X rays with an initial wavelength of $0.900\times {10}^{-10}$ m undergo Compton scattering. For what scattering angle is the wavelength of the scattered x rays greater by $1.0\%$ than that of the incident x rays?

An electron and a positron are moving toward each other and each has speed $0.500c$ in the lab frame. What is the kinetic energy of each particle?

Model a hydrogen atom as an electron in a cubical box with side length $L$. Set the value of $L$ so that the volume of the box equals the volume of a sphere of radius $a=5.29\times {10}^{-11}$ m, the Bohr radius. Calculate the energy separation between the ground and first excited levels, and compare the result to this energy separation calculated from the Bohr model.

A photon is emitted when an electron in a three-dimensional cubical box of side length $8.00\times {10}^{-11}$ m makes a transition from the $n_X=2$, $n_Y=2$, $n_Z=1$ state to the $n_X=1$, $n_Y=1$, $n_Z=1$ state. What is the wavelength of this photon?

Consider an electron in the $N$ shell. What is the largest orbital angular momentum it could have? Express your answers in terms of $\(\hslash\)$ and in SI units.

Consider an electron in the $N$ shell. What is the largest orbital angular momentum this electron could have in any chosen direction? Express your answers in terms of $\hslash$ and in SI units.

Consider an electron in the $N$ shell. What is the largest spin angular momentum this electron could have in any chosen direction? Express your answers in terms of $\(\hslash\)$ and in SI units.

The orbital angular momentum of an electron has a magnitude of $4.716\times {10}^{-34}$ kg-m²/s. What is the angular momentum quantum number $l$ for this electron?