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𝐸 = 𝐸𝑔+ ℎ2
8𝑅2 ( 1
𝑚𝑒+ 1
𝑚ℎ) −1.8𝑒2
4𝜋𝜀𝑅
𝐸𝑔
ℎ 𝑚𝑒 𝑚ℎ
𝑅 𝜀
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χ
I(t) = ∫ ρ(Γ) · e0∞ −iΓtdt ρ Γ 𝜌(Γ) = 1
𝜎Γ√2𝜋𝑒−
1 2(lnΓ−𝜇
𝜎 )2
Γ σ
Γ Γ
τ = 1 𝛤⁄ 𝑚𝑓
Γ Γ
τ
47 Γ
τ
Γ τ Γ
Γ
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α β
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Γ Γ
τ
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Γ Γ
χ τ
Γ Γ τ χ Γ Γ τ
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𝐷(𝑛𝑚) = 59.60816 − 0.54736𝜆 + 1.8873𝑥10−3𝜆2− 2.85743𝑥10−6𝜆3+ 1.62974𝑥10−9𝜆4 = 2.5 𝑛𝑚
𝜆
𝛥𝐸1𝑆,𝐹𝑊𝐻𝑀 (𝐸1𝑆
λ
155
𝐸1𝑆 (𝑒𝑉) = ℎ (eV s−1) 𝑥 𝑐(𝑚s−1)
𝜆 (𝑚) = 2.4486 𝑒𝑉(AI. 2)
ℎ 𝑐 𝜆
𝜀1𝑆 𝛥𝐸1𝑆,𝐹𝑊𝐻𝑀
𝐸1𝑆 𝑙
[𝐶𝑑𝑆𝑒] = 𝐴𝑏𝑠
𝑙(𝑐𝑚)𝜀1𝑆(𝑀−1cm−1)𝑥𝛥𝐸1𝑆,𝐹𝑊𝐻𝑀
0.06 = 2.4 𝑥10−6𝑀(AI. 3)
𝑃𝑀 (𝑑𝑜𝑡)
𝑃𝑀 (𝑑𝑜𝑡) ∶ 𝑑(𝑛𝑚)
𝑙𝑎𝑡𝑡𝑖𝑐𝑒 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡(𝐶𝑑𝑆𝑒) = 2.5
0.35= 7.1428 (AI. 4)
𝐶𝑑𝑆𝑒 𝑢𝑛𝑖𝑡𝑠 − 𝑛𝑢𝑚𝑏𝑒𝑟 𝑝𝑒𝑟 𝑑𝑜𝑡: 4
3𝑥𝜋𝑥(𝑃𝑀(𝑑𝑜𝑡)
2 ) 3 = 190.71(AI. 5)
𝑃𝑀
𝐷𝑜𝑡 𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑎𝑟 𝑚𝑎𝑠𝑠: 𝐶𝑑𝑆𝑒 𝑢𝑛𝑖𝑡𝑠 𝑥 𝑃𝑀(𝐶𝑑𝑆𝑒) = 190.71 𝑥 191.37
= 36496.1727(AI. 6)
156
𝑛 𝑑𝑜𝑡𝑠 ∶ [𝐶𝑑𝑆𝑒] 𝑥 𝑣𝑜𝑙𝑢𝑚𝑒 = 2.4 𝑥10−6𝑥 2 𝑥10−3
= 4.8 nmol(AI. 7)
𝑇𝑜𝑡𝑎𝑙 𝐶𝑑𝑆𝑒 𝑚𝑎𝑠𝑠: 𝑛 𝑑𝑜𝑡𝑠 𝑥 𝐷𝑜𝑡 𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑎𝑟 𝑚𝑎𝑠𝑠
= 4.8𝑥10−9𝑥 36496.1727 = 1.7518𝑥10−4𝑔(AI. 8) 𝑁𝐴
𝐶𝑑𝑆𝑒 𝑚𝑎𝑠𝑠 𝑝𝑒𝑟 𝑑𝑜𝑡: 𝐷𝑜𝑡 𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑎𝑟 𝑚𝑎𝑠𝑠
𝑁𝐴 = 36496.1727
6.023𝑥1023
= 6.05946𝑥10−20𝑔(AI. 9)
𝐷𝑜𝑡𝑠 𝑛𝑢𝑚𝑏𝑒𝑟: 𝑇𝑜𝑡𝑎𝑙 𝐶𝑑𝑆𝑒 𝑚𝑎𝑠𝑠
𝐶𝑑𝑆𝑒 𝑚𝑎𝑠𝑠 𝑝𝑒𝑟 𝑑𝑜𝑡 𝐷𝑜𝑡 = 1.7518𝑥10−4 6.05946𝑥10−20
