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Problem 2
What is the angular momentum of a hydrogen atom in (a) a 6s state and (b) a 4f state? Give your answers as a multiple of ℏ .
Problem 5b
A hydrogen atom has orbital angular momentum 3.65 × 10⁻³⁴ J s. What is the atom's minimum possible energy? Explain.
Problem 6
How many lines of atoms would you expect to see on the collector plate of a Stern-Gerlach apparatus if the experiment is done with (a) lithium and (b) beryllium? Explain.
Problem 10a
Identify the element for each of these electron configurations. Then determine whether this configuration is the ground state or an excited state. 1s² 2s² 2p⁵
Problem 11b
Identify the element for each of these electron configurations. Then determine whether this configuration is the ground state or an excited state. 1s2 2s2 2p6 3s2 3p6 4s2 3d2
Problem 13
Draw a series of pictures, similar to Figure 41.21, for the ground states of Ca, Ni, As, and Kr.
Problem 19
An excited state of an atom has a 25 ns lifetime. What is the probability that an excited atom will emit a photon during a 0.50 ns interval?
Problem 20b
1.0×106 atoms are excited to an upper energy level at t = 0 s. At the end of 20 ns, 90% of these atoms have undergone a quantum jump to the ground state. What is the lifetime of the excited state?
Problem 23a
A laser emits 1.0 × 1019 photons per second from an excited state with energy E2 = 1.17 eV. The lower energy level is E1 = 0 eV. What is the wavelength of this laser?
Problem 27a
There exist subatomic particles whose spin is characterized by s = 1, rather than the s = ½ of electrons. These particles are said to have a spin of one. What is the magnitude ( as a multiple of ℏ ) of the spin angular momentum S for a particle with a spin of one?
Problem 29
A hydrogen atom in its fourth excited state emits a photon with a wavelength of 1282 nm. What is the atom's maximum possible orbital angular momentum (as a multiple of ℏ ) after the emission?
Problem 31
For an electron in the 1s state of hydrogen, what is the probability of being in a spherical shell of thickness 0.010aB at distance (a) ½ aB, (b) aB, and (c) 2aB from the proton?
Problem 33
Prove that the normalization constant of the 2p radial wave function of the hydrogen atom is (24πaB3)-1/2, as shown in Equations 41.7. Hint: See the hint in Problem 32.
Problem 40
A sodium atom emits a photon with wavelength 818 nm shortly after being struck by an electron. What minimum speed did the electron have before the collision?
Problem 44b
Suppose you put five electrons into a 0.50-nm-wide one-dimensional rigid box (i.e., an infinite potential well). What is the ground-state energy—that is, the total energy of all five electrons in the ground-state configuration?
Problem 47b
During what interval of time will 10% of a sample of 2p hydrogen atoms decay?
Problem 49
A ruby laser emits a 100 MW, 10-ns-long pulse of light with a wavelength of 690 nm. How many chromium atoms undergo stimulated emission to generate this pulse?
Problem 54
What is the probability of finding a 1s hydrogen electron at distance r > aB from the proton?