$19.$ An electron is moving at a speed of $1\mathrm{.}0k\frac{m}{s}$ perpendicular to a magnetic field with a magnitude of $1\mathrm{.}5$ T $.$ How much force does the magnetic field exert on the electron?

Transitions to or from the $n=3$ energy level produce the Paschen series of lines in the hydrogen spectrum.

$($a$)$ Find the change in energy level for the first three Paschen transitions.

$($b$)$ Find the wavelengths and frequencies of the first three Paschen transitions.

$($c$)$ Use $E=hf$ to calculate the energy of the photon produced by a transition from the $n=5$ to the $n=3$ energy level. Is your calculation consistent with your answer to part $($a$)?$ Why or why not?

$($d$)$ In what part of the electromagnetic spectrum would you find the Paschen lines?