I'll solve these f-block chemistry problems question by question.

Question 6 from page 1-2 (Lanthanide complexes)

(a) The denticity of edta⁴⁻ and dtpa⁵⁻:

• edta⁴⁻: 6 (hexadentate) - four O donors from carboxylate groups and two N donors
• dtpa⁵⁻: 8 (octadentate) - five O donors from carboxylate groups and three N donors

(b) Balanced aqueous equilibrium reactions with ytterbium:

1. Yb³⁺(aq) + F⁻(aq) ⇌ [YbF(H₂O)₈]²⁺(aq)
2. Yb³⁺(aq) + edta⁴⁻(aq) ⇌ [Yb(edta)(H₂O)₂]⁻(aq)
3. Yb³⁺(aq) + dtpa⁵⁻(aq) ⇌ [Yb(dtpa)(H₂O)]²⁻(aq)

(c) Stability constant K for ytterbium-dtpa complex: K = [[Yb(dtpa)(H₂O)]²⁻] / ([Yb³⁺][dtpa⁵⁻])

(d) Calculating free lanthanide concentration: For the equilibrium: Ln³⁺ + F⁻ ⇌ [LnF]²⁺

K = [LnF²⁺]/([Ln³⁺][F⁻]) 10^(log K) = [LnF²⁺]/([Ln³⁺][F⁻])

Initial concentrations: [Ln³⁺]₀ = [F⁻]₀ = 1 mol/L Let x = equilibrium [Ln³⁺], then [LnF²⁺] = 1-x and [F⁻] = 1-(1-x) = x

K = (1-x)/(x·x) = (1-x)/x²

For Tb³⁺: 10^3.42 = (1-x)/x² x² = (1-x)/10^3.42 x² = (1-x)/2630 x² + 2630x - 2630 = 0 x = 0.0196 mol/L

For Er³⁺: 10^3.54 = (1-x)/x² Using similar calculation: x = 0.0171 mol/L

For Yb³⁺: 10^3.58 = (1-x)/x² Using similar calculation: x = 0.0161 mol/L

(e) Tb³⁺ has a higher concentration of free ions compared to Er³⁺ and Yb³⁺ because:

• Tb³⁺ has a smaller stability constant (log K = 3.42)
• This is due to lanthanide contraction - Tb³⁺ has a larger ionic radius than Er³⁺ and Yb³⁺
• Larger ionic radius results in weaker metal-ligand interactions and less stable complexes

(f) The stability constant for Yb³⁺-edta⁴⁻ (log K = 19.48) is much larger than Yb³⁺-F⁻ (log K = 3.58) because:

Enthalpic factors:

• edta⁴⁻ is a multidentate ligand (chelate effect), forming multiple bonds with the metal ion
• This creates stronger overall binding compared to monodentate F⁻
• More donor atoms in edta⁴⁻ contribute to stronger electrostatic interactions

Entropic factors:

• When edta⁴⁻ binds to Yb³⁺, multiple water molecules are displaced, increasing entropy
• The chelate effect produces less decrease in entropy because one edta⁴⁻ molecule replaces multiple water or F⁻ ligands
  螯合剂效应产生的熵减少较少，因为一个 edta⁴- 分子取代了多个水或 F- 配体
• This favorable entropy change significantly contributes to the higher stability constant
  这种有利的熵变极大地促进了稳定常数的提高

