Electrolysis of an aqueous solution with a certain concentration of $\mathrm{HF}$ and $\mathrm{AgHF_2}$ yields a crystalline substance $\mathbf{X}$ when the current density is high. $\mathbf{X}$ exhibits paramagnetism and good conductivity. Experimental results confirm that $\mathbf{X}$ has a face-centered cubic lattice structure. The structural description of $\mathbf{X}$ is as follows:  

The $\mathrm{O_8}$ small cubes composed of oxygen occupy all the vertices and face centers of the unit cell, while randomly oriented $\mathrm{HF_2^-}$ occupy all the edge centers and body centers. Each small cube has a $\mathrm{Ag(I)}$ at its center, and the remaining silver atoms are distributed between the cubes, with one silver atom located at the midpoint of the line connecting the centers of any two nearest $\mathrm{O_8}$ small cubes.  

Which of the following statements is correct:
电解一定浓度的 $\mathrm{HF}$ 和 $\mathrm{AgHF_2}$ 混合水溶液,当电流密度较高时,可析出一种晶体 $\mathbf{X}$ 。 $\mathbf{X}$ 具有顺磁性和较好的导电性。实验证实, $\mathbf{X}$ 的点阵类型为面心立方。对 $\mathbf{X}$ 的结构描述如下:

由氧组成的 $\mathrm{O_8}$ 小立方体占据晶胞全部顶点和面心, $\mathrm{HF_2^-}$取向随机, 占据晶胞全部棱心和体心, 每个小立方体的中心均有一个 $\mathrm{Ag(I)}$, 其余的银分布在立方体之间, 任意两个距离最近的 $\mathrm{O_8}$ 小立方体体心连线的中点处均有一个银。

下列说法正确的是：
The simplest chemical formula of $\mathbf{X}$ contains 8 metal atoms
The structural unit of $\mathbf{X}$ contains 36 atoms
The $\mathrm{Ag}$ between the cubes is $\mathrm{sp^3}$ hybridized.
In a conventional unit cell, there are 4 tetrahedral voids composed of $\mathrm{O_8}$.
Crystal $\mathbf{X}$ is deposited at the cathode
Given that $a = 982 ~pm$, the density of this crystal is greater than $8 ~g/cm^3$.
None of the above options is correct.
$\mathbf{X}$的最简化学式含有8个金属原子
$\mathbf{X}$的结构基元含有36个原子
立方体之间的$\mathrm{Ag}$为$\mathrm{sp^3}$杂化
一个正当晶胞中有4个由$\mathrm{O_8}$组成的正四面体空隙
晶体$\mathbf{X}$在阴极析出
已知$a = 982 ~pm$，该晶体的密度大于$8 ~g/cm^3$
以上选项均不正确。
The $\mathrm{O_8}$ small cubes occupy all the vertices and face centers of the unit cell, so there are 4 $\mathrm{O_8}$ small cubes in a unit cell.

$\mathrm{HF_2^-}$ is randomly oriented, occupying all the edge centers and body center of the unit cell, and similarly, there are 4 $\mathrm{HF_2^-}$ in a unit cell.

<Checkpoint>[A unit cell contains 4 $\mathrm{O_8}$ small cubes and 4 $\mathrm{HF_2^-}$](1)</Checkpoint>

The midpoint of the line connecting the centers of any two nearest $\mathrm{O_8}$ small cubes should coincide with the midpoints of the lines connecting all vertices and face centers, as well as the midpoints of the lines connecting two face centers. Thus, there are four $\mathrm{Ag}$ on each face and 12 $\mathrm{Ag}$ inside the crystal, totaling $4\times6/2+4+12=28$ $\mathrm{Ag}$ in the crystal.

<Checkpoint>[The midpoint of the line connecting the centers of the nearest $\mathrm{O_8}$ small cubes coincides with the midpoints of the lines connecting all vertices and face centers, as well as the midpoints of the lines connecting two face centers](1)</Checkpoint>

<Checkpoint>[The crystal contains a total of $4\times6/2+4+12=28$ $\mathrm{Ag}$](1)</Checkpoint>

Since this crystal has a face-centered cubic lattice, a primitive unit cell contains 4 structural motifs. The chemical formula in one unit cell is $\mathrm{(O_8)_4(HF_2^-)_4Ag_{28}}$, so the structural motif is $\mathrm{(O_8)(HF_2^-)Ag_{7}}$, which is also the simplest chemical formula. Options B and A are both incorrect.

