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 .

A hydrogen atom has orbital angular momentum 3.65 × 10⁻³⁴ J s. What is the atom's minimum possible energy? Explain.

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.

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

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

Draw a series of pictures, similar to Figure 41.21, for the ground states of Ca, Ni, As, and Kr.

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?

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?

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?

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?

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?

For an electron in the 1s state of hydrogen, what is the probability of being in a spherical shell of thickness 0.010a_B at distance (a) ½ a_B, (b) a_B, and (c) 2a_B from the proton?

Prove that the normalization constant of the 2p radial wave function of the hydrogen atom is (24πa_B³)^-1/2, as shown in Equations 41.7. Hint: See the hint in Problem 32.

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?

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?

During what interval of time will 10% of a sample of 2p hydrogen atoms decay?

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?

What is the probability of finding a 1s hydrogen electron at distance r > a_B from the proton?