A triply ionized beryllium ion, Be3+ (a beryllium atom

Chapter 39, Problem 39.21

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A triply ionized beryllium ion, \(\mathrm{Be}^{3+}\) (a beryllium atom with three electrons removed), behaves very much like a hydrogen atom except that the nuclear charge is four times as great. (a) What is the ground-level energy of \(\mathrm{Be}^{3+}\)? How does this compare to the ground-level energy of the hydrogen atom? (b) What is the ionization energy of \(\mathrm{Be}^{3+}\)? How does this compare to the ionization energy of the hydrogen atom? (c) For the hydrogen atom, the wavelength of the photon emitted in the n = 2 to n = 1 transition is 122 nm (see Example 39.6). What is the wavelength of the photon emitted when a \(\mathrm{Be}^{3+}\) ion undergoes this transition? (d) For a given value of n, how does the radius of an orbit in \(\mathrm{Be}^{3+}\) compare to that for hydrogen?