The energy-level scheme for the hypothetical oneelectron 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. (b) 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.

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. (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 Be3+ ion undergoes this transition?

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. (a) What is the ground-level energy of Be3+? How does this compare to the ground-level energy of the hydrogen atom?

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?

In a set of experiments on a hypothetical oneelectron 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. E39.27

. You also observe that it takes 17.50 eV to ionize this atom. (a) What is the energy of the atom in each of the levels (n = 1, n = 2, etc.) shown in the figure?

10.0-g marble is gently placed on a horizontal tabletop that is 1.75 m wide. (a) What is the maximum uncertainty in the horizontal position of the marble? (b) According to the Heisenberg uncertainty principle, what is the minimum uncertainty in the horizontal velocity of the marble? (c) In light of your answer to part (b), what is the longest time the marble could remain on the table? Compare this time to the age of the universe, which is approximately 14 billion years. (Hint: Can you know that the horizontal velocity of the marble is exactly zero?)

FIGURE EX39.13 shows the probability density for an electron that has passed through an experimental apparatus. What is the probability that the electron will land in a 0.010-mm-wide strip at (a) x=0.000 mm,

A Geiger counter is used to measure the decay of a radioactive isotope produced in a nuclear reactor. Initially, when the sample is first removed from the reactor, the Geiger counter registers 15,000 decays/s. 15 h later the count is down to 5500 decays/s.b. At what time after the sample's removal from the reactor is the count 1200 decays/s?

It might seem strange that in beta decay the positive proton, which is repelled by the positive nucleus, remains in the nucleus while the negative electron, which is attracted to the nucleus, is ejected. To understand beta decay, let's analyze the decay of a free neutron that is at rest in the laboratory. We'll ignore the antineutrino and consider the decay n → p⁺ + e⁻. The analysis requires the use of relativistic energy and momentum, from Chapter 36.b. Write the equation that expresses the conservation of relativistic energy for this decay. Your equation will be in terms of the three masses mₙ, mₚ and mₑ and the relativistic factors yₚ and yₑ.