The energy-level scheme for the hypothetical one-electron element Searsium is shown in Fig. $E39.25$. The potential energy is taken to be zero for an electron at an infinite distance from the nucleus. An $18$-eV photon is absorbed by a Searsium atom in its ground level. As the atom returns to its ground level, what possible energies can the emitted photons have? Assume that there can be transitions between all pairs of levels.

In a set of experiments on a hypothetical one-electron atom, you measure the wavelengths of the photons emitted from transitions ending in the ground level ($n=1$), as shown in the energy-level diagram in Fig. E$39.27$. You also observe that it takes $17.50$ eV to ionize this atom. What is the energy of the atom in each of the levels ($n=1$, $n=2$, etc.) shown in the figure?

A hydrogen atom is in a state with energy $-1.51$ eV. In the Bohr model, what is the angular momentum of the electron in the atom, with respect to an axis at the nucleus?

A triply ionized beryllium ion, Be³⁺ (a beryllium atom with three electrons removed), behaves very much like a hydrogen atom except that the nuclear charge is four times as great. What is the ground-level energy of Be³⁺? How does this compare to the ground-level energy of the hydrogen atom?

Use Balmer's formula to calculate (a) the wavelength, (b) the frequency, and (c) the photon energy for the Hg line of the Balmer series for hydrogen.

A triply ionized beryllium ion, Be³⁺ (a beryllium atom with three electrons removed), behaves very much like a hydrogen atom except that the nuclear charge is four times as great. 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 Be³⁺ ion undergoes this transition?

Find the longest and shortest wavelengths in the Lyman and Paschen series for hydrogen. In what region of the electromagnetic spectrum does each series lie?