuphela. Lapho i-electron yehla isuka ezingeni eliphakeme iya kwelingaphansi, i-athomu ikhipha i-photon eyodwa amandla ayo alingana negebe: ΔE = hν. Ngoba kukhona amagebe athile kuphela, kuvela ubude begagasi obuthile kuphela.

Ukumunca kungukuphambene. Khanyisa ukukhanya okumhlophe ngegesi epholile futhi ama-athomu asusa ncamashi ubude begagasi obuhambisana nokugxumela kwawo phezulu, ashiye imigqa emnyama ku-spectrum ebingaqhubeka. Ukugxuma phakathi kwamazinga amabili afanayo kunobude begagasi obufanayo noma ngabe i-athomu iyamunca noma iyakhipha. Iqoqo lamagebe esakhi ngasinye liyingqayizivele, ngakho ama-spectrum ahlonza izakhi emalangabini, ezibanini nasezinkanyezini ezikude.

Amazinga amandla e-hydrogen nesibalo se-Rydberg

Ku-athomu ene-electron eyodwa, amazinga amandla alandela ifomula elula. I-OpenStax Chemistry 2e (Isigaba 6.2) inikeza u-Eₙ = −kZ²/n², lapho k = 2.179 × 10⁻¹⁸ J, u-Z eyishaji yenyukliya no-n = 1, 2, 3, …. Amandla angelihle ngoba i-electron eboshiwe inamandla aphansi kune-electron ekhululekile emile, emiswe ku-zero. Njengoba u-n ekhula, amazinga ayaminyana asondela ku-zero.

I-photon ekhishwa lapho i-electron iwa isuka ku-nᵢ iya ku-n_f ophansi inamandla ΔE = kZ²(1/n_f² − 1/nᵢ²). Ukuhlukanisa ngo-hc kunikeza isibalo se-Rydberg se-hydrogen, 1/λ = R(1/n_f² − 1/nᵢ²), lapho R = 1.097 × 10⁷ m⁻¹.

Isibonelo esisebenzile 3. Thola ubude begagasi bomugqa we-hydrogen ka-n = 3 → n = 2. ΔE = (2.179 × 10⁻¹⁸ J)(1/4 − 1/9) = (2.179 × 10⁻¹⁸ J)(5/36) = 3.0264 × 10⁻¹⁹ J, kugcinwa inombolo eyodwa eyengeziwe kuze kube sekugcineni. Ngo-hc = 1.9864 × 10⁻²⁵ J·m, λ = hc/ΔE = 6.564 × 10⁻⁷ m, noma 656.4 nm. I-NIST Handbook of Basic Atomic Spectroscopic Data ibhala lo mugqa obomvu ku-656.3 nm emoyeni. Umehluko wenombolo yokugcina uvela ekuyiseni u-k nasejubaneni lokukhanya elincane kancane emoyeni.

Isibonelo esisebenzile 4. Amandla e-ionization e-hydrogen angamandla okususa i-electron ku-n = 1 iye ku-n = ∞, okungu-k uqobo: 2.179 × 10⁻¹⁸ J nge-athomu ngayinye. Nge-mole ngayinye, (2.179 × 10⁻¹⁸ J)(6.022 × 10²³ mol⁻¹) = 1.312 × 10⁶ J, noma 1312 kJ/mol. Inani le-NIST Atomic Spectra Database, 13.598 eV, liguquka libe ngu-1312.0 kJ/mol.

Uchungechunge lwe-Lyman, lwe-Balmer nolwe-Paschen

Imigqa egcina ezingeni elifanayo eliphansi yakha uchungechunge. Yonke isondelana kakhulu njengoba u-nᵢ ekhula futhi isondela emkhawulweni wochungechunge, lapho i-electron iqala ikhululekile.

• Uchungechunge lwe-Lyman, olugcina ku-n = 1: i-ultraviolet. Umugqa ka-2 → 1 use-121.6 nm, futhi umkhawulo wochungechunge useduze no-91.2 nm.
• Uchungechunge lwe-Balmer, olugcina ku-n = 2: imigqa emine ebonakalayo ye-hydrogen, cishe ku-656, 486, 434 no-410 nm ku-nᵢ = 3, 4, 5 no-6. Umkhawulo wochungechunge useduze no-365 nm, ku-ultraviolet.
• Uchungechunge lwe-Paschen, olugcina ku-n = 3: i-infrared. Umugqa ka-4 → 3 useduze no-1875 nm.

Amaphutha e-spectrum nokuhlola okusheshayo

Amaphutha amaningi kulezi zinkinga angamaphutha amayunithi noma amaphutha ophawu. Ukuhlola okubili kubamba amaningi awo: i-photon ebonakalayo kufanele iphathe cishe u-2.8 kuya ku-5.0 × 10⁻¹⁹ J, futhi igebe elikhulu lamandla kufanele linikeze ubude begagasi obufushane.

• Ukushiya ubude begagasi bungama-nanometer lapho usebenzisa u-c = λν noma u-E = hc/λ. Guqula ube amamitha kuqala.
• Ukusebenzisa isibalo se-Rydberg u-nᵢ no-n_f beshintshanisiwe, okunikeza ubude begagasi obungelihle.
• Ukulindela ukuthi wonke umugqa we-hydrogen ubonakale. Lonke uchungechunge lwe-Lyman luyi-ultraviolet kanti uchungechunge lwe-Paschen luyi-infrared.
• Ukucabanga ukuthi ukukhanya okugqame kakhulu kukhipha ama-photoelectron ashesha kakhulu. Ukuqina kushintsha inani lama-electron, hhayi amandla awo aphezulu.
• Ukusebenzisa u-Eₙ = −kZ²/n² ku-helium noma kunoma iyiphi i-athomu enama-electron angaphezu kweyodwa. Kusebenza kuphela ezinhlotsheni ezine-electron eyodwa njengo-H, He⁺ no-Li²⁺.
• Ukukhohlwa inombolo ka-Avogadro lapho uguqula amandla e-photon ngayinye abe ku-kJ/mol, noma ukuyisebenzisa kabili.

Lokho umqondo ka-Bohr okuchazayo nalapho ugcina khona

Imodeli ka-Bohr ye-athomu ye-hydrogen, ene-electron emizileni eyindilinga enamandla angaguquki, iphinda imigqa ye-hydrogen nokukala kuka-Z² kuma-ayoni afana no-He⁺. Ku-He⁺, wonke amandla okuguquka e-hydrogen makhulu ngokuphindwe kane, ngakho umugqa wayo ka-2 → 1 useduze no-30.4 nm.

Imodeli iyehluleka kuma-athomu anama-electron amabili noma ngaphezulu, ngoba ukuxoshana kwe-electron–electron kushintsha amazinga. Iphinde ibonise ama-electron emizileni ecacile, into i-quantum mechanics engayivumeli. Ithiyori yanamuhla igcina amazinga amandla ka-Bohr e-hydrogen kodwa ithathela imizila indawo ngama-orbital, achaza lapho i-electron kungenzeka itholakale khona.