Izinombolo ze-quantum nama-orbital: imithetho, ukubala nezimo

Ama-electron njengamagagasi: ubude begagasi buka-de Broglie

Ngo-1924 u-de Broglie wasikisela ukuthi noma iyiphi inhlayiya ehambayo inobude begagasi λ = h/(mv), lapho u-h eyi-Planck constant, u-m isisindo no-v ijubane. Ezintweni zansuku zonke ubude begagasi buncane kakhulu ukuthi bunakwe. I-baseball engu-0.145 kg ku-40.0 m/s ino-λ = 1.14 × 10⁻³⁴ m. Ku-electron, enesisindo esingu-9.109 × 10⁻³¹ kg (NIST CODATA), ubude begagasi buqhathaniseka nosayizi we-athomu.

Isibonelo esisebenzile 1. I-electron ehamba ngo-2.188 × 10⁶ m/s ino-λ = h/(mv). Ngamanani e-CODATA h = 6.62607 × 10⁻³⁴ J·s no-m = 9.10938 × 10⁻³¹ kg, λ = (6.62607 × 10⁻³⁴)/[(9.10938 × 10⁻³¹)(2.188 × 10⁶)] = 3.324 × 10⁻¹⁰ m, noma 0.3324 nm. Leli jubane yilo imodeli ka-Bohr eliyinikeza i-electron emzileni ophansi kakhulu we-hydrogen, irediyasi yawo eyirediyasi ka-Bohr, a₀ = 5.29177 × 10⁻¹¹ m (NIST CODATA). Umjikelezo womzila ungu-2πa₀ = 3.325 × 10⁻¹⁰ m, ngakho ubude begagasi obubodwa be-electron bungena kuwo, nokuvumelana okungcono kuno-0.02%. Amazinga amandla ane-quantum yilokho okutholayo lapho igagasi le-electron kufanele lingene esikhaleni salo ngaphandle kokuzikhansela, njengoba nje intambo yesiginci ingadlidliza kuma-frequency athile kuphela.

Ukungaqiniseki nokuphela kwemizila engaguquki

Isimiso sokungaqiniseki sika-Heisenberg sibeka umkhawulo wokuthi indawo ne-momentum kungaziwa kahle kangakanani ndawonye: Δx·Δp ≥ ħ/2, lapho ħ = h/2π = 1.0546 × 10⁻³⁴ J·s.

Isibonelo esisebenzile 2. Valela i-electron endaweni ebanzi ngo-1.0 × 10⁻¹⁰ m, cishe usayizi we-athomu. Bese Δp ≥ (1.0546 × 10⁻³⁴ J·s)/(2 × 1.0 × 10⁻¹⁰ m) = 5.3 × 10⁻²⁵ kg·m/s, futhi Δv = Δp/m ≥ 5.8 × 10⁵ m/s. Ukungaqiniseki kwejubane kuyingxenye enkulu yejubane ngokwalo, ngakho umzila ocacile, njengomzila weplanethi, awunancazelo ku-electron ese-athomu.

I-quantum mechanics ithathela umzila indawo nge-wavefunction, ψ. Isikwele sayo, ψ², yi-probability density: uma iphindaphindwe ngevolumu yendawo encane, inikeza amathuba okuthola i-electron lapho. I-orbital iyi-wavefunction ye-electron eyodwa, futhi izithombe ezijwayelekile zama-orbital zingamangaphezulu avalela iningi lalawo mathuba, ngokuvamile u-90%.

Amanani avunyelwe ka-n, l, mₗ no-mₛ

Ukuxazulula isibalo segagasi se-athomu ye-hydrogen kukhiqiza izinombolo ze-quantum ezintathu, ngayinye ikhawulelwe yileyo eyandulelayo. Eyesine ichaza i-spin ye-electron. Imikhawulo iyikho konke.

• Inombolo ye-quantum eyinhloko n = 1, 2, 3, …. Inquma i-shell futhi, ku-hydrogen, amandla. U-n omkhulu usho i-orbital enkulu enamandla aphakeme.
• Inombolo ye-quantum ye-angular momentum l = 0, 1, …, n − 1. Inquma i-subshell nesimo: l = 0, 1, 2, 3 ngu-s, p, d, f.
• Inombolo ye-quantum ye-magnetic mₗ = −l, …, 0, …, +l, inikeza amanani angu-2l + 1. Inquma ukubheka kwe-orbital emkhathini.
• Inombolo ye-quantum ye-spin mₛ = +½ noma −½. Ayincikile kwezinye ezintathu.

Isibonelo esisebenzile: ukuhlola amaqoqo ayisithupha ezinombolo ze-quantum

Ukuhlola iqoqo (n, l, mₗ, mₛ), hlola inombolo ngayinye uyiqhathanise naleyo eyandulelayo, ngokulandelana. Yima ekwephulweni kokuqala.

(3, 3, 0, +½) alivunyelwe: u-l kufanele abe ngu-n − 1 = 2 noma ngaphansi. (4, 2, −3, −½) alivunyelwe: uma l = 2, u-mₗ usuka ku-−2 kuphela kuya ku-+2. (3, 2, 1, 0) alivunyelwe: u-mₛ kufanele abe ngu-+½ noma −½, angalokothi abe ngu-0. (2, 1, −1, −½) liyavunyelwa futhi lichaza i-electron ku-orbital ye-2p. (5, 0, 0, +½) liyavunyelwa futhi lichaza i-electron ye-5s. (4, 3, −3, +½) liyavunyelwa futhi lichaza i-electron ye-4f.