(g) Lanthanide purification using edta⁴⁻:
(g) 使用 edta⁴- 纯化镧系元素：

(i) Process of lanthanide purification:
(i) 镧系元素提纯工艺：

1. The crude mixture of lanthanide chlorides is dissolved in water
   将镧系元素氯化物的粗混合物溶于水
2. The pH is carefully adjusted to control the degree of edta⁴⁻ complexation
   pH 值经过仔细调节，以控制 edta⁴的络合程度。
3. Ion exchange chromatography is used where complexed lanthanides move at different rates
   使用离子交换色谱法时，镧系元素的络合移动速度不同
4. As solution passes through the column, lanthanides separate due to different stability constants
   当溶液通过色谱柱时，镧系元素会因不同的稳定常数而分离出来
5. Sequential elution allows collection of individual lanthanide fractions
   顺序洗脱可收集单个镧系元素馏分
6. The purified lanthanides can be recovered by adjusting pH to release them from edta⁴⁻ complexes
   通过调节 pH 值，使镧系元素从 edta⁴-络合物中释放出来，从而回收纯化的镧系元素。

(ii) edta⁴⁻ is better than F⁻ or dtpa⁵⁻ because:
(ii) edta⁴- 优于 F- 或 dtpa⁵-，因为：

• The log K values for edta⁴⁻ show a significant trend across the lanthanide series (17.92 for Tb³⁺ to 19.48 for Yb³⁺)
  edta⁴-的对数 K 值在整个镧系元素系列中呈现出显著的趋势（Tb³⁺为 17.92，Yb³⁺为 19.48）。
• This large difference in stability constants allows better separation
  稳定常数的这种巨大差异可以更好地分离
• F⁻ has much smaller differences in log K values (3.42 to 3.58), making separation difficult
  F- 的对数 K 值差异要小得多（3.42 至 3.58），因此难以分离
• dtpa⁵⁻ has inconsistent trend (values peak at Er³⁺ then decrease for Yb³⁺), making separation unpredictable
  dtpa⁵- 的趋势不一致（Er³⁺ 的值达到峰值，Yb³⁺ 的值降低），因此分离效果难以预测
• edta⁴⁻ provides the optimal balance of binding strength and selectivity across the lanthanide series
  edta⁴- 在镧系元素的结合强度和选择性方面达到最佳平衡

I'll solve all the f-block chemistry questions from the document.
我会解决文件中所有的化学问题。

Page 1-2: Lanthanide complexes with ligands
第 1-2 页：镧系元素与配体的配合物

(a) Denticity of ligands
(a) 配体的齿性

• edta⁴⁻: 6 (hexadentate) - four O donors from carboxylate groups and two N donors
  edta⁴-：6（六价）- 来自羧基的四个 O 供体和两个 N 供体
• dtpa⁵⁻: 8 (octadentate) - five O donors from carboxylate groups and three N donors
  dtpa⁵-：8（八义齿）--来自羧基的五个 O 供体和三个 N 供体

(b) Balanced equilibrium reactions with Yb³⁺
(b) 与 Yb³⁺ 的平衡反应

• Yb³⁺(aq) + F⁻(aq) ⇌ [YbF(H₂O)₈]²⁺(aq)
  Yb³⁺(aq) + F-(aq) ⇌ [YbF(H₂O)₈]²⁺(aq)
• Yb³⁺(aq) + edta⁴⁻(aq) ⇌ [Yb(edta)(H₂O)₂]⁻(aq)
  Yb³⁺(aq) + edta⁴-(aq)⇌[Yb(edta)(H₂O)₂]-(aq)
• Yb³⁺(aq) + dtpa⁵⁻(aq) ⇌ [Yb(dtpa)(H₂O)]²⁻(aq)
  Yb³⁺(aq) + dtpa⁵-(aq) ⇌ [Yb(dtpa)(H₂O)]²-(aq)

(c) Stability constant definition
(c) 稳定常数的定义

K = [[Yb(dtpa)(H₂O)]²⁻] / ([Yb³⁺][dtpa⁵⁻])
K = [[Yb(dtpa)(H₂O)]²-] / ([Yb³⁺][dtpa⁵-])/ ([Yb³⁺][dtpa⁵-])

(d) Free lanthanide concentrations
(d) 游离镧系元素浓度

For equilibrium: Ln³⁺ + F⁻ ⇌ [LnF]²⁺, where K = [LnF²⁺]/([Ln³⁺][F⁻])
平衡 Ln³⁺ + F- ⇌ [LnF]²⁺，其中 K = [LnF²⁺]/([Ln³⁺][F-])

