The chemical formula $\mathrm { N a } _ { 3 } \mathrm { N O } _ { 3 }$ represents a cubic crystal in which all sodium atoms exist as $\mathrm {Na}^+$ ions and are located at the face centers of the unit cell. In addition to $\mathrm {Na}^+$, there are two other ions in the unit cell. If the one with the larger mass is labeled **A** and the smaller one is labeled **B**, what are the charge ratio of **A** to **B** and the difference in the number of nearest-neighbor $\mathrm {Na}^+$ ions between **A** and **B** in the crystal?
化学式为 $\mathrm { N a } _ { 3 } \mathrm { N O } _ { 3 }$ 的物质是一种立方晶体，所有的钠均以$\mathrm {Na}^+$的形式存在，且位于晶胞的面心。除$\mathrm {Na}^+$之外，晶胞中还存在两个离子，若将其中质量较大的编号为**A**，较小的编号为**B**，则**A**与**B**的电荷比值和**A**与**B**在晶体中最近邻$\mathrm {Na}^+$数量之差分别为多少？
0.5; 6
0.5; 3
0.5; -3
0.5; -6
2; 6
2; 3
2; -3
2; -6
0.5; 6
0.5; 3
0.5; -3
0.5; -6
2; 6
2; 3
2; -3
2; -6
A unit cell contains 3 face-centered $\mathrm{Na}^+$ ions and two other ions. From the chemical formula $\mathrm{N a } _ { 3 } \mathrm{N O } _ { 3 }$, it is known that these two ions collectively contain 1 N and 3 O atoms, with a total charge of -3. Among common ions, only two combinations correspond to this:

1. $\mathrm{NO}^-$ and $\mathrm{O}_2^{2-}$  
2. $\mathrm{NO}_2^-$ and $\mathrm{O}^{2-}$  

Considering the strong oxidizing property of $\mathrm{O}_2^{2-}$ and the reducing property of $\mathrm{NO}^-$, the second scenario is more reasonable. The molecular weight of $\mathrm{NO}_2^-$ is approximately 46, and that of $\mathrm{O}^{2-}$ is approximately 16. Therefore, **A** is $\mathrm{NO}_2^-$, and **B** is $\mathrm{O}^{2-}$. Their charges are -1 and -2, respectively, giving a ratio of 0.5.  

<Checkpoint>[**A** is $\mathrm{NO}_2^-$, **B** is $\mathrm{O}^{2-}$](3)</Checkpoint>  

<Checkpoint>[The charge ratio of **A** to **B** is 0.5](1)</Checkpoint>  

Next, consider the crystal structure. The $\mathrm{Na}^+$ ions occupy face-centered positions, generating within a single unit cell one vertex and one body-centered position, totaling two voids that satisfy cubic symmetry, which can be allocated to the two anions.  

Let the edge length of the unit cell be *a*. The distance between a vertex and an adjacent $\mathrm{Na}^+$ is $\frac{\sqrt{2}}{2}a$, with 4 $\mathrm{Na}^+$ ions along the xy, yz, and xz plane directions each, totaling 12 nearest neighbors. The distance between the body center and an adjacent $\mathrm{Na}^+$ is 0.5a, with 2 $\mathrm{Na}^+$ ions along the x, y, and z-axis directions each, totaling 6 nearest neighbors.  

<Checkpoint>[The vertex has 12 nearest-neighbor $\mathrm{Na}^+$ ions, and the body center has 6 nearest-neighbor $\mathrm{Na}^+$ ions](2)</Checkpoint>  

The vertex has a larger distance to $\mathrm{Na}^+$ and is thus suitable for the larger, less-charged anion. Therefore, **A** should occupy the vertex, and **B** should occupy the body center. The numbers of nearest-neighbor $\mathrm{Na}^+$ ions for **A** and **B** are 12 and 6, respectively, giving a difference of 6. Option A corresponds to this.  

<Checkpoint>[**A** is located at the vertex, **B** is located at the body center](1)</Checkpoint>  

<Checkpoint>[The difference in the number of nearest-neighbor $\mathrm{Na}^+$ ions between **A** and **B** is 6](1)</Checkpoint>
一个晶胞中含有3个面心位置的$\mathrm {Na}^+$，还有两个其它离子，由化学式$\mathrm { N a } _ { 3 } \mathrm { N O } _ { 3 }$可知，这两个离子中共含1个N与3个O，总电荷为-3。常见离子中只有两种组合与之对应：

1.$\mathrm {NO}^-$与$\mathrm {O}_2^{2-}$

2.$\mathrm {NO}_2^-$与$\mathrm {O}^{2-}$

考虑到$\mathrm {O}_2^{2-}$的强氧化性与$\mathrm {NO}^-$的还原性，第二种情况更为合理，$\mathrm {NO}_2^-$的分子量约为46，$\mathrm {O}^{2-}$约为16，所以**A**是$\mathrm {NO}_2^-$，**B**是$\mathrm {O}^{2-}$。两者电荷分别为-1与-2，比值为0.5。

<Checkpoint>[**A**是$\mathrm {NO}_2^-$，**B**是$\mathrm {O}^{2-}$](3)</Checkpoint>

<Checkpoint>[**A**与**B**电荷比值为0.5](1)</Checkpoint>

接下来考虑晶体结构。$\mathrm {Na}^+$占据面心位置，在单个晶胞内会产生1个顶点与1个体心，共两个满足立方对称性的空隙，正好可以分配给两个阴离子。

设晶胞棱长为a，则其中顶点与相邻$\mathrm {Na}^+$的距离为$\frac{\sqrt{2}}{2}$a，沿xy,yz,xz面方向各有4个$\mathrm {Na}^+$与其最近邻，共有12个。体心与相邻$\mathrm {Na}^+$的距离为0.5a，沿x，y，z轴方向各有2个$\mathrm {Na}^+$与其最近邻，共有6个。

<Checkpoint>[顶点周围最近邻$\mathrm {Na}^+$有12个，体心周围最近邻$\mathrm {Na}^+$有6个](2)</Checkpoint>

顶点与$\mathrm {Na}^+$距离更大，适合大小较大，电荷较小的阴离子，所以**A**应位于顶点处，**B**应位于体心。**A**与**B**最近邻的$\mathrm {Na}^+$数量分别为12与6，两者差为6。选项A与之对应。

<Checkpoint>[**A**位于顶点，**B**位于体心](1)</Checkpoint>

<Checkpoint>[**A**与**B**最近邻的$\mathrm {Na}^+$数量差为6](1)</Checkpoint>