35. Special Relativity

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?

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?

A classical atom that has an electron orbiting at frequency ⨍ would emit electromagnetic waves of frequency ⨍ because the electron's orbit, seen edge-on, looks like an oscillating electric dipole. What is the total mechanical energy of this atom?

Physicists first attempted to understand the hydrogen atom by applying the laws of classical physics. Consider an electron of mass m and charge −e in a circular orbit of radius r around a proton of charge +e. Use Newtonian physics to show that the total energy of the atom is E =−e²/8πϵ₀𝓇

Physicists first attempted to understand the hydrogen atom by applying the laws of classical physics. Consider an electron of mass m and charge −e in a circular orbit of radius r around a proton of charge +e. The minimum energy needed to ionize a hydrogen atom (i.e., to remove the electron) is found experimentally to be 13.6 eV. From this information, what are the electron's speed and the radius of its orbit?