= 2.8910𝑥1015𝑁𝐶𝑠(AI. 10)
𝑉𝑖
𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝑁𝐶𝑠 𝑣𝑜𝑙𝑢𝑚𝑒 (𝑉𝑖): 4
3 𝑥 𝜋 𝑥 𝑟𝑖3 = 8.177 𝑛𝑚3(AI. 11) 𝑑𝑓
𝑑𝑖 𝑎
𝑑𝑓: 𝑑𝑖 + 𝑎(𝑍𝑛𝑆) + 𝑎(𝑍𝑛𝑆) = 2.5 + 0.541 + 0.541
= 3.582 𝑛𝑚(AI. 12)
(𝑉𝑓) 𝐹𝑖𝑛𝑎𝑙 𝑁𝐶 𝑣𝑜𝑙𝑢𝑚𝑒𝑛 (𝑉𝑓): 4
3 𝑥 𝜋 𝑥 𝑟𝑓3 = 24.052 𝑛𝑚3(AI. 13)
157
𝑉(𝑍𝑛𝑆) = 𝑉𝑓 – 𝑉𝑖 = 15.8752 𝑛𝑚3(AI. 14)
𝑍𝑛𝑆 𝑐𝑒𝑙𝑙 𝑛𝑢𝑚𝑏𝑒𝑟: 𝑉(𝑍𝑛𝑆)
𝑉(𝑍𝑛𝑆𝑢𝑛𝑖𝑡𝑐𝑒𝑙𝑙) = 15.8752 0.1583
= 100.28 𝑐𝑒𝑙𝑙𝑠(AI. 15)
𝑚(𝑍𝑛𝑆 )𝑝𝑒𝑟 𝑑𝑜𝑡: 𝑚(𝑍𝑛𝑆) 𝑢𝑛𝑖𝑡 𝑐𝑒𝑙𝑙 𝑥 𝑐𝑒𝑙𝑙𝑠 𝑛𝑢𝑚𝑏𝑒𝑟
= 6.32𝑥10−22𝑥 100.28
= 6.338𝑥10−20𝑔 𝑜𝑓 𝑍𝑛𝑆(AI. 16)
𝑇𝑜𝑡𝑎𝑙 𝑍𝑛𝑆 𝑚𝑎𝑠𝑠 𝑛𝑒𝑐𝑒𝑠𝑠𝑎𝑟𝑦: 𝑚(𝑍𝑛𝑆)𝑝𝑒𝑟 𝑑𝑜𝑡 𝑥 𝑑𝑜𝑡 𝑛𝑢𝑚𝑏𝑒𝑟
= 6.338𝑥10−20𝑥 2.8910𝑥1015
= 1.832𝑥10−4𝑔(AI. 17)
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Φ𝐹 = 𝑁𝑜. 𝑜𝑓 𝑒𝑚𝑚𝑖𝑡𝑒𝑑 𝑝ℎ𝑜𝑡𝑜𝑛𝑠
𝑁𝑜. 𝑜𝑓 𝑎𝑏𝑠𝑜𝑟𝑏𝑒𝑑 𝑝ℎ𝑜𝑡𝑜𝑛𝑠
⁄ (AII. 1)
Φ𝐹(𝑋) = (𝐴𝑆 𝐴𝑋
⁄ (𝐹𝑋 𝐹𝑆
⁄ (𝑛𝑋 𝑛𝑆
⁄ )2 𝛷𝐹(𝑆)(AII. 2) Φ𝐹(𝑋)
164
φ
165
𝜑 =𝐸𝑐 − 𝐸𝑎
𝐿𝑎− 𝐿𝑐 (AII. 3)
166
λ
χ
I(t) = ∫ ρ(Γ) · e0∞ −iΓtdt (AII. 4) ρ Γ
𝜌(Γ) = 1
𝜎Γ√2𝜋𝑒−
1 2(lnΓ−𝜇
𝜎 ) 2
(AII. 5)
Γ σ
Γ Γ
𝛤𝑚𝑓 = 𝑒𝜇−𝜎2(AII. 6) 𝛥𝛤 = = 2 · 𝛤 · 𝑠𝑖𝑛ℎ(𝜎)(AII. 7)
τ = 1 𝛤⁄ 𝑚𝑓(AII. 8)
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Γ Γ
λ
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α
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ν
ν
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δ
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α
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ρ ρ
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(𝑉𝑜𝑙)2 × (𝜌 − 𝜌𝑠𝑜𝑙𝑣𝑒𝑛𝑡)2 × 𝑁 = 𝐹(AII. 9)
ρ ρ
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