**X**, **Y**, and **Z** are three elements with sequentially increasing atomic numbers, among which **X** and **Y** are third-period elements, and only **Y** is a nonmetallic element. **X** and **Z** belong to the same main group, and the number of electrons in the M shell and N shell of the ground-state **Z** atom is the same. The simple substances of both **X** and **Z** can react violently with water to release gas **A**. When the simple substance of **Y** is added to the solution obtained from the reaction, gas **A** is still produced.  

A cubic crystal system contains only the elements **X**, **Y**, and **Z**, where **Y** atoms are stacked in a specific manner, forming only pentagonal dodecahedral cages and hexadecahedral cages in a ratio of 2:1. These cages are tightly connected solely through face-sharing. **X** atoms occupy all dodecahedral cages, **Z** atoms occupy all hexadecahedral cages, and each **Y** atom is connected to four other **Y** atoms. Focusing on a single hexadecahedral cage, it has 4 hexagonal faces and 12 pentagonal faces, with four threefold rotation axes.  

Which of the following statements is correct:
**X**、**Y**、**Z**是原子序数依次增大的三种元素,其中**X**和**Y**是第三周期元素,仅**Y**为非金属元素,**X**和**Z**属同一主族,**Z**基态原子的M能层和N能层电子数相同。**X**和**Z**的单质均能与水剧烈反应放出气体**A**,向反应所得的溶液中投入**Y**单质发生反应,仍能得到气体**A**。

某立方晶系的晶体仅含**X**、**Y**、**Z**三种元素,其中**Y**原子按一定的方式进行堆积,仅形成五角十二面体笼和十六面体笼,其比例为2:1,这些笼之间仅通过共面的方式紧密连接,**X**原子占据所有十二面体笼,**Z**原子占据所有十六面体笼,每个**Y**原子与4个**Y**原子相连。若只看一个十六面体笼,则其具有4个六边形面和12个五边形面,具有4根三重旋转轴。

下列说法正确的是：
The sixteen-hedral cages of the crystal are not interconnected with each other.
A conventional unit cell contains 4 **Z** atoms
The simplest integer ratio chemical formula of this crystal contains 18 atoms
The simplest integer ratio chemical formula of this crystal contains 4 atoms of the metallic element.
It is known that the conventional unit cell of this crystal has $\mathrm{a = 1475.6 ~pm}$, and the crystal density is $\mathrm{2.714 ~g/cm^3}$.
None of the above options is correct
晶体的十六面体笼之间不相互连接
一个正当晶胞中含有4个**Z**原子
该晶体最简整数比的化学式含有18个原子
该晶体最简整数比的化学式含有4个金属元素的原子
已知该晶体正当晶胞的$\mathrm{a = 1475.6 ~pm}$，则晶体密度为$\mathrm{2.714 ~g/cm^3}$
以上选项均不正确
The number of electrons in the M and N shells of the ground-state atom **Z** is the same, indicating that **Z** is located in the fifth period or later. Both the elemental forms of **X** and **Z** can react violently with water to release gas **A**, suggesting that **X** and **Z** are alkali metals or alkaline earth metals, and **A** is hydrogen.

**X** and **Y** are third-period elements. **X** can only be **Na** or **Mg**, but **Mg** does not react violently with water, so **X** should be **Na**, and **Z** is **Cs** (radioactive elements are generally not considered). In this case, the reaction system with water forms an alkaline sodium hydroxide solution, and the addition of elemental **Y** still produces hydrogen gas, so **Y** can only be **Si**.

<Checkpoint>[**Z** is located in the fifth period or later](1)</Checkpoint>

<Checkpoint>[**X,Z** are alkali metals or alkaline earth metals, and **A** is hydrogen](1)</Checkpoint>

<Checkpoint>[**X** is **Na**, **Z** is **Cs**, and **Y** is **Si**](2)</Checkpoint>

If the hexadecahedra are not connected by sharing faces, then the hexadecahedra and dodecahedra can only be connected through pentagonal faces. This would result in the hexagonal faces of the hexadecahedra being isolated, and the cubic symmetry would inevitably cause multiple hexagonal faces to form new cages, which contradicts the given conditions. Therefore, the hexadecahedra must be connected by sharing faces, making option A incorrect.

<Checkpoint>[The hexadecahedra must be connected by sharing faces](1)</Checkpoint>

The hexadecahedral cages possess a threefold rotation axis. For the cubic system, the hexagonal faces of the hexadecahedral cages must be perpendicular to the threefold rotation axis in the conventional unit cell. Based on symmetry, it can be inferred that the hexadecahedral cages must lie along the body diagonals of the conventional unit cell. Thus, the hexadecahedral cages can only occupy the vertex-body center equivalent positions or the equivalent positions at (1/4,1/4,1/4). However, since the hexadecahedral cages share faces, the vertex-body center equivalent positions cannot fully share faces (half the length of the body diagonal is not equal to the edge length). Therefore, in the conventional cubic unit cell, the hexadecahedral cages are located at the equivalent positions of (1/4,1/4,1/4), totaling 8 cages, meaning there are 8 **Z** atoms per conventional unit cell. Option B is incorrect.

