Consider a muonic hydrogen atom in which the electron is replaced...

Let us evaluate each statement based on the Bohr model, where the mass of the orbiting particle is $m$.

Statement A: The radius of the $n^{\text{th}}$ Bohr orbit is $r_n = \dfrac{\epsilon_0 n^2 h^2}{\pi m e^2}$. Thus, $r \propto \dfrac{1}{m}$. Since the muon is $207$ times heavier, the radius is $207$ times smaller. (Correct)

Statement B: The speed of the particle in the $n^{\text{th}}$ orbit is $v_n = \dfrac{e^2}{2 \epsilon_0 n h}$. It is independent of the mass $m$. The speed remains the same. (Incorrect)

Statement C: The total energy is $E_n = -\dfrac{m e^4}{8 \epsilon_0^2 n^2 h^2}$. Thus, $E \propto m$. The ionization energy (magnitude of total energy) is $207$ times greater. (Correct)

Statement D: The angular momentum is $L = \dfrac{nh}{2\pi}$. It depends only on $n$ and is independent of mass. (Incorrect)

Statement E: The potential energy is $U = -\dfrac{e^2}{4 \pi \epsilon_0 r}$. Since $r$ is $207$ times smaller, the magnitude of potential energy is $207$ times greater. (Correct)

Therefore, exactly three statements (A, C, and E) are correct.

Answer: Three