Initial: [Ln³⁺]₀ = [F⁻]₀ = 1 mol/L Let x = equilibrium [Ln³⁺]; then [LnF²⁺] = 1-x and [F⁻] = x
初始：[Ln³⁺]₀ = [F-]₀ = 1 摩尔/升 设 x = 平衡 [Ln³⁺]；则 [LnF²⁺] = 1-x，[F-] = x

K = (1-x)/x²

Tb³⁺: 10³·⁴² = (1-x)/x² x = 0.0196 mol/L
Tb³⁺: 10³-⁴² = (1-x)/x² x = 0.0196 摩尔/升

Er³⁺: 10³·⁵⁴ = (1-x)/x² x = 0.0171 mol/L
Er³⁺: 10³-⁵⁴ = (1-x)/x² x = 0.0171 摩尔/升

Yb³⁺: 10³·⁵⁸ = (1-x)/x² x = 0.0161 mol/L
Yb³⁺: 10³-⁵⁸ = (1-x)/x² x = 0.0161 摩尔/升

(e) Higher concentration of free Tb³⁺
(e) 游离态 Tb³⁺ 的浓度更高

Tb³⁺ has higher free ion concentration because:
锑³⁺的游离离子浓度较高，这是因为

• Smaller stability constant (K = 10³·⁴²)
  稳定常数较小（K = 10³-⁴²）
• Larger ionic radius due to position in lanthanide series
  由于位于镧系元素中，离子半径较大
• Lanthanide contraction means Tb³⁺ > Er³⁺ > Yb³⁺ in size
  镧系元素的收缩意味着 Tb³⁺ > Er³⁺ > Yb³⁺ 的大小
• Smaller charge density leads to weaker metal-ligand interactions
  电荷密度越小，金属与配体之间的相互作用越弱

(f) Higher stability of Yb³⁺-edta⁴⁻ vs Yb³⁺-F⁻
(f) Yb³⁺-edta⁴- 对 Yb³⁺-F- 的稳定性更高

Enthalpic factors:  惰性因子

• Chelate effect: edta⁴⁻ forms multiple bonds with Yb³⁺
  螯合效应：edta⁴- 与 Yb³⁺ 形成多重键合
• Multiple donor atoms create stronger overall binding
  多个供体原子可产生更强的整体结合力
• Higher negative charge on edta⁴⁻ (4- vs 1-)
  edta⁴- 带有较多负电荷（4- 对 1-）

Entropic factors:  熵因子

• When edta⁴⁻ binds, multiple water molecules are displaced
  当 edta⁴- 结合时，多个水分子会发生位移
• One edta⁴⁻ molecule replaces multiple water/F⁻ ligands
  一个 edta⁴- 分子取代多个水/F- 配体
• Favorable entropy change significantly contributes to higher stability
  有利的熵变大大有助于提高稳定性

(g) Lanthanide purification with edta⁴⁻
(g) 用 edta⁴- 纯化镧系元素

(i) Purification process:
(i) 净化过程：

1. Dissolve lanthanide chlorides in water
   将镧系元素氯化物溶于水
2. Adjust pH to control edta⁴⁻ complexation
   调节 pH 值以控制 edta⁴-复合物
3. Pass through ion exchange column
   通过离子交换柱
4. Lanthanides separate due to different stability constants
   镧系元素因稳定常数不同而分离
5. Collect fractions containing individual lanthanides
   收集含有单个镧系元素的馏分
6. Recover pure lanthanides by pH adjustment
   通过 pH 值调整回收纯镧系元素

