In muonic hydrogen, the electron in hydrogen has been replaced by a muon. For the muonic hydrogren: find the values of the Bohr energies and the Bohr radius in terms of the values for hydrogen.

An electron within the hydrogen atom is excited from n1 to n4. The electron then "falls" back to ni in two steps (n4 -> n2, n2 -> n1). Which of the following statements is true about the light emitted during this process? One photons will be emitted. Two photons will be emitted. O Three photons will be emitted. Four photons will be emitted.

The geometry of spacetime in the Universe on large scales is determined by the mean energy density of the matter in the Universe, ρ. The critical density of the Universe is denoted by ρ0 and can be used to define the parameter Ω0 = ρ/ρ0. Describe the geometry of space when: (i) Ω0 < 1; (ii) Ω0 = 1; (iii) Ω0 > 1. Explain how measurements of the angular sizes of the hot- and cold-spots in the CMB projected on the sky can inform us about the geometry of spacetime in our Universe. What do measurements of these angular sizes by the WMAP and PLANCK satellites tell us about the value of Ω0?

2.3. Find the de Broglie wavelength of (a) an electron, and (b) a proton with speeds of 5 × 106 m/s and compare with the radius of the hydrogen atom, ao. Would either of these particles behave like a wave inside the H atom?