Consider a muonic hydrogen atom in which the electron is replaced by a muon (a particle with the same charge as an electron but with a mass 207 times that of an electron). Read the following statements comparing the muonic hydrogen atom with a normal hydrogen atom: A. The radius of the first Bohr orbit is 207 times smaller. B. The speed of the muon in the first Bohr orbit is 207 times greater. C. The ionization energ

Step-by-step solution

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^ th Bohr orbit is r_n = ₀ n^2 h^2 m e^2 . Thus, r 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^ th orbit is v_n = e^2 2 ₀ n h . It is independent of the mass m . The speed remains the same. (Incorrect) Statement C: The total energy is E_n = - m e^4 8 ₀^2 n^2 h^2 . Thus, E m . The ionization ene