(ii) edta⁴⁻ advantages:  (ii) EDTA⁴- 的优势：

• Significant trend in stability constants across series (17.92→19.48)
  各系列的稳定性常数呈显著变化趋势（17.92→19.48）
• Large difference enables effective separation
  差异大，可有效分离
• F⁻ has small differences (3.42→3.58)
  F- 差异较小（3.42→3.58）
• dtpa⁵⁻ shows inconsistent trend (peaks at Er³⁺, decreases for Yb³⁺)
  dtpa⁵- 显示出不一致的趋势（在 Er³⁺ 时达到峰值，在 Yb³⁺ 时下降）。
• edta⁴⁻ provides optimal balance of binding strength and selectivity
  edta⁴- 在结合强度和选择性之间取得最佳平衡

Page 3-4: Promethium and Neptunium
第 3-4 页：钷和镎

(a) Electronic structure and properties
(a) 电子结构和特性

(i) Electronic configurations:
(i) 电子配置：

• Pm³⁺: [Xe]4f⁴  Pm³⁺：[Xe]4f⁴
• Np³⁺: [Rn]5f⁴  Np³⁺：[Rn]5f⁴

(ii) Ground state term for Pm³⁺:
(ii) Pm³⁺ 的基态项：

• 4f⁴ configuration  4f⁴ 配置
• Using Hund's rules:  使用 Hund 的规则：
  • Maximum S = 2
    最大 S = 2
  • Maximum L = 8-2 = 6
    最大 L = 8-2 = 6
  • Less than half-filled shell: J = |L-S| = 4
    小于半填充外壳：J = |L-S| = 4
• Term symbol: ⁵I₄  术语符号：⁵I₄

(iii) Magnetic moment:  (iii) 磁矩：

• Theoretical: μ = g√(J(J+1)) where g = 1 + [J(J+1)+S(S+1)-L(L+1)]/[2J(J+1)]
  理论：μ = g√(J(J+1))，其中 g = 1 + [J(J+1)+S(S+1)-L(L+1)]/[2J(J+1)]
• Calculating g and μ gives approximately 2.7 μB
  计算 g 和 μ 得到约 2.7 μB
• Experimental values (2.4-2.6 μB) align reasonably with calculation
  实验值（2.4-2.6 μB）与计算值相当吻合

(iv) Spectral differences:
(iv) 光谱差异：

• Pm³⁺: 4f orbitals are shielded by filled 5s and 5p orbitals
  Pm³⁺：4f 轨道被填充的 5s 和 5p 轨道屏蔽
• 4f orbitals don't participate significantly in bonding
  4f 轨道在成键过程中的作用不大
• Limited interaction with ligand field explains invariant spectra
  与配体场的有限相互作用解释了不变光谱的原因
• Np³⁺: 5f orbitals extend further spatially
  Np³⁺：5f 轨道在空间上进一步扩展
• Greater overlap with ligand orbitals
  与配体轨道的重叠更多
• More susceptible to ligand field effects
  更易受配体场效应的影响
• Results in variable spectra depending on coordination environment
  根据配位环境的不同，产生不同的光谱

(b) Contrasting redox chemistry
(b) 氧化还原化学的对比

• Pm is limited to +3 oxidation state because:
  Pm 只限于 +3 氧化态，因为
  • 4f electrons are core-like and shielded
    4f 电子具有核心和屏蔽作用
  • High ionization energies for removing more electrons
    电离能高，可移除更多电子
  • Stability of half-filled (4f⁷) or filled (4f¹⁴) configurations doesn't favor other states
    半填充（4f⁷）或填充（4f¹⁴）构型的稳定性并不倾向于其他状态
• Np shows multiple oxidation states because:
  镎呈现多种氧化态是因为
  • 5f orbitals are more accessible energetically
    5f 轨道在能量上更容易获得
  • Less effective shielding
    屏蔽效果较差
  • Smaller energy differences between 5f, 6d, and 7s
    5f、6d 和 7s 之间的能量差异较小
  • Relativistic effects increase stability of higher oxidation states
    相对论效应增加了高氧化态的稳定性
  • Greater covalent character in bonding
    更强的共价键特性

