Problem 49
What is the shortest possible wavelength of the Lyman series in hydrogen?
Problem 51
By what percentage is the electron mass changed in using the reduced mass for the hydrogen atom? What would the reduced mass be if the proton had the same mass as the electron?
Problem 52
Show that the number of different electron states possible for a given value of \(n\) is \(2 n^{2}\).
Problem 53
Section 38.2 established that an electron, if observed in the ground state of hydrogen, would be expected to have an observed speed of \(0.0073 c .\) For what atomic charge \(Z\) would an innermost electron have a speed of approximately \(0.500 c,\) when considered classically?
Problem 54
A collection of hydrogen atoms have all been placed into the \(n=4\) excited state. What wavelengths of photons will be emitted by the hydrogen atoms as they transition back to the ground state?
Problem 55
Consider a muonic hydrogen atom, in which an electron is replaced by a muon of mass \(105.66 \mathrm{MeV} / \mathrm{c}^{2}\) that orbits a proton. What are the first three energy levels of the muon in this type of atom?
Problem 56
What is the ionization energy of a hydrogen atom excited to the \(n=2\) state?
Problem 58
What is the energy of a transition capable of producing light of wavelength \(10.6 \mu \mathrm{m}\) ? (This is the wavelength of light associated with a commonly available infrared laser.)
Problem 59
What is the energy of the orbiting electron in a hydrogen atom with a quantum number of \(45 ?\)
Problem 60
A beam of electrons is incident upon a gas of hydrogen atoms. What minimum speed must the electrons have to cause the emission of light from the \(n=3\) to \(n=2\) transition of hydrogen?
