7. Let the set $M=\left\{(x, y) \left\lvert\, \frac{1}{\sqrt{x}}-\frac{1}{\sqrt{y}}=\frac{1}{\sqrt{45}}\right., x, y \in \mathbf{N}^{*}\right\}$, then the number of elements in the set $M$ is
A. 0
B. 1
C. 2
D. 3
$$
\begin{array}{l}
\frac{1}{\sqrt{5 x}}-\frac{1}{\sqrt{5 y}}=\frac{1}{15} \Rightarrow \frac{1}{5 x}=\frac{1}{225}+\frac{1}{5 y}+\frac{2}{15 \sqrt{5 y}} \in \mathbf{Q} \Rightarrow \sqrt{5 y} \in \mathbf{Q}, \text { similarly } \sqrt{5 x} \in \mathbf{Q} . \\
\frac{1}{\sqrt{x}}-\frac{1}{\sqrt{y}}=\frac{1}{\sqrt{45}} \Rightarrow \frac{\sqrt{5}}{\sqrt{x}}-\frac{\sqrt{5}}{\sqrt{y}}=\frac{1}{3}, \text { let } x=5 x_{1}^{2}, y=5 y_{1}^{2},
\end{array}
$$

Then we have $\frac{1}{x_{1}}-\frac{1}{y_{1}}=\frac{1}{3} \Rightarrow x_{1} y_{1}+3 x_{1}-3 y_{1}-9=-9 \Rightarrow\left(x_{1}-3\right)\left(y_{1}+3\right)=-9 \Rightarrow x_{1}=2, y_{1}=6$.
Thus, the number of elements in set $M$ is 1, so the answer is $B$.