(c) Neptunyl bond lengths
(c) 镎键长度

• Bond lengths: NpO₂⁺ (1.765 Å) > NpO₂²⁺ (1.707 Å) > NpO₂³⁺ (1.701 Å)
  键长：NpO₂⁺ (1.765 Å) > NpO₂²⁺ (1.707 Å) > NpO₂³⁺ (1.701 Å)
• Higher oxidation states create stronger bonds due to:
  较高的氧化态会产生更强的化学键，这是因为
  • Increased effective nuclear charge
    增加有效核电荷
  • More electron withdrawal from oxygen
    从氧气中获取更多电子
  • Enhanced π-bonding between Np and O
    增强 Np 和 O 之间的 π 键作用
  • Greater ionic character  离子性更强
  • Multiple bonding (σ + π) becomes stronger with higher oxidation states
    氧化态越高，多重键合（σ + π）越强
• Diminishing difference between NpO₂²⁺ and NpO₂³⁺ suggests approaching limit of bond strengthening
  NpO₂²⁺ 和 NpO₂³⁺ 之间的差异逐渐减小，表明键合强化的极限正在接近

Page 5: Lanthanide properties and bonding
第 5 页：镧系元素的性质和成键

(a) Lanthanide size trends
(a) 镧系元素的尺寸趋势

General trend:  总体趋势：

• Atomic and ionic radii decrease with increasing atomic number ("lanthanide contraction")
  原子半径和离子半径随原子序数的增加而减小（"镧系收缩"）。
• Caused by poor shielding of 4f electrons
  由 4f 电子屏蔽不良引起
• Increasing effective nuclear charge across the series
  增加整个系列的有效核电荷
• Greater attraction between nucleus and outer electrons
  原子核与外层电子之间的吸引力更大

Anomalies in metals:  金属异常

• Eu and Yb have larger atomic radii
  Eu 和 Yb 的原子半径较大
• Adopt +2 oxidation state in metallic form (vs typical +3)
  在金属形态下采用 +2 氧化态（与典型的 +3 氧化态相比）
• Electronic configurations: Eu ([Xe]4f⁷6s²) and Yb ([Xe]4f¹⁴6s²)
  电子构型：Eu ([Xe]4f⁷6s²) 和 Yb ([Xe]4f¹⁴6s²)
• Half-filled (Eu) and completely filled (Yb) 4f subshells are especially stable
  半填充（Eu）和完全填充（Yb）的 4f 子壳尤其稳定
• Larger radius due to weaker metallic bonding with fewer valence electrons
  半径较大是因为金属键较弱，价电子较少

(b) Ground state term symbol for Dy³⁺
(b) Dy³⁺ 的基态项符号

• Dy³⁺: [Xe]4f⁹ configuration
  Dy³⁺：[Xe]4f⁹构型
• Using Hund's rules:  使用 Hund 的规则：
  • Maximum S = 5/2
    最大 S = 5/2
  • Maximum L = 5
    最大 L = 5
  • More than half-filled shell: J = L+S = 15/2
    超过半满的外壳：J = L+S = 15/2
• Term symbol: ⁶H₁₅/₂  术语符号：⁶H₁₅/₂

(c) Absence of lanthanide carbonyls
(c) 不含镧系羰基化合物

• Lanthanide carbonyls are unknown because:
  镧系羰基化合物之所以不为人知，是因为
  • 4f orbitals are too contracted to overlap with CO orbitals
    4f 轨道过于收缩，无法与 CO 轨道重叠
  • Limited ability for π-backbonding (essential for carbonyl stability)
    π-反键能力有限（对羰基稳定性至关重要）
  • Larger ionic radii lead to steric hindrance
    较大的离子半径会导致立体阻碍
  • Preference for higher coordination numbers
    偏好较高的协调数
  • Harder Lewis acid character (poor match for soft CO ligands)
    较硬的路易斯酸特性（与软 CO 配体不匹配）
  • Tendency toward ionic rather than covalent bonding
    倾向于离子键而非共价键