Ukuqamba i-orbital kusuka eqoqweni elivunyelwe, bhala u-n bese ulandelisa ngohlamvu luka-l. Inani lika-mₗ likhetha i-orbital eyodwa ngaphakathi kwe-subshell kodwa alishintshi igama layo kule ndlela yokubhala.

Ukubala ama-orbital nama-electron ngaphansi komkhawulo

Imibuzo yokubala iba yinto ejwayelekile uma ubhala amanani avunyelwe ka-l, bese amanani ka-mₗ ngalinye, bese kuphela usebenzisa umkhawulo. I-orbital ngayinye, okusho inhlanganisela ngayinye evunyelwe ye-(n, l, mₗ), iphatha ama-electron amabili, elilodwa nge-spin ngayinye.

I-shell enenombolo ye-quantum eyinhloko n iqukethe ama-orbital angu-n² nama-electron angu-2n². Ku-n = 4, u-l angaba ngu-0, 1, 2 noma 3, kunikeze ama-orbital angu-1 + 3 + 5 + 7 = 16 nama-electron angu-32.

Isibonelo esisebenzile 3. Mangaki ama-electron ku-athomu angaba no-n = 3 no-mₗ = +1? Amanani ka-l ku-n = 3 ngu-0, 1 no-2. U-mₗ = +1 ungenzeka kuphela lapho l ≥ 1, ngakho kukhona i-orbital eyodwa enjalo ku-3p neyodwa ku-3d: ama-orbital amabili, ama-electron amane. Mangaki angaba no-n = 5 no-mₛ = +½? I-shell 5 inama-orbital angu-5² = 25, ngalinye line-electron eyodwa engu-+½, ngakho angu-25. Mangaki angaba no-n = 4 no-l = 2? Leyo yi-subshell ye-4d: ama-orbital angu-5 nama-electron angu-10.

Izimo zama-orbital nokubala ama-node

I-node yindawo lapho u-ψ, ngakho namathuba okuthola i-electron, eyi-zero. I-orbital inama-node angu-n − 1 esewonke. Kulawa, angu-l angama-angular node, amapulane noma amakhoni adlula ku-nucleus, kanti angu-n − l − 1 asele angama-radial node, ama-shell ayindilinga emabangeni angaguquki. I-OpenStax Chemistry 2e (Isigaba 6.3) inikeza umthetho we-radial node.

Ama-orbital e-s (l = 0) ayindilinga ngaphandle kwama-angular node, ngakho i-orbital ye-2s ine-radial node eyodwa kanti i-orbital ye-3s inamabili. Ama-orbital e-p (l = 1) anama-lobe amabili ezinhlangothini eziphambene ze-nucleus ne-nodal plane eyodwa phakathi kwawo; amathathu abhalwe ngokuthi pₓ, p_y no-p_z ngokwe-eksisi abheke ngakuyo. Ama-orbital e-d (l = 2) anama-angular node amabili. Amane awo anama-lobe amane; elesihlanu, u-d_z², linama-lobe amabili eduze ne-eksisi ye-z nendandatho ezungeze maphakathi.

Isibonelo esisebenzile 4. I-orbital ye-3p ine-radial node engu-3 − 1 − 1 = 1 ne-angular node engu-1. I-orbital ye-4d ine-radial node engu-1 nama-angular node angu-2, angu-3 esewonke. I-orbital ye-3d ayinawo ama-radial node, kanti i-orbital ye-6s inangu-5.

Lapho ama-orbital ku-shell efanayo ehluka ngamandla

Ku-hydrogen, amandla ancike ku-n kuphela, ngakho u-3s, 3p no-3d banamandla afanayo. Kuma-athomu anama-electron angaphezu kweyodwa, amanye ama-electron avikela i-nucleus ngokungalingani. I-electron ye-s ingena eduze kakhulu ne-nucleus kune-electron ye-p noma ye-d ye-shell efanayo, izwa ishaji yenyukliya eningi futhi inamandla aphansi. Umphumela uwukuhlukana kuka-s < p < d < f ngaphakathi kwe-shell, okunquma ukulandelana kokugcwaliswa okuchazwe esihlahlandleleni sokulungiswa kwama-electron.

Ama-orbital ku-subshell efanayo, njengama-orbital amathathu e-2p, ahlala elingana ngamandla ku-athomu ehlukanisiwe. Abizwa ngokuthi ama-degenerate. Ama-athomu azungezile emolekyulini noma ku-crystal angakwephula lokho kulingana.

Amaphutha ezinombolo ze-quantum okufanele uwahlole

Cishe lonke iphutha livela ekweqeni isinyathelo sokubhala uhlu. Uma ungabaza, bhala wonke amanani avunyelwe ngaphambi kokubala.

• Ukuvumela u-l alingane no-n. U-l omkhulu kakhulu ovunyelwe ngu-n − 1, ngakho ayikho i-orbital ye-1p noma ye-2d.
• Ukubala amanani ka-mₗ kusuka ku-0 kuya ku-l esikhundleni sokusuka ku-−l kuya ku-+l, okubala ama-orbital ambalwa kunangempela.
• Ukubala ama-orbital lapho umbuzo ubuza ama-electron, noma okuphambene. I-orbital ngayinye iphatha ama-electron amabili.
• Ukunikeza u-mₛ inani elingu-0 noma 1. I-spin ingu-+½ noma −½ kuphela.
• Ukusebenzisa u-n − l − 1 njengenani eliphelele lama-node. Leyo fomula ibala ama-radial node kuphela; isamba singu-n − 1.
• Ukuthatha ingaphezulu lomngcele elingu-90% njengonqenqema oluqinile. Ukuminyana kwama-electron kuyafiphala kancane kancane futhi akunamngcele obukhali.