A hydrogen atom initially at rest in the n = 3 state decays to the ground state with the emission of a photon. (a) Calculate the wavelength of the emitted photon. (b) Estimate the recoil momentum of the atom and the kinetic energy of the recoiling atom. Where does this energy come from?

Liquid oxygen has a bluish color, meaning that it preferentially absorbs light toward the red end of the visible spectrum. Although the oxygen molecule $\left(\mathrm{O}_{2}\right)$ does not strongly absorb visible radiation, it does absorb strongly at 1269 nm, which is in the infrared region of the spectrum. Research has shown that it is possible for two colliding ${O}_{2}$ molecules to absorb a single photon, sharing its energy equally. The transition that both molecules undergo is the same transition that results when they absorb 1269-nm radiation. What is the wavelength of the single photon that causes this double transition? What is the color of this radiation?

A photon with an energy 2.28 eV is absorbed by a hydrogen atom. Find the minimum n for a hydrogen atom that can be ionized by such a photon.

Two hydrogen atoms collide head-on and end up with zero kinetic energy. Each then emits a 121.6-nm photon ( $n=2$ to $n=1$ transition). At what speed were the atoms moving before the collision?

Find the de Broglie wavelength of a ball of mass 0.20 kg just before it strikes the Earth after being dropped from a building 50 m tall.

A photon with energy 2.28 eV is absorbed by a hydrogen atom. Find the minimum n for a hydrogen atom that can be ionized by such a photon.

Calculate the longest and shortest wavelengths in the Lyman series for hydrogen, indicating the underlying electronic transition that gives rise to each. Are any of the Lyman spectral lines in the visible spectrum? Explain.

Why did the economic problems in some EU countries have such a widespread impact?

An electron collides inelastically and head-on with a mercury atom at rest. (a) If the separation of the first excited state and the ground state of the atom is exactly 4.9 eV, what is the minimum initial electron kinetic energy needed to raise the atom to its first excited state and also conserve momentum? Assume that the collision is completely inelastic. (b) What is the initial speed of the electron in this case? (c) What is the speed of the electron and atom after the collision? (d) What is the kinetic energy (in electron volts) of the electron after collision? Is the approximation that the electron loses all of its kinetic energy in an inelastic collision justified?

Suppose Fuzzy, a quantum-mechanical duck, lives in a world in which $h=2 \pi \mathrm{J} \cdot \mathrm{s}$. Fuzzy has a mass of 2.0 kg and is initially known to be within a region 1.0 m wide.

Consider a freely moving quantum particle with mass m and speed v. Its energy is $E=K+U=\frac{1}{2} m v^{2}+0$. Determine the phase speed of the quantum wave representing the particle and show that it is different from the speed at which the particle transports mass and energy.

Consider a freely moving quantum particle with mass m and speed u. Its energy is E = K = $\frac { 1 } { 2 }$mu$^2$. Determine the phase speed of the quantum wave representing the particle.

Draw a line under each indefinite pronoun and circle each demonstrative pronoun. Everybody wants a copy of Taylor Joyce's newest novel.

(a) Consider a particle in a cubic box What is the degeneracy of the level that has an energy three times that of the lowest level? (b) Consider a particle in a cubic box. What is the degeneracy of the level that has an energy $\frac{14}{3}$ times that of the lowest level?