(Solved): X-ray diffraction is often used to determine the spacing between atoms in a crystal, but electrons ...

$\mathrm{X}$-ray diffraction is often used to determine the spacing between atoms in a crystal, but electrons could be used as well. Suppose electrons with an energy of $14.7\mathrm{eV}$ are diffracted by a regular crystal, and the first order diffraction angle in a certain direction is 37.6 degrees. a) What is the spacing between the atoms in the crystal in that direction? b) Explain why lower-energy electrons (for example, those with an energy in the UV energy range) could not be used to determine the spacing of the crystal. The Paschen series is the spectrum consisting of transitions from a higher The Bohr Atom a) What would be the longest and shortest wavelengths of the Paschen energy state down to the $n=3$ state. b) Any atom or ion with a single electron will have the same spectral pattern series? as the hydrogen atom (i.e., ${\mathrm{He}}^{+},{\mathrm{Li}}^{2+}$, etc.) The difference is that the Rydberg constant is multiplied by the charge of the nucleus, $Z$. Will the wavelengths of transitions to the $n=2$ (Balmer series) for a singly-ionized helium atom, ${\mathrm{He}}^{+}$, be longer or shorter than the comparable wavelengths of the hydrogen atom, or will they be unchanged? Explain your answer.