(d) Isolation of cerium and europium
(d) 铈和铕的分离

• Cerium is easily isolated because:
  铈很容易分离出来，因为
  • Forms stable Ce⁴⁺ state (unique among lanthanides)
    形成稳定的 Ce⁴⁺态（在镧系元素中独一无二）
  • Ce⁴⁺ compounds (e.g., CeO₂) are less soluble
    Ce⁴⁺ 化合物（如 CeO₂）的溶解度较低
  • Oxidation provides separation method
    氧化提供分离方法
• Europium is easily isolated because:
  铕很容易分离，因为
  • Forms stable Eu²⁺ state
    形成稳定的 Eu²⁺ 态
  • Different solubility of Eu²⁺ compounds
    Eu²⁺ 化合物的不同溶解度
  • Reduction allows separation from other lanthanides
    还原后可与其他镧系元素分离
  • Distinctive precipitation behavior
    独特的降水行为

Pages 6-7: Lanthanide colors and Fermium chemistry
第 6-7 页：镧系元素的颜色和镄的化学性质

(a) Color in f-block trifluorides
(a) f-block 三氟化物的颜色

(i) Process responsible: f-f electronic transitions
(i) 负责过程：f-f 电子转变

(ii) GdF₃ and CmF₃ are colorless because:
(ii) GdF₃ 和 CmF₃ 是无色的，因为：

• Gd³⁺: [Xe]4f⁷ has half-filled 4f shell (stable)
  钆³⁺：[Xe]4f⁷具有半填充的 4f 壳（稳定）
• Cm³⁺: [Rn]5f⁷ has half-filled 5f shell (stable)
  Cm³⁺：[Rn]5f⁷具有半填充的 5f 壳（稳定）
• Both have large energy gaps to excited states
  两者到激发态的能隙都很大
• No transitions in visible range
  可见光范围内无过渡
• EuF₃ and AmF₃ are colored due to accessible f-f transitions
  EuF₃ 和 AmF₃因可发生 f-f 转换而着色

(b) Einsteinium properties
(b) 爱因斯坦特性

(i) Es³⁺ electronic configuration: [Rn]5f¹⁰
(i) Es³⁺ 电子构型：[Rn]5f¹⁰

(ii) Ground state term:  (ii) 基态项：

• 5f¹⁰ configuration  5f¹⁰ 配置
• Using Hund's rules:  使用 Hund 的规则：
  • Maximum S = 3
    最大 S = 3
  • Maximum L = 9-3 = 6
    最大 L = 9-3 = 6
  • More than half-filled: J = L+S = 9
    超过半数：J = L+S = 9
• Term symbol: ⁷F₉  术语符号：⁷F₉

(iii) Magnetic moment:  (iii) 磁矩：

• Theoretical: μ = g√(J(J+1))μB ≈ 10.6 μB
  理论值：μ = g√(J(J+1))μB ≈ 10.6 μB
• Measured: 10.5 μB  测量值： 10.5 μB
• Good agreement between theoretical and experimental values
  理论值与实验值非常吻合
• Slight discrepancy due to crystal field effects or orbital quenching
  晶体场效应或轨道淬火导致的轻微差异

(c) Fermium chemistry  (c) 镄化学

(i) Reaction with water:  (i) 与水反应：

• Using given potentials, Fm² completes reaction:
  利用给定的电位，Fm² 完成反应：
• Fm + 2H₂O → Fm²⁺ + H₂ + 2OH⁻
  Fm + 2H₂O → Fm²⁺ + H₂ + 2OH-

(ii) Stability ranking of Fm³⁺ complexes (strongest to weakest):
(ii) Fm³⁺ 复合物的稳定性排名（从强到弱）：

