Read the statements carefully and respond to the tasks that follow, keeping your reasoning explicit.
a. (i) Describe qualitatively how the orbital radius, electron speed and total energy of a hydrogen-like atom depend on the principal quantum number n and the atomic number Z.
b. (ii) Using these dependences, explain why an electron in a He+ ion is more tightly bound (has a larger magnitude of negative energy) than an electron in a hydrogen atom when both electrons share the same principal quantum number.
c. (iii) For electrons in the second orbit (n=2) of hydrogen and Be3+ (Z = 4) respectively, predict which electron has the shorter de Broglie wavelength and justify your answer without detailed numerical calculation.