4-hidrogen-kuantum
DESCRIPTION
fisika kuantumTRANSCRIPT
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Atom Hidrogen, PersamaanAtom Hidrogen, Persamaan
Schrodinger
I Wayan Sudiarta, Ph.D
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Vibrating String/Guitar etc
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Pola Getaran, Vibrating drum
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Persamaan Schrodinger
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Solusi?
• Karena Potensial U(r) mempunyai simetri bola, Kita perlu mengubah persamaan Schrodinger Kita perlu mengubah persamaan Schrodinger dalam koordinat bola
Metode separasi variabel
Dihasilkan tiga persamaan diferensial
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Bilangan Kuantum, n l m
• Bilangan kuantum nn
n = 1, 2, 3, . . .
• Bilangan kuantum llll
l l l l = 0, 1, 2, …, (n-1)
Bilangan kuantum m• Bilangan kuantum mm = -l l l l , . . ., +llll
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Bilangan kuantum
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Penamaan Shell dan Subshell
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Energi elektron
Bernilai sama dengan Energi dari teori Bohr yaituBernilai sama dengan Energi dari teori Bohr yaitu
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Fungsi Gelombang keadaan dasar n =1
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2Pz
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Interpretasi Bilangan Kuantum
Bilangan n berhubungan dengan energi elektron
Bilangan l berhubungan dengan momentum Bilangan l berhubungan dengan momentum
angular elektron
Bilangan m berhubungan komponen z dariBilangan m berhubungan komponen z dari
angular momentum (orbital magnetik)
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Berapa Energi untuk keadaan kuantum
dengan bilangan n=2?
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Contoh:
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Spin Elektron, bilangan kuantum ms
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Hati-hati tentant Spin
• Spin Elektron yang sebenarnya tidak seperti
spin yang kita lihat sehari-hari. Kita bisa hanyaspin yang kita lihat sehari-hari. Kita bisa hanya
melakukan analogi saja.
• Merupakan sifat relativitas
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Eksperimen Stern-Gerlach
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Momentum angular spin
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n = 2
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Atom dengan elektron banyak
• Pada kenyataannya bilangan kuantum n l m
ms dapat digunakan untuk atom denganms dapat digunakan untuk atom dengan
elektron banyak.
• Untuk elektron atau fermion, prinsip larangan
Pauli harus dipenuhi: “No two electrons can
ever be in the same quantum state; therefore, ever be in the same quantum state; therefore,
no two electrons in the same atom can have
the same set of quantum numbers”.
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Contoh Keadaan elektron yang
diperbolehkan
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Aturan Hund
• when an atom has orbitals of equal energy,
the order in which they are filled by electrons the order in which they are filled by electrons
is such that a maximum number of electrons
have unpaired spins.
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Cara pengisian elektron
1s < 2s < 2p < 3s < 3p <4s < 3d <4p < 5s < 4d < 5p < 6s < 4f < 5d < 6p < 7s < 5f < 6d < 7p < 8s ...
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Aturan Transisi elektron
• Transisi yang diperbolehkan jika syarat berikut
ini terpenuhiini terpenuhi