1. edta⁴⁻ (strongest)  EDTA⁴- (最强)
2. ox²⁻  ox²-
3. F⁻  F-
4. Cl⁻ (weakest)  Cl-（最弱）

Explanation:  解释：

• Follows HSAB principle  遵循 HSAB 原则
• Multidentate ligands form stronger complexes (chelate effect)
  多叉配体形成更强的络合物（螯合效应）
• Higher negative charge increases electrostatic attraction
  较高的负电荷会增加静电吸引力
• Fm³⁺ is a hard Lewis acid preferring hard donors (O > F > Cl)
  Fm³⁺ 是一种硬路易斯酸，喜欢硬供体（O > F > Cl）。

Pages 8-9: Californium and Berkelium chemistry
第 8-9 页：锎和锫的化学性质

(a) Chemical differences between Am and Cf
(a) Am 和 Cf 的化学差异

• Electronic configurations:
  电子配置：
  • Am³⁺: [Rn]5f⁶  Am³⁺：[Rn]5f⁶
  • Cf³⁺: [Rn]5f⁹  Cf³⁺：[Rn]5f⁹
• Am shows multiple oxidation states (+3 to +6)
  Am 显示多种氧化态（+3 至 +6）
• Cf predominantly exists in +3 state
  Cf 主要以 +3 状态存在
• Am forms stable dioxo species (AmO₂⁺, AmO₂²⁺)
  Am 形成稳定的二氧物种（AmO₂⁺、AmO₂²⁺）。
• Cf has smaller ionic radius due to actinide contraction
  由于锕系元素收缩，Cf 的离子半径较小
• Different coordination preferences and complex stabilities
  不同的协调偏好和复杂的稳定性

(b) Electronic configuration of Cf in CfCl₃
(b) CfCl₃ 中 Cf 的电子构型

[Rn]5f⁹

(c) Ground state term symbol for Cf³⁺
(c) Cf³⁺ 的基态项符号

• 5f⁹ configuration  5f⁹ 配置
• Using Hund's rules:  使用 Hund 的规则：
  • Maximum S = 5/2
    最大 S = 5/2
  • Maximum L = 5
    最大 L = 5
  • More than half-filled: J = L+S = 15/2
    装满一半以上：J = L+S = 15/2
• Term symbol: ⁶H₁₅/₂  术语符号：⁶H₁₅/₂

(d) Problems in synthesizing ²⁴⁹Cf from ²³⁸U
(d) 从 ²³⁸U 合成 ²⁴⁹Cf 的问题

• Requires multiple neutron captures and beta decays
  需要多次中子俘获和β衰变
• Low probability of sequential neutron captures
  连续俘获中子的概率低
• Short half-lives of intermediate nuclei
  中间核的短半衰期
• Competing fission reactions
  相互竞争的裂变反应
• Low yield of desired isotope
  所需同位素产量低

(e) Use of ²⁴⁹Cf instead of ²⁵¹Cf
(e) 使用 ²⁴⁹Cf 代替 ²⁵¹Cf

• ²⁴⁹Cf is more readily produced in nuclear reactors
  核反应堆更容易产生 ²⁴⁹Cf
• Production methods favor ²⁴⁹Cf synthesis
  生产方法有利于 ²⁴⁹Cf 合成
• Half-life of 351 years is sufficient for studies
  351 年的半衰期足以进行研究
• Different neutron cross-sections affect production
  不同的中子截面会影响产生量

(f) Surprising stability of ²⁵⁰Cf
(f) ²⁵⁰Cf 令人惊讶的稳定性

• Unusual because neighboring isotopes have longer half-lives
  不寻常是因为邻近同位素的半衰期更长
• Related to nuclear shell structure
  与核壳结构有关
• Even-even nuclei typically more stable than odd-even or odd-odd
  偶数原子核通常比奇数原子核或奇数原子核更稳定
• ²⁵⁰Cf may have unfavorable neutron/proton ratio
  ²⁵⁰Cf 可能具有不利的中子/质子比

