1. Use Bohr model relations for a hydrogen-like atom

For a particle of mass $m$ and charge magnitude $e$ bound to a proton:

• Radius of $n$th orbit: $r_n \propto \frac{1}{m}$
• Speed in $n$th orbit: $v_n \propto \frac{e^2}{\hbar}$ so for the same nuclear charge $Z=1$, it is independent of mass in the Bohr model.
• Ionization energy: $E_n \propto m$
• Momentum: $p_n = mv_n \propto m$

Given for muon: $m_\mu = 200m_e$

So we compare muonic hydrogen with ordinary hydrogen.

2. Check statement (A)

Since $r_n \propto \frac{1}{m}$ we get $\frac{r_\mu}{r_e} = \frac{m_e}{m_\mu} = \frac{1}{200}$ Thus the muonic orbit radius is 200 times smaller.

✅ (A) is correct

3. Check statement (B)

For Bohr orbits, $v_n = \frac{Ze^2}{4\pi\varepsilon_0\hbar}\cdot \frac{1}{n}$ This does not depend on the mass of the orbiting particle.

So for the same $n$, $v_\mu = v_e$ not $\frac{1}{200}$ times.

❌ (B) is incorrect

4. Check statement (C)

Energy levels in Bohr model: $E_n \propto m$ Hence ionization energy also scales directly with mass.

Therefore, $\frac{E_{\text{ion, muon}}}{E_{\text{ion, H}}} = \frac{m_\mu}{m_e} = 200$ So the ionization energy is 200 times larger.

✅ (C) is correct

5. Check statement (D)

Momentum is $p_n = mv_n$ Since $v_n$ is unchanged while mass becomes 200 times, $\frac{p_\mu}{p_e} = \frac{m_\mu}{m_e} = 200$

✅ (D) is correct

6. Final selection

Correct statements are: $\boxed{(A), (C), (D)}$ This corresponds to Option B.

7. Comparison with stored answer

Stored correct answer: B

Our derived answer: B

So they agree.