<Checkpoint>[The structural motif is $\mathrm{(O_8)(HF_2^-)Ag_{7}}$](1)</Checkpoint>

$\mathrm{Ag(I)}$ is located between the $\mathrm{O_8}$ cubes. In the simplest chemical formula, only one exists. Since the crystal is paramagnetic and $\mathrm{Ag(I)}$ has no unpaired electrons, the $\mathrm{Ag}$ between the cubes has unpaired electrons and a valence of +2/+3, resulting in $dsp^2$ hybridization. Option C is incorrect.

<Checkpoint>[The $\mathrm{Ag}$ between the cubes has unpaired electrons and exhibits $dsp^2$ hybridization](1)</Checkpoint>

In a primitive unit cell, $\mathrm{O_8}$ occupies the vertices and face centers, which are actually the positions of cubic close packing. Therefore, $\mathrm{O_8}$ forms 8 regular tetrahedral voids. Option D is incorrect.

<Checkpoint>[The oxygen atoms are actually in cubic close packing positions, forming 8 regular tetrahedral voids](1)</Checkpoint>

Considering the simplest chemical formula, the apparent oxidation state of silver is +17/7, indicating an oxidation process. Thus, the crystal should precipitate at the anode. Option E is incorrect.

<Checkpoint>[The formation of the crystal is an oxidation process, and the crystal should precipitate at the anode](1)</Checkpoint>

The density calculated based on the unit cell parameters and the simplest chemical formula is $6.47 ~g~/cm^3$. Option F is incorrect.

<Checkpoint>[The density is $6.47 ~g~/cm^3$](1)</Checkpoint>

In conclusion, options A-F are all incorrect, and option G is correct.
$\mathrm{O_8}$ 小立方体占据晶胞全部顶点和面心，故一个晶胞中有4个$\mathrm{O_8}$ 小立方体。

$\mathrm{HF_2^-}$取向随机, 占据晶胞全部棱心和体心，同样一个晶胞中有4个$\mathrm{HF_2^-}$。

<Checkpoint>[一个晶胞中有4个$\mathrm{O_8}$ 小立方体，4个$\mathrm{HF_2^-}$](1)</Checkpoint>

任意两个距离最近的 $\mathrm{O_8}$ 小立方体体心连线的中点应当在所有顶点与面心的连线中点，以及两个面心之间的连线中点；从而一个面上有四个$\mathrm{Ag}$，内部有12个$\mathrm{Ag}$，晶体中共有$4\times6/2+4+12=28$个$\mathrm{Ag}$。

<Checkpoint>[距离最近的 $\mathrm{O_8}$ 小立方体体心连线的中点在所有顶点与面心的连线中点，以及两个面心之间的连线中点](1)</Checkpoint>

<Checkpoint>[晶体中共有$4\times6/2+4+12=28$个$\mathrm{Ag}$](1)</Checkpoint>

由于该晶体为面心立方点阵，一个正当晶胞具有4个结构基元，一个晶胞中的化学式为$\mathrm{(O_8)_4(HF_2^-)_4Ag_{28}}$，从而结构基元为$\mathrm{(O_8)(HF_2^-)Ag_{7}}$，同时也是最简化学式，选项B,A均错误。

<Checkpoint>[结构基元为$\mathrm{(O_8)(HF_2^-)Ag_{7}}$](1)</Checkpoint>

$\mathrm{Ag(I)}$在$\mathrm{O_8}$立方体之间，在最简化学式中只存在一个，因为晶体呈顺磁性，$\mathrm{Ag(I)}$无单电子，因此立方体之间的$\mathrm{Ag}$有单电子且化合价为+2/+3，从而为$dsp^2$杂化，选项C错误。

<Checkpoint>[立方体之间的$\mathrm{Ag}$有单电子，为$dsp^2$杂化](1)</Checkpoint>

一个正当晶胞中$\mathrm{O_8}$处于顶点和面心，实际上为立方最密堆积的位置，因此$\mathrm{O_8}$组成8个正四面体空隙，选项D错误。

<Checkpoint>[氧原子实际上为立方最密堆积的位置，组成8个正四面体空隙](1)</Checkpoint>

考虑最简化学式，银的表观氧化态为+17/7，从而实际上是氧化过程，晶体应当在阳极析出，选项E错误。

<Checkpoint>[产生晶体是氧化过程，晶体应当在阳极析出](1)</Checkpoint>

根据晶胞参数和最简化学式计算密度为$6.47 ~g~/cm^3$，选项F错误。

<Checkpoint>[密度为$6.47 ~g~/cm^3$](1)</Checkpoint>

综上，选项A-F均错误，选项G正确。