(g) Magnetic moment of berkelium
(g) 锫的磁矩

• Term symbol ⁷F₆ indicates:
  术语符号 ⁷F₆ 表示：
  • S = 3
  • L = 3
  • J = 6
• Using μ = g√(J(J+1))μB
  使用 μ = g√（J（J+1））μB
• Calculate g-factor: g = 1 + [J(J+1)+S(S+1)-L(L+1)]/[2J(J+1)]
  计算 g 因子： g = 1 + [J(J+1)+S(S+1)-L(L+1)]/[2J(J+1)].
• Magnetic moment ≈ 9.7 μB
  磁矩 ≈ 9.7 μB

(h) Coordination of [Bk(H₂O)ₙ]³⁺
(h) [Bk(H₂O)ₙ]³⁺的配位

• Coordination number: 8-9
  协调编号：8-9
• Geometry: square antiprismatic or tricapped trigonal prismatic
  几何形状：正方反棱柱形或三顶三棱柱形
• Based on ionic radius and charge density
  基于离子半径和电荷密度
• Similar to other heavy actinide trications
  与其他重锕系元素类似

Page 10-11: Plutonium chemistry
第 10-11 页：钚的化学性质

(a) Plutonyl cation properties
(a) 质子阳离子的特性

(i) Oxidation state: +6  (i) 氧化态：+6

(ii) Electronic configuration: [Rn]5f²
(ii) 电子构型：[Rn]5f²

(iii) Term symbol: ³H₄  (iii) 术语符号：³H₄

• 5f² configuration  5f² 配置
• Maximum S = 1
  最大 S = 1
• Maximum L = 5
  最大 L = 5
• Less than half-filled: J = |L-S| = 4
  不足半满：J = |L-S| = 4

(iv) Magnetic moment close to spin-only value because:
(iv) 磁矩接近自旋值，因为

• Strong axial field from O atoms
  来自 O 原子的强轴向场
• Orbital contribution quenched
  淬火轨道贡献
• Linear O=Pu=O geometry creates strong crystal field
  线性 O=Pu=O 几何结构可产生强大的晶体场
• 5f orbitals participate in covalent bonding
  5f 轨道参与共价键合

(b) 4f wavefunctions  (b) 4f 波函数

[This would require sketches of the seven 4f orbitals with their coordinate axes, signs, and labels]
[这需要绘制 7 个 4f 轨道的草图，并标明坐标轴、符号和标签。］

(c) Plutonium phase behavior
(c) 钚相行为

(i) Engineering problems with molten Pu:
(i) 有关熔融钚的工程问题：

• Extreme volume changes during cooling
  冷却过程中的极端体积变化
• Different phases with varying densities
  密度不同的不同阶段
• Cracking and dimensional instability
  开裂和尺寸不稳定
• Difficult to predict final dimensions
  难以预测最终尺寸

(ii) Phases with negative thermal expansion:
(ii) 负热膨胀相：

• β phase  β阶段
• δ phase  δ阶段

(iii) Coordination in δ phase (FCC):
(iii) δ 相配位（FCC）：

• Coordination number: 12  协调编号：12

(iv) Inconsistencies with close packing:
(iv) 与紧密包装不一致：

• Large volume per atom (not dense)
  每个原子体积大（不致密）
• Negative thermal expansion coefficient
  负热膨胀系数

(v) Attributes causing complicated phase diagram:
(v) 造成复杂相图的属性：

• 5f electron delocalization varies with temperature
  5f 电子析出随温度而变化
• Competing electronic configurations
  相互竞争的电子配置
• Balance between localized and itinerant behavior
  本地化行为与巡回行为之间的平衡
• Relativistic effects on bonding
  相对论对粘合的影响
• Anomalous bonding from 5f/6d hybridization
  来自 5f/6d 杂化的反常键合