<Checkpoint>[The hexadecahedral cages must lie along the body diagonals of the conventional unit cell](2)</Checkpoint>

<Checkpoint>[In the conventional cubic unit cell, the hexadecahedral cages are located at the equivalent positions of (1/4,1/4,1/4)](2)</Checkpoint>

<Checkpoint>[There are 8 **Z** atoms per conventional unit cell](1)</Checkpoint>

Since the ratio of dodecahedral cages to hexadecahedral cages is 2:1, and there are 8 **Cs** atoms per unit cell, there must be 16 **Na** atoms per unit cell.

The number of vertices in a hexadecahedral cage:  
$n _ { 1 6 } = ( \ 5 \times 1 2 + 6 \times 4 ) \div 3 = 2 8$  
The number of vertices in a dodecahedral cage: $n _ { 1 2 } = 2 0$  
Each silicon atom is shared by four cages, so the number of silicon atoms per unit cell:  
$n _ { \mathrm { S i } } { = } ( 2 0 \times 1 6 + 2 8 \times 8 ) \div 4 { = } 1 3 6$  
Thus, the simplest chemical formula of this crystal is $\mathrm {Na_2CsSi_{17}}$. Options C and D are both incorrect.

<Checkpoint>[The simplest chemical formula of the crystal is $\mathrm {Na_2CsSi_{17}}$](2)</Checkpoint>

Calculating the crystal density:  
$\mathrm{\rho=ZM/N_Aa^3=2.714 ~g/cm^3}$, making option E correct.

<Checkpoint>[$\mathrm{\rho=ZM/N_Aa^3=2.714 ~g/cm^3}$](1)</Checkpoint>

In conclusion, option E is correct.
**Z**基态原子的M能层和N能层电子数相同，说明**Z**处于第五周期往后；**X**和**Z**的单质均能与水剧烈反应放出气体**A**，猜测**X,Z**为碱金属或碱土金属元素，**A**为氢气。

**X**和**Y**是第三周期元素，**X**只能为**Na**或者**Mg**，但**Mg**与水的反应不剧烈，所以**X**应当为**Na**，**Z**为**Cs**（一般不考虑放射性元素），此时与水反应体系为氢氧化钠碱性体系，加入单质**Y**仍旧产生氢气，那么**Y**只能为**Si**。

<Checkpoint>[**Z**处于第五周期往后](1)</Checkpoint>

<Checkpoint>[**X,Z**为碱金属或碱土金属元素，**A**为氢气](1)</Checkpoint>

<Checkpoint>[**X**为**Na**，**Z**为**Cs**，**Y**为**Si**](2)</Checkpoint>

如果十六面体之间不共面连接，那么十六面体与十二面体之间只能通过五边形面连接，会导致十六面体的六边形面独立出来，从而立方晶系的对称性一定会导致多个六边形面形成新的笼，与题设不符。因此十六面体之间一定共面连接，选项A错误。

<Checkpoint>[十六面体之间一定共面连接](1)</Checkpoint>

十六面体笼具有三重旋转轴，对立方晶系来说，十六面体的笼六边形在正当晶胞中一定垂直于三重旋转轴，根据对称性可以推断十六面体笼一定位于正当晶胞的体对角线上。那么十六面体笼只能位于正当晶胞的顶点-体心等效点系，或者(1/4,1/4,1/4)处的等效点系。但因为十六面体笼相互共面，顶点-体心等效点系无法完全共面相连（体对角线长度的一半不等于棱长），从而立方正当晶胞中十六面体笼位于(1/4,1/4,1/4)处的等效点系，有8个，因此一个正当晶胞有8个**Z**原子。选项B错误。

<Checkpoint>[十六面体笼一定位于正当晶胞的体对角线上](2)</Checkpoint>

<Checkpoint>[立方正当晶胞中十六面体笼位于(1/4,1/4,1/4)处的等效点系](2)</Checkpoint>

<Checkpoint>[一个正当晶胞有8个**Z**原子](1)</Checkpoint>

由于十二面体笼和十六面体笼的比例为2:1，一个晶胞中含8个**Cs**原子，所以一个晶胞中含16个**Na**原子。

十六面体笼的顶点数：
$n _ { 1 6 } = ( \ 5 \times 1 2 + 6 \times 4 ) \div 3 = 2 8$  
而十二面体笼的顶点数 $n _ { 1 2 } = 2 0$   
每个硅原子被四个笼共用，所以一个晶胞中的硅原子个数：  
$n _ { \mathrm { S i } } { = } ( 2 0 \times 1 6 + 2 8 \times 8 ) \div 4 { = } 1 3 6$  
所以此晶体的最简化学式为 $\mathrm {Na_2CsSi_{17}}$。选项C,D均错误。

<Checkpoint>[晶体的最简化学式为 $\mathrm {Na_2CsSi_{17}}$](2)</Checkpoint>

计算晶体密度：
$\mathrm{\rho=ZM/N_Aa^3=2.714 ~g/cm^3}$，选项E正确。

<Checkpoint>[$\mathrm{\rho=ZM/N_Aa^3=2.714 ~g/cm^3}$](1)</Checkpoint>

